https://wiki.endmyopia.org/api.php?action=feedcontributions&feedformat=atom&user=UserEndmyopia Wiki - User contributions [en]2026-04-25T15:06:06ZUser contributionsMediaWiki 1.39.3https://wiki.endmyopia.org/index.php?title=Presbyopia&diff=16556Presbyopia2022-03-28T16:20:14Z<p>User: Reverted edits by Ninebalasan (talk) to last revision by User</p>
<hr />
<div>Presbyopia is the hardening of the [[lens]] in the [[eyeballs]] such that it becomes difficult to see [[near work]]. This is common in older adults and is commonly treated with [[reading glasses]] (reduced minus for myopes), progressive lenses, or [[bifocals]].<br />
<br />
==Correction==<br />
As you age, the lens in your eye becomes less flexible. This makes [[accommodation]] more difficult and brings on "arms are not long enough to read" symptoms. Someone may be both [[myopic]] and presbyopic, and have deficits in both near and far vision. Your [[Prescription]] will have an "Add" section specifying bifocals or multifocals if you have diagnosed presbyopia, or if your doctor thinks it best to reduce eye strain.<br />
<br />
===Two glasses===<br />
It is an option to have two pairs of glasses, one for close-up, and one for distance, instead of trying to combine both near and far corrections in one pair of glasses.<br />
<br />
===Bifocals===<br />
Glasses with a lower section that is specifically for close work.<br />
<br />
===Progressive lenses===<br />
Glasses with a gradient from zero to near plus addition spherical power from top to bottom.<br />
<br />
===Multifocals===<br />
Contacts that have sections for near and far work, which the [[visual cortex]] will selectively use when looking at different distances.<br />
<br />
== Measuring ==<br />
To determine '''power of accommodation''', also sometimes called '''amplitude of accommodation''', measure '''far power''' and '''near power'''.<br />
<br />
'''Far power''' is straightforward, and it’s the typical [[cm measurement]]: just measure the furthest distance you can see clearly without blur, with a lens to adjust as needed. The far power is ''1/(distance to blur) - (lens power)''.<br />
<br />
* For example, 80 cm with a -0.25 lens is calculated as 1/(80 cm) - (-0.25 D) = 1.25 D + 0.25 D = 1.5 D.<br />
* It might be useful to use a plus lens to measure low myopia. For example, 80 cm with a +0.75 lens is calculated as 1/(80 cm) - (+0.75 D) = 0.5 D.<br />
<br />
'''Near power''' is the same, but measure the '''closest''' distance you can see clearly without blur.<br />
<br />
* For example, if the closest you can see is 10 cm without lenses, it’s calculated as 1/(10 cm) - 0 = 10 D.<br />
* It might be useful to use a big minus lens to measure young people (don’t look through it for too long!). In the example above, you expect to see as close as 50 cm with a -8 lens, which is 1/(50 cm) - (-8 D) = 2 D + 8 D = 10 D.<br />
<br />
The '''power of accommodation''' is (near power) - (far power). With the first example in each of the above, it would be 10 D - 1.5 D = 8.5 D.<br />
<br />
A person is generally considered to have presbyopia [[wikipedia:if and only if | iff]] his power of accommodation is less than 2.5 D.<br />
<br />
===Caveats===<br />
<br />
This technique might need to be refined for cylinder, if spherical equivalent is not used.<br />
<br />
The cornea and lens actually have more power because the total power has to focus the image on your retina, but they cancel out in the subtraction step, so it’s easier to ignore them.<br />
<br />
== Videos ==<br />
<br />
{{#ev:vimeo|284921410||inline}}<br/><br />
{{#ev:youtube|UMAjh11RL5A||inline}}<br/><br />
{{#ev:youtube|QvmOkVjwPyI||inline}}<br />
<br />
== Resources ==<br />
<br />
* Here is a resource that may be of interest to people with presbyopia that was found in the Discord chat. The resource is used for training convergence. http://www.i-see.org/rizzi_charts_readvertical.pdf<br />
<br />
[[Category:Articles]]<br />
[[Category:Eye conditions]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Diopters&diff=16555Diopters2022-03-28T16:18:24Z<p>User: /* Examples */</p>
<hr />
<div><br />
Diopter is a measure of the [https://en.wikipedia.org/wiki/Optical_power optical power] P of a [[lens]] (or mirror) and is equal to the reciprocal of [[focal length]] in meters. The most common unit symbol for diopters is dpt, D, or m<sup>-1</sup>.<br />
<br />
<math>P = \frac{1}{f} = -\frac{1}{d}</math><br />
<br />
* In [[EM]], we use the [[cm measurement]] to calculate diopters needed to correct [[refraction]] of the eye. If you can see 50 cm clearly, your diopters will be <math>-\frac{1}{0.50}=-2 dpt</math>.<br />
<br />
* Lenses in series add their powers: if you're wearing -2 diopter contacts ([[vertex distance|adjusted for glasses strength]]) and put +1 diopter reading glasses over the contacts you're in effect wearing -1 diopters.<br />
** There are some caveats such as vertex distance, since moving the lens away effectively gives you a weaker negative lens or stronger positive lens. There is also decentration, which induces prism when the lens is moved to the side. These effects become negligible for weaker lenses.<br />
* According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.<br />
** A lens with a negative diopter sign compensates for [[nearsightedness]] while a lens with a positive diopter sign compensates for [[farsightedness]].<br />
<br />
{| class="wikitable"<br />
|+ Approximate categorizations of myopia by [[spherical]] lens power:<br />
|-<br />
| 0.00 to -0.50 dpt || Not really considered myopic, probably don't need glasses<br />
|-<br />
| -0.50 to -1.00 dpt || Mild myopia, [[normalized]] sometimes not needed<br />
|-<br />
| -1.00 to -2.50 dpt || Mild myopia, [[differentials]] possibly not needed<br />
|-<br />
| -2.50 to -3.00 dpt || Mild myopia, differentials probably needed<br />
|-<br />
| -3.00 to -6.00 dpt || Moderate myopia, glasses always needed<br />
|-<br />
| -6.00 to -10.00 dpt || High myopia<br />
|-<br />
| -10.00+ dpt || Very high myopia. Field of view significantly reduced.<br />
|}<br />
<br />
==Gap and ratio==<br />
<br />
Comparisons between two diopters is typically expressed using one of these terms:<br />
<br />
* ''diopter gap'' (or ''diopter difference''): absolute difference in diopters between two values<br />
* ''diopter ratio'': ratio of one diopter value to another (such as right eye / left eye)<br />
<br />
For example, consider the following correction:<br />
<br />
OD: -1.5 SPH / -1.5 CYL<br />
OS: -1.0 SPH / -2.0 CYL<br />
<br />
It can be expressed as a 0.5 dpt gap in both SPH and CYL, a 1.5 ratio in SPH and a 0.75 ratio in CYL:<br />
<br />
|(-1.5 dpt) - (-1.0 dpt)| = 0.5 dpt<br />
|(-1.5 dpt) - (-2.0 dpt)| = 0.5 dpt<br />
(-1.5 dpt) / (-1.0 dpt) = 1.5<br />
(-1.5 dpt) / (-2.0 dpt) = 0.75<br />
<br />
In EM articles, the term ''diopter ratio'' is often used interchangeably for left-right ''diopter gap''<ref>{{cite jake|https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/|The Diopter Ratio Trap: Don’t Favor One Eye}}</ref>, for example when talking about reducing a correction while keeping the ''gap'' the same. This can also be expressed as a [[wikipedia:Percent difference|percentage difference]] between the two diopter values<ref>{{cite jake|https://endmyopia.org/reducing-diopter-ratio-diy-patching-solution-pro-topic/|Reducing Diopter Ratio: DIY Patching Solution (PRO TOPIC)}}</ref> (e.g. the <tt>0.5 dpt</tt> difference between the right and left eyes here is equivalent to <tt>0.5 dpt / |-1.5 dpt| = 0.33</tt> or 33%).<br />
<br />
The general recommendation is that the left-right diopter gap is constant across all lenses being used. However, some old EM articles show successful cases where differentials are equalized but normalized have a 0.25 D gap.<ref>https://endmyopia.org/progress-improving-centimeter-62-90/ and https://endmyopia.org/saras-journey-truth-long-term-vision-improvement-potential/</ref><br />
<br />
Confusingly, diopter gap is also sometimes used to refer to the diff-norm gap, the difference between [[differentials]] and [[normalized]] or the [[spherical equivalent]] of that difference.<ref>https://endmyopia.org/pro-topic-managing-your-maximum-diopter-gap/</ref><br />
<br />
It is often useful to disambiguate what is being compared:<br />
* ''left-right gap'': left eye diopters minus right eye diopters, ignoring axis<br />
** In the example above, the left-right gap is +0.5 SPH -0.5 CYL.<br />
** The axis is ignored, and the cylinder powers are subtracted without using [[Diopters#Adding/Combining Lenses|lens combination calculations]].<br />
* ''diff-norm gap'': differentials diopter minus normalized diopters, ignoring axis<br />
** For example, if normalized is -2 SPH -0.5 CYL, and differentials are -0.75 SPH, the diff-norm gap is 1.25 SPH 0.5 CYL or 1.5 SPH equivalent.<br />
** The axis is ignored.<br />
** This quantity is generally positive, as more plus sphere is needed for [[close-up]] than [[distance vision]].<br />
<br />
==Technical Details==<br />
This section is for the math-savvy people. It explains concepts in more detail, but knowledge of it is not strictly necessary to use the EM method.<br />
<br />
===Thin Lens Equation===<br />
The focal length of a lens is given by the lensmaker's equation. By assuming the lens is much thinner than the radius of curvature, therefore assuming lens thickness is zero, we get a simplified version of the lensmaker's equation. We can do some further derivation, we arrive at the thin-lens equation:<ref>see derivations at https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses</ref><br />
<br />
<math>\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}</math><br />
<br />
According to the thin lens sign convention,<br />
* di is positive if it is a real image on the opposite side of the lens as the object, and it is negative if it is a virtual image on the same side of the lens as the object.<br />
* f is positive for converging lens and negative for diverging.<br />
<br />
This is also sometimes presented in the Newtonian form:<br />
<br />
<math>\left(d_o-f\right)\left(d_i-f\right)=f^2</math><br />
<br />
====Examples====<br />
"Full correction" takes an object at infinity and produces a virtual image at your far point distance d:<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{-d}=-\frac{1}{d}</math><br />
<br />
<br />
This is the resulting equation at the beginning of the article. It also explains why the focal power is increased for objects at closer distances: mainstream optometry calls this the "add" for [[presbyopia]], although they typically use the minimum amount required for you to see at 40 cm with full distance correction using accommodation. For example, if you choose 80 cm as the working distance for your [[differentials]] (resulting in a +1.25 dpt "add"), and your blur horizon is 50 cm (resulting in -2 dpt), the formula is<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{80\ cm}+\frac{1}{-50\ cm}=1.25\ dpt + \left(-2\ dpt\right) = -0.75\ dpt</math><br />
<br />
=== Cylinder ===<br />
A cylindrical lens of focal power P<sub>cyl</sub> has power P at angle θ from its axis:<br />
<br />
<math>P = P_{cyl} (\sin\theta)^2</math><br />
<br />
==== Axis ====<br />
Axis is usually in degrees modulo 180. It is popular for 0 to be written as 180 in some areas.<br />
<br />
==== Transposition ====<br />
We can understand why there are two different ways to write a spherical and cylindrical lens combination, using the Pythagorean trigonometric identity and the complementary angle identity:<br />
<br />
<math>(\sin\theta)^2 + (\cos\theta)^2 = 1</math><br />
<br />
<math>\cos\theta = \sin{\left(90^{\circ} - \theta\right)} = -\sin{\left(\theta - 90^{\circ}\right)}</math><br />
<br />
<br />
<math>P = P_{cyl} \left( 1 - (\cos\theta)^2 \right) = P_{cyl} + \left(-P_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math><br />
<br />
We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (same as subtracting 90 degrees, since the axis is in modulo 180 degrees) to the axis, we get an equivalent combination.<br />
<br />
For example, -1 sph -1 cyl 1 axis is the same as -2 sph +1 cyl 91 axis.<br />
<br />
In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two forms are equivalent.<br />
<br />
==== Spherical Equivalent ====<br />
{{See also|Astigmatism#Spherical equivalent}}<br />
<br />
By calculating the average value over all angles using an integral, the result<ref>it is only necessary to integrate one or two periods: https://www.wolframalpha.com/input/?i=average+of+%28sin+x%29%5E2+from+0+to+2+pi</ref> is<br />
<br />
<math>P_{avg} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} P_{cyl} (\sin{t})^2 \,dt = \frac{1}{2} P_{cyl}</math><br />
<br />
This is why the spherical equivalent has power equal to half of the cylinder's power.<br />
<br />
==== Adding/Combining Lenses ====<br />
Multiple lens, each with spherical and cylindrical components (not necessarily at the same axis) can be added to form one lens with a spherical and cylindrical component.<br />
<br />
We can use the double angle formula to convert each cylindrical lens into a constant plus a cosine:<br />
<br />
<math>\cos{2\theta}=1-2(\sin\theta)^2</math><br />
<br />
<br />
<math>P = P_{cyl} (\sin{\left(\theta + \phi\right)})^2 = P_{cyl} \left( \frac{1-\cos{\left(2\theta + 2\phi\right)}}{2} \right) = \frac{1}{2} P_{cyl} + \frac{-P_{cyl}}{2} \cos{\left(2\theta + 2\phi\right)}</math><br />
<br />
The constant parts are added with the spherical components. The cosines can be added by converting them to [https://en.wikipedia.org/wiki/Phasor phasors] and adding the phasors together. The resulting phasor corresponds to one of two cylindrical lenses (see the section on Transposition), and its corresponding spherical component must be subtracted from the total spherical component.<br />
<br />
There are implementations of this at<br />
* http://opticampus.opti.vision/tools/cylinders.php<br />
* http://billauer.co.il/simulator.html<br />
<br />
=== Decentration ===<br />
Induced prism can be calculated using Prentice's rule. Similar to Vertex Distance, decentration is less of an issue for smaller power lenses.<br />
<br />
The amount of prism power P induced by decentration c of a lens of power f is<br />
<br />
<math>P=cf</math><br />
<br />
1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm, and f is in diopters, then P is in prism diopters.<br />
<br />
A prism with apex angle a and refractive index n results in angle of deviation of the light d, which is equal to P prism diopters:<br />
<br />
<math>d=(n-1)a</math><br />
<br />
<br />
<math>P=100\tan{d}=100\tan((n-1)a)</math><br />
<br />
=== Vertex Distance ===<br />
See [[Vertex distance#Calculation]]<br />
<br />
==References==<br />
{{reflist}}<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Diopters&diff=16554Diopters2022-03-28T16:16:55Z<p>User: /* Decentration */</p>
<hr />
<div><br />
Diopter is a measure of the [https://en.wikipedia.org/wiki/Optical_power optical power] P of a [[lens]] (or mirror) and is equal to the reciprocal of [[focal length]] in meters. The most common unit symbol for diopters is dpt, D, or m<sup>-1</sup>.<br />
<br />
<math>P = \frac{1}{f} = -\frac{1}{d}</math><br />
<br />
* In [[EM]], we use the [[cm measurement]] to calculate diopters needed to correct [[refraction]] of the eye. If you can see 50 cm clearly, your diopters will be <math>-\frac{1}{0.50}=-2 dpt</math>.<br />
<br />
* Lenses in series add their powers: if you're wearing -2 diopter contacts ([[vertex distance|adjusted for glasses strength]]) and put +1 diopter reading glasses over the contacts you're in effect wearing -1 diopters.<br />
** There are some caveats such as vertex distance, since moving the lens away effectively gives you a weaker negative lens or stronger positive lens. There is also decentration, which induces prism when the lens is moved to the side. These effects become negligible for weaker lenses.<br />
* According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.<br />
** A lens with a negative diopter sign compensates for [[nearsightedness]] while a lens with a positive diopter sign compensates for [[farsightedness]].<br />
<br />
{| class="wikitable"<br />
|+ Approximate categorizations of myopia by [[spherical]] lens power:<br />
|-<br />
| 0.00 to -0.50 dpt || Not really considered myopic, probably don't need glasses<br />
|-<br />
| -0.50 to -1.00 dpt || Mild myopia, [[normalized]] sometimes not needed<br />
|-<br />
| -1.00 to -2.50 dpt || Mild myopia, [[differentials]] possibly not needed<br />
|-<br />
| -2.50 to -3.00 dpt || Mild myopia, differentials probably needed<br />
|-<br />
| -3.00 to -6.00 dpt || Moderate myopia, glasses always needed<br />
|-<br />
| -6.00 to -10.00 dpt || High myopia<br />
|-<br />
| -10.00+ dpt || Very high myopia. Field of view significantly reduced.<br />
|}<br />
<br />
==Gap and ratio==<br />
<br />
Comparisons between two diopters is typically expressed using one of these terms:<br />
<br />
* ''diopter gap'' (or ''diopter difference''): absolute difference in diopters between two values<br />
* ''diopter ratio'': ratio of one diopter value to another (such as right eye / left eye)<br />
<br />
For example, consider the following correction:<br />
<br />
OD: -1.5 SPH / -1.5 CYL<br />
OS: -1.0 SPH / -2.0 CYL<br />
<br />
It can be expressed as a 0.5 dpt gap in both SPH and CYL, a 1.5 ratio in SPH and a 0.75 ratio in CYL:<br />
<br />
|(-1.5 dpt) - (-1.0 dpt)| = 0.5 dpt<br />
|(-1.5 dpt) - (-2.0 dpt)| = 0.5 dpt<br />
(-1.5 dpt) / (-1.0 dpt) = 1.5<br />
(-1.5 dpt) / (-2.0 dpt) = 0.75<br />
<br />
In EM articles, the term ''diopter ratio'' is often used interchangeably for left-right ''diopter gap''<ref>{{cite jake|https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/|The Diopter Ratio Trap: Don’t Favor One Eye}}</ref>, for example when talking about reducing a correction while keeping the ''gap'' the same. This can also be expressed as a [[wikipedia:Percent difference|percentage difference]] between the two diopter values<ref>{{cite jake|https://endmyopia.org/reducing-diopter-ratio-diy-patching-solution-pro-topic/|Reducing Diopter Ratio: DIY Patching Solution (PRO TOPIC)}}</ref> (e.g. the <tt>0.5 dpt</tt> difference between the right and left eyes here is equivalent to <tt>0.5 dpt / |-1.5 dpt| = 0.33</tt> or 33%).<br />
<br />
The general recommendation is that the left-right diopter gap is constant across all lenses being used. However, some old EM articles show successful cases where differentials are equalized but normalized have a 0.25 D gap.<ref>https://endmyopia.org/progress-improving-centimeter-62-90/ and https://endmyopia.org/saras-journey-truth-long-term-vision-improvement-potential/</ref><br />
<br />
Confusingly, diopter gap is also sometimes used to refer to the diff-norm gap, the difference between [[differentials]] and [[normalized]] or the [[spherical equivalent]] of that difference.<ref>https://endmyopia.org/pro-topic-managing-your-maximum-diopter-gap/</ref><br />
<br />
It is often useful to disambiguate what is being compared:<br />
* ''left-right gap'': left eye diopters minus right eye diopters, ignoring axis<br />
** In the example above, the left-right gap is +0.5 SPH -0.5 CYL.<br />
** The axis is ignored, and the cylinder powers are subtracted without using [[Diopters#Adding/Combining Lenses|lens combination calculations]].<br />
* ''diff-norm gap'': differentials diopter minus normalized diopters, ignoring axis<br />
** For example, if normalized is -2 SPH -0.5 CYL, and differentials are -0.75 SPH, the diff-norm gap is 1.25 SPH 0.5 CYL or 1.5 SPH equivalent.<br />
** The axis is ignored.<br />
** This quantity is generally positive, as more plus sphere is needed for [[close-up]] than [[distance vision]].<br />
<br />
==Technical Details==<br />
This section is for the math-savvy people. It explains concepts in more detail, but knowledge of it is not strictly necessary to use the EM method.<br />
<br />
===Thin Lens Equation===<br />
The focal length of a lens is given by the lensmaker's equation. By assuming the lens is much thinner than the radius of curvature, therefore assuming lens thickness is zero, we get a simplified version of the lensmaker's equation. We can do some further derivation, we arrive at the thin-lens equation:<ref>see derivations at https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses</ref><br />
<br />
<math>\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}</math><br />
<br />
According to the thin lens sign convention,<br />
* di is positive if it is a real image on the opposite side of the lens as the object, and it is negative if it is a virtual image on the same side of the lens as the object.<br />
* f is positive for converging lens and negative for diverging.<br />
<br />
This is also sometimes presented in the Newtonian form:<br />
<br />
<math>\left(d_o-f\right)\left(d_i-f\right)=f^2</math><br />
<br />
====Examples====<br />
"Full correction" takes an object at infinity and produces a virtual image at your far point distance d:<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{-d}=-\frac{1}{d}</math><br />
<br />
<br />
This is the resulting equation at the beginning of the article. It also explains why the focal power is increased for objects at closer distances: mainstream optometry calls this the "add" for presbyopia, although they typically use the minimum amount required for you to see at 40 cm with full distance correction using accommodation. For example, if you choose 80 cm as the working distance for your [[differentials]] (resulting in a +1.25 dpt "add"), and your blur horizon is 50 cm (resulting in -2 dpt), the formula is<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{80\ cm}+\frac{1}{-50\ cm}=1.25\ dpt + \left(-2\ dpt\right) = -0.75\ dpt</math><br />
<br />
=== Cylinder ===<br />
A cylindrical lens of focal power P<sub>cyl</sub> has power P at angle θ from its axis:<br />
<br />
<math>P = P_{cyl} (\sin\theta)^2</math><br />
<br />
==== Axis ====<br />
Axis is usually in degrees modulo 180. It is popular for 0 to be written as 180 in some areas.<br />
<br />
==== Transposition ====<br />
We can understand why there are two different ways to write a spherical and cylindrical lens combination, using the Pythagorean trigonometric identity and the complementary angle identity:<br />
<br />
<math>(\sin\theta)^2 + (\cos\theta)^2 = 1</math><br />
<br />
<math>\cos\theta = \sin{\left(90^{\circ} - \theta\right)} = -\sin{\left(\theta - 90^{\circ}\right)}</math><br />
<br />
<br />
<math>P = P_{cyl} \left( 1 - (\cos\theta)^2 \right) = P_{cyl} + \left(-P_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math><br />
<br />
We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (same as subtracting 90 degrees, since the axis is in modulo 180 degrees) to the axis, we get an equivalent combination.<br />
<br />
For example, -1 sph -1 cyl 1 axis is the same as -2 sph +1 cyl 91 axis.<br />
<br />
In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two forms are equivalent.<br />
<br />
==== Spherical Equivalent ====<br />
{{See also|Astigmatism#Spherical equivalent}}<br />
<br />
By calculating the average value over all angles using an integral, the result<ref>it is only necessary to integrate one or two periods: https://www.wolframalpha.com/input/?i=average+of+%28sin+x%29%5E2+from+0+to+2+pi</ref> is<br />
<br />
<math>P_{avg} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} P_{cyl} (\sin{t})^2 \,dt = \frac{1}{2} P_{cyl}</math><br />
<br />
This is why the spherical equivalent has power equal to half of the cylinder's power.<br />
<br />
==== Adding/Combining Lenses ====<br />
Multiple lens, each with spherical and cylindrical components (not necessarily at the same axis) can be added to form one lens with a spherical and cylindrical component.<br />
<br />
We can use the double angle formula to convert each cylindrical lens into a constant plus a cosine:<br />
<br />
<math>\cos{2\theta}=1-2(\sin\theta)^2</math><br />
<br />
<br />
<math>P = P_{cyl} (\sin{\left(\theta + \phi\right)})^2 = P_{cyl} \left( \frac{1-\cos{\left(2\theta + 2\phi\right)}}{2} \right) = \frac{1}{2} P_{cyl} + \frac{-P_{cyl}}{2} \cos{\left(2\theta + 2\phi\right)}</math><br />
<br />
The constant parts are added with the spherical components. The cosines can be added by converting them to [https://en.wikipedia.org/wiki/Phasor phasors] and adding the phasors together. The resulting phasor corresponds to one of two cylindrical lenses (see the section on Transposition), and its corresponding spherical component must be subtracted from the total spherical component.<br />
<br />
There are implementations of this at<br />
* http://opticampus.opti.vision/tools/cylinders.php<br />
* http://billauer.co.il/simulator.html<br />
<br />
=== Decentration ===<br />
Induced prism can be calculated using Prentice's rule. Similar to Vertex Distance, decentration is less of an issue for smaller power lenses.<br />
<br />
The amount of prism power P induced by decentration c of a lens of power f is<br />
<br />
<math>P=cf</math><br />
<br />
1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm, and f is in diopters, then P is in prism diopters.<br />
<br />
A prism with apex angle a and refractive index n results in angle of deviation of the light d, which is equal to P prism diopters:<br />
<br />
<math>d=(n-1)a</math><br />
<br />
<br />
<math>P=100\tan{d}=100\tan((n-1)a)</math><br />
<br />
=== Vertex Distance ===<br />
See [[Vertex distance#Calculation]]<br />
<br />
==References==<br />
{{reflist}}<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Diopters&diff=16553Diopters2022-03-28T16:16:10Z<p>User: /* Cylinder */ change variable to P for power, instead of F for focal power, since f is used for focal length</p>
<hr />
<div><br />
Diopter is a measure of the [https://en.wikipedia.org/wiki/Optical_power optical power] P of a [[lens]] (or mirror) and is equal to the reciprocal of [[focal length]] in meters. The most common unit symbol for diopters is dpt, D, or m<sup>-1</sup>.<br />
<br />
<math>P = \frac{1}{f} = -\frac{1}{d}</math><br />
<br />
* In [[EM]], we use the [[cm measurement]] to calculate diopters needed to correct [[refraction]] of the eye. If you can see 50 cm clearly, your diopters will be <math>-\frac{1}{0.50}=-2 dpt</math>.<br />
<br />
* Lenses in series add their powers: if you're wearing -2 diopter contacts ([[vertex distance|adjusted for glasses strength]]) and put +1 diopter reading glasses over the contacts you're in effect wearing -1 diopters.<br />
** There are some caveats such as vertex distance, since moving the lens away effectively gives you a weaker negative lens or stronger positive lens. There is also decentration, which induces prism when the lens is moved to the side. These effects become negligible for weaker lenses.<br />
* According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.<br />
** A lens with a negative diopter sign compensates for [[nearsightedness]] while a lens with a positive diopter sign compensates for [[farsightedness]].<br />
<br />
{| class="wikitable"<br />
|+ Approximate categorizations of myopia by [[spherical]] lens power:<br />
|-<br />
| 0.00 to -0.50 dpt || Not really considered myopic, probably don't need glasses<br />
|-<br />
| -0.50 to -1.00 dpt || Mild myopia, [[normalized]] sometimes not needed<br />
|-<br />
| -1.00 to -2.50 dpt || Mild myopia, [[differentials]] possibly not needed<br />
|-<br />
| -2.50 to -3.00 dpt || Mild myopia, differentials probably needed<br />
|-<br />
| -3.00 to -6.00 dpt || Moderate myopia, glasses always needed<br />
|-<br />
| -6.00 to -10.00 dpt || High myopia<br />
|-<br />
| -10.00+ dpt || Very high myopia. Field of view significantly reduced.<br />
|}<br />
<br />
==Gap and ratio==<br />
<br />
Comparisons between two diopters is typically expressed using one of these terms:<br />
<br />
* ''diopter gap'' (or ''diopter difference''): absolute difference in diopters between two values<br />
* ''diopter ratio'': ratio of one diopter value to another (such as right eye / left eye)<br />
<br />
For example, consider the following correction:<br />
<br />
OD: -1.5 SPH / -1.5 CYL<br />
OS: -1.0 SPH / -2.0 CYL<br />
<br />
It can be expressed as a 0.5 dpt gap in both SPH and CYL, a 1.5 ratio in SPH and a 0.75 ratio in CYL:<br />
<br />
|(-1.5 dpt) - (-1.0 dpt)| = 0.5 dpt<br />
|(-1.5 dpt) - (-2.0 dpt)| = 0.5 dpt<br />
(-1.5 dpt) / (-1.0 dpt) = 1.5<br />
(-1.5 dpt) / (-2.0 dpt) = 0.75<br />
<br />
In EM articles, the term ''diopter ratio'' is often used interchangeably for left-right ''diopter gap''<ref>{{cite jake|https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/|The Diopter Ratio Trap: Don’t Favor One Eye}}</ref>, for example when talking about reducing a correction while keeping the ''gap'' the same. This can also be expressed as a [[wikipedia:Percent difference|percentage difference]] between the two diopter values<ref>{{cite jake|https://endmyopia.org/reducing-diopter-ratio-diy-patching-solution-pro-topic/|Reducing Diopter Ratio: DIY Patching Solution (PRO TOPIC)}}</ref> (e.g. the <tt>0.5 dpt</tt> difference between the right and left eyes here is equivalent to <tt>0.5 dpt / |-1.5 dpt| = 0.33</tt> or 33%).<br />
<br />
The general recommendation is that the left-right diopter gap is constant across all lenses being used. However, some old EM articles show successful cases where differentials are equalized but normalized have a 0.25 D gap.<ref>https://endmyopia.org/progress-improving-centimeter-62-90/ and https://endmyopia.org/saras-journey-truth-long-term-vision-improvement-potential/</ref><br />
<br />
Confusingly, diopter gap is also sometimes used to refer to the diff-norm gap, the difference between [[differentials]] and [[normalized]] or the [[spherical equivalent]] of that difference.<ref>https://endmyopia.org/pro-topic-managing-your-maximum-diopter-gap/</ref><br />
<br />
It is often useful to disambiguate what is being compared:<br />
* ''left-right gap'': left eye diopters minus right eye diopters, ignoring axis<br />
** In the example above, the left-right gap is +0.5 SPH -0.5 CYL.<br />
** The axis is ignored, and the cylinder powers are subtracted without using [[Diopters#Adding/Combining Lenses|lens combination calculations]].<br />
* ''diff-norm gap'': differentials diopter minus normalized diopters, ignoring axis<br />
** For example, if normalized is -2 SPH -0.5 CYL, and differentials are -0.75 SPH, the diff-norm gap is 1.25 SPH 0.5 CYL or 1.5 SPH equivalent.<br />
** The axis is ignored.<br />
** This quantity is generally positive, as more plus sphere is needed for [[close-up]] than [[distance vision]].<br />
<br />
==Technical Details==<br />
This section is for the math-savvy people. It explains concepts in more detail, but knowledge of it is not strictly necessary to use the EM method.<br />
<br />
===Thin Lens Equation===<br />
The focal length of a lens is given by the lensmaker's equation. By assuming the lens is much thinner than the radius of curvature, therefore assuming lens thickness is zero, we get a simplified version of the lensmaker's equation. We can do some further derivation, we arrive at the thin-lens equation:<ref>see derivations at https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses</ref><br />
<br />
<math>\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}</math><br />
<br />
According to the thin lens sign convention,<br />
* di is positive if it is a real image on the opposite side of the lens as the object, and it is negative if it is a virtual image on the same side of the lens as the object.<br />
* f is positive for converging lens and negative for diverging.<br />
<br />
This is also sometimes presented in the Newtonian form:<br />
<br />
<math>\left(d_o-f\right)\left(d_i-f\right)=f^2</math><br />
<br />
====Examples====<br />
"Full correction" takes an object at infinity and produces a virtual image at your far point distance d:<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{-d}=-\frac{1}{d}</math><br />
<br />
<br />
This is the resulting equation at the beginning of the article. It also explains why the focal power is increased for objects at closer distances: mainstream optometry calls this the "add" for presbyopia, although they typically use the minimum amount required for you to see at 40 cm with full distance correction using accommodation. For example, if you choose 80 cm as the working distance for your [[differentials]] (resulting in a +1.25 dpt "add"), and your blur horizon is 50 cm (resulting in -2 dpt), the formula is<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{80\ cm}+\frac{1}{-50\ cm}=1.25\ dpt + \left(-2\ dpt\right) = -0.75\ dpt</math><br />
<br />
=== Cylinder ===<br />
A cylindrical lens of focal power P<sub>cyl</sub> has power P at angle θ from its axis:<br />
<br />
<math>P = P_{cyl} (\sin\theta)^2</math><br />
<br />
==== Axis ====<br />
Axis is usually in degrees modulo 180. It is popular for 0 to be written as 180 in some areas.<br />
<br />
==== Transposition ====<br />
We can understand why there are two different ways to write a spherical and cylindrical lens combination, using the Pythagorean trigonometric identity and the complementary angle identity:<br />
<br />
<math>(\sin\theta)^2 + (\cos\theta)^2 = 1</math><br />
<br />
<math>\cos\theta = \sin{\left(90^{\circ} - \theta\right)} = -\sin{\left(\theta - 90^{\circ}\right)}</math><br />
<br />
<br />
<math>P = P_{cyl} \left( 1 - (\cos\theta)^2 \right) = P_{cyl} + \left(-P_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math><br />
<br />
We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (same as subtracting 90 degrees, since the axis is in modulo 180 degrees) to the axis, we get an equivalent combination.<br />
<br />
For example, -1 sph -1 cyl 1 axis is the same as -2 sph +1 cyl 91 axis.<br />
<br />
In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two forms are equivalent.<br />
<br />
==== Spherical Equivalent ====<br />
{{See also|Astigmatism#Spherical equivalent}}<br />
<br />
By calculating the average value over all angles using an integral, the result<ref>it is only necessary to integrate one or two periods: https://www.wolframalpha.com/input/?i=average+of+%28sin+x%29%5E2+from+0+to+2+pi</ref> is<br />
<br />
<math>P_{avg} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} P_{cyl} (\sin{t})^2 \,dt = \frac{1}{2} P_{cyl}</math><br />
<br />
This is why the spherical equivalent has power equal to half of the cylinder's power.<br />
<br />
==== Adding/Combining Lenses ====<br />
Multiple lens, each with spherical and cylindrical components (not necessarily at the same axis) can be added to form one lens with a spherical and cylindrical component.<br />
<br />
We can use the double angle formula to convert each cylindrical lens into a constant plus a cosine:<br />
<br />
<math>\cos{2\theta}=1-2(\sin\theta)^2</math><br />
<br />
<br />
<math>P = P_{cyl} (\sin{\left(\theta + \phi\right)})^2 = P_{cyl} \left( \frac{1-\cos{\left(2\theta + 2\phi\right)}}{2} \right) = \frac{1}{2} P_{cyl} + \frac{-P_{cyl}}{2} \cos{\left(2\theta + 2\phi\right)}</math><br />
<br />
The constant parts are added with the spherical components. The cosines can be added by converting them to [https://en.wikipedia.org/wiki/Phasor phasors] and adding the phasors together. The resulting phasor corresponds to one of two cylindrical lenses (see the section on Transposition), and its corresponding spherical component must be subtracted from the total spherical component.<br />
<br />
There are implementations of this at<br />
* http://opticampus.opti.vision/tools/cylinders.php<br />
* http://billauer.co.il/simulator.html<br />
<br />
=== Decentration ===<br />
Induced prism can be calculated using Prentice's rule. Similar to Vertex Distance, decentration is less of an issue for smaller power lenses.<br />
<br />
The amount of prism P induced by decentration c of a lens of power f is<br />
<br />
<math>P=cf</math><br />
<br />
1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm, and f is in diopters, then P is in prism diopters.<br />
<br />
A prism with apex angle a and refractive index n results in angle of deviation of the light d, which is equal to P prism diopters:<br />
<br />
<math>d=(n-1)a</math><br />
<br />
<br />
<math>P=100\tan{d}=100\tan((n-1)a)</math><br />
<br />
=== Vertex Distance ===<br />
See [[Vertex distance#Calculation]]<br />
<br />
==References==<br />
{{reflist}}<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Diopters&diff=16552Diopters2022-03-28T16:12:11Z<p>User: /* Gap and ratio */</p>
<hr />
<div><br />
Diopter is a measure of the [https://en.wikipedia.org/wiki/Optical_power optical power] P of a [[lens]] (or mirror) and is equal to the reciprocal of [[focal length]] in meters. The most common unit symbol for diopters is dpt, D, or m<sup>-1</sup>.<br />
<br />
<math>P = \frac{1}{f} = -\frac{1}{d}</math><br />
<br />
* In [[EM]], we use the [[cm measurement]] to calculate diopters needed to correct [[refraction]] of the eye. If you can see 50 cm clearly, your diopters will be <math>-\frac{1}{0.50}=-2 dpt</math>.<br />
<br />
* Lenses in series add their powers: if you're wearing -2 diopter contacts ([[vertex distance|adjusted for glasses strength]]) and put +1 diopter reading glasses over the contacts you're in effect wearing -1 diopters.<br />
** There are some caveats such as vertex distance, since moving the lens away effectively gives you a weaker negative lens or stronger positive lens. There is also decentration, which induces prism when the lens is moved to the side. These effects become negligible for weaker lenses.<br />
* According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.<br />
** A lens with a negative diopter sign compensates for [[nearsightedness]] while a lens with a positive diopter sign compensates for [[farsightedness]].<br />
<br />
{| class="wikitable"<br />
|+ Approximate categorizations of myopia by [[spherical]] lens power:<br />
|-<br />
| 0.00 to -0.50 dpt || Not really considered myopic, probably don't need glasses<br />
|-<br />
| -0.50 to -1.00 dpt || Mild myopia, [[normalized]] sometimes not needed<br />
|-<br />
| -1.00 to -2.50 dpt || Mild myopia, [[differentials]] possibly not needed<br />
|-<br />
| -2.50 to -3.00 dpt || Mild myopia, differentials probably needed<br />
|-<br />
| -3.00 to -6.00 dpt || Moderate myopia, glasses always needed<br />
|-<br />
| -6.00 to -10.00 dpt || High myopia<br />
|-<br />
| -10.00+ dpt || Very high myopia. Field of view significantly reduced.<br />
|}<br />
<br />
==Gap and ratio==<br />
<br />
Comparisons between two diopters is typically expressed using one of these terms:<br />
<br />
* ''diopter gap'' (or ''diopter difference''): absolute difference in diopters between two values<br />
* ''diopter ratio'': ratio of one diopter value to another (such as right eye / left eye)<br />
<br />
For example, consider the following correction:<br />
<br />
OD: -1.5 SPH / -1.5 CYL<br />
OS: -1.0 SPH / -2.0 CYL<br />
<br />
It can be expressed as a 0.5 dpt gap in both SPH and CYL, a 1.5 ratio in SPH and a 0.75 ratio in CYL:<br />
<br />
|(-1.5 dpt) - (-1.0 dpt)| = 0.5 dpt<br />
|(-1.5 dpt) - (-2.0 dpt)| = 0.5 dpt<br />
(-1.5 dpt) / (-1.0 dpt) = 1.5<br />
(-1.5 dpt) / (-2.0 dpt) = 0.75<br />
<br />
In EM articles, the term ''diopter ratio'' is often used interchangeably for left-right ''diopter gap''<ref>{{cite jake|https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/|The Diopter Ratio Trap: Don’t Favor One Eye}}</ref>, for example when talking about reducing a correction while keeping the ''gap'' the same. This can also be expressed as a [[wikipedia:Percent difference|percentage difference]] between the two diopter values<ref>{{cite jake|https://endmyopia.org/reducing-diopter-ratio-diy-patching-solution-pro-topic/|Reducing Diopter Ratio: DIY Patching Solution (PRO TOPIC)}}</ref> (e.g. the <tt>0.5 dpt</tt> difference between the right and left eyes here is equivalent to <tt>0.5 dpt / |-1.5 dpt| = 0.33</tt> or 33%).<br />
<br />
The general recommendation is that the left-right diopter gap is constant across all lenses being used. However, some old EM articles show successful cases where differentials are equalized but normalized have a 0.25 D gap.<ref>https://endmyopia.org/progress-improving-centimeter-62-90/ and https://endmyopia.org/saras-journey-truth-long-term-vision-improvement-potential/</ref><br />
<br />
Confusingly, diopter gap is also sometimes used to refer to the diff-norm gap, the difference between [[differentials]] and [[normalized]] or the [[spherical equivalent]] of that difference.<ref>https://endmyopia.org/pro-topic-managing-your-maximum-diopter-gap/</ref><br />
<br />
It is often useful to disambiguate what is being compared:<br />
* ''left-right gap'': left eye diopters minus right eye diopters, ignoring axis<br />
** In the example above, the left-right gap is +0.5 SPH -0.5 CYL.<br />
** The axis is ignored, and the cylinder powers are subtracted without using [[Diopters#Adding/Combining Lenses|lens combination calculations]].<br />
* ''diff-norm gap'': differentials diopter minus normalized diopters, ignoring axis<br />
** For example, if normalized is -2 SPH -0.5 CYL, and differentials are -0.75 SPH, the diff-norm gap is 1.25 SPH 0.5 CYL or 1.5 SPH equivalent.<br />
** The axis is ignored.<br />
** This quantity is generally positive, as more plus sphere is needed for [[close-up]] than [[distance vision]].<br />
<br />
==Technical Details==<br />
This section is for the math-savvy people. It explains concepts in more detail, but knowledge of it is not strictly necessary to use the EM method.<br />
<br />
===Thin Lens Equation===<br />
The focal length of a lens is given by the lensmaker's equation. By assuming the lens is much thinner than the radius of curvature, therefore assuming lens thickness is zero, we get a simplified version of the lensmaker's equation. We can do some further derivation, we arrive at the thin-lens equation:<ref>see derivations at https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses</ref><br />
<br />
<math>\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}</math><br />
<br />
According to the thin lens sign convention,<br />
* di is positive if it is a real image on the opposite side of the lens as the object, and it is negative if it is a virtual image on the same side of the lens as the object.<br />
* f is positive for converging lens and negative for diverging.<br />
<br />
This is also sometimes presented in the Newtonian form:<br />
<br />
<math>\left(d_o-f\right)\left(d_i-f\right)=f^2</math><br />
<br />
====Examples====<br />
"Full correction" takes an object at infinity and produces a virtual image at your far point distance d:<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{-d}=-\frac{1}{d}</math><br />
<br />
<br />
This is the resulting equation at the beginning of the article. It also explains why the focal power is increased for objects at closer distances: mainstream optometry calls this the "add" for presbyopia, although they typically use the minimum amount required for you to see at 40 cm with full distance correction using accommodation. For example, if you choose 80 cm as the working distance for your [[differentials]] (resulting in a +1.25 dpt "add"), and your blur horizon is 50 cm (resulting in -2 dpt), the formula is<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{80\ cm}+\frac{1}{-50\ cm}=1.25\ dpt + \left(-2\ dpt\right) = -0.75\ dpt</math><br />
<br />
=== Cylinder ===<br />
A cylindrical lens of power F<sub>c</sub> has focal power F at angle θ from its axis:<br />
<br />
<math>F = F_{cyl} (\sin\theta)^2</math><br />
<br />
==== Transposition ====<br />
We can understand why there are two different ways to write a spherical and cylindrical lens combination, using the Pythagorean trigonometric identity and the complementary angle identity:<br />
<br />
<math>(\sin\theta)^2 + (\cos\theta)^2 = 1</math><br />
<br />
<math>\cos\theta = \sin{\left(90^{\circ} - \theta\right)} = -\sin{\left(\theta - 90^{\circ}\right)}</math><br />
<br />
<br />
<math>F = F_{cyl} \left( 1 - (\cos\theta)^2 \right) = F_{cyl} + \left(-F_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math><br />
<br />
We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (same as subtracting 90 degrees, since the axis is in modulo 180 degrees) to the axis, we get an equivalent combination.<br />
<br />
For example, -1 sph -1 cyl 1 axis is the same as -2 sph +1 cyl 91 axis.<br />
<br />
In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two forms are equivalent.<br />
<br />
==== Spherical Equivalent ====<br />
{{See also|Astigmatism#Spherical equivalent}}<br />
<br />
By calculating the average value over all angles using an integral, the result<ref>it is only necessary to integrate one or two periods: https://www.wolframalpha.com/input/?i=average+of+%28sin+x%29%5E2+from+0+to+2+pi</ref> is<br />
<br />
<math>F_{avg} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} F_{cyl} (\sin{t})^2 \,dt = \frac{1}{2} F_{cyl}</math><br />
<br />
This is why the spherical equivalent has power equal to half of the cylinder's power.<br />
<br />
==== Adding/Combining Lenses ====<br />
Multiple lens, each with spherical and cylindrical components (not necessarily at the same axis) can be added to form one lens with a spherical and cylindrical component.<br />
<br />
We can use the double angle formula to convert each cylindrical lens into a constant plus a cosine:<br />
<br />
<math>\cos{2\theta}=1-2(\sin\theta)^2</math><br />
<br />
<br />
<math>F = F_{cyl} (\sin{\left(\theta + \phi\right)})^2 = F_{cyl} \left( \frac{1-\cos{\left(2\theta + 2\phi\right)}}{2} \right) = \frac{1}{2} F_{cyl} + \frac{-F_{cyl}}{2} \cos{\left(2\theta + 2\phi\right)}</math><br />
<br />
The constant parts are added with the spherical components. The cosines can be added by converting them to [https://en.wikipedia.org/wiki/Phasor phasors] and adding the phasors together. The resulting phasor corresponds to one of two cylindrical lenses (see the section on Transposition), and its corresponding spherical component must be subtracted from the total spherical component.<br />
<br />
There are implementations of this at<br />
* http://opticampus.opti.vision/tools/cylinders.php<br />
* http://billauer.co.il/simulator.html<br />
<br />
=== Decentration ===<br />
Induced prism can be calculated using Prentice's rule. Similar to Vertex Distance, decentration is less of an issue for smaller power lenses.<br />
<br />
The amount of prism P induced by decentration c of a lens of power f is<br />
<br />
<math>P=cf</math><br />
<br />
1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm, and f is in diopters, then P is in prism diopters.<br />
<br />
A prism with apex angle a and refractive index n results in angle of deviation of the light d, which is equal to P prism diopters:<br />
<br />
<math>d=(n-1)a</math><br />
<br />
<br />
<math>P=100\tan{d}=100\tan((n-1)a)</math><br />
<br />
=== Vertex Distance ===<br />
See [[Vertex distance#Calculation]]<br />
<br />
==References==<br />
{{reflist}}<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Diopters&diff=16551Diopters2022-03-28T16:11:58Z<p>User: /* Gap and ratio */</p>
<hr />
<div><br />
Diopter is a measure of the [https://en.wikipedia.org/wiki/Optical_power optical power] P of a [[lens]] (or mirror) and is equal to the reciprocal of [[focal length]] in meters. The most common unit symbol for diopters is dpt, D, or m<sup>-1</sup>.<br />
<br />
<math>P = \frac{1}{f} = -\frac{1}{d}</math><br />
<br />
* In [[EM]], we use the [[cm measurement]] to calculate diopters needed to correct [[refraction]] of the eye. If you can see 50 cm clearly, your diopters will be <math>-\frac{1}{0.50}=-2 dpt</math>.<br />
<br />
* Lenses in series add their powers: if you're wearing -2 diopter contacts ([[vertex distance|adjusted for glasses strength]]) and put +1 diopter reading glasses over the contacts you're in effect wearing -1 diopters.<br />
** There are some caveats such as vertex distance, since moving the lens away effectively gives you a weaker negative lens or stronger positive lens. There is also decentration, which induces prism when the lens is moved to the side. These effects become negligible for weaker lenses.<br />
* According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.<br />
** A lens with a negative diopter sign compensates for [[nearsightedness]] while a lens with a positive diopter sign compensates for [[farsightedness]].<br />
<br />
{| class="wikitable"<br />
|+ Approximate categorizations of myopia by [[spherical]] lens power:<br />
|-<br />
| 0.00 to -0.50 dpt || Not really considered myopic, probably don't need glasses<br />
|-<br />
| -0.50 to -1.00 dpt || Mild myopia, [[normalized]] sometimes not needed<br />
|-<br />
| -1.00 to -2.50 dpt || Mild myopia, [[differentials]] possibly not needed<br />
|-<br />
| -2.50 to -3.00 dpt || Mild myopia, differentials probably needed<br />
|-<br />
| -3.00 to -6.00 dpt || Moderate myopia, glasses always needed<br />
|-<br />
| -6.00 to -10.00 dpt || High myopia<br />
|-<br />
| -10.00+ dpt || Very high myopia. Field of view significantly reduced.<br />
|}<br />
<br />
==Gap and ratio==<br />
<br />
Comparisons between two diopters is typically expressed using one of these terms:<br />
<br />
* ''diopter gap'' (or ''diopter difference''): absolute difference in diopters between two values<br />
* ''diopter ratio'': ratio of one diopter value to another (such as right eye / left eye)<br />
<br />
For example, consider the following correction:<br />
<br />
OD: -1.5 SPH / -1.5 CYL<br />
OS: -1.0 SPH / -2.0 CYL<br />
<br />
It can be expressed as a 0.5 dpt gap in both SPH and CYL, a 1.5 ratio in SPH and a 0.75 ratio in CYL:<br />
<br />
|(-1.5 dpt) - (-1.0 dpt)| = 0.5 dpt<br />
|(-1.5 dpt) - (-2.0 dpt)| = 0.5 dpt<br />
(-1.5 dpt) / (-1.0 dpt) = 1.5<br />
(-1.5 dpt) / (-2.0 dpt) = 0.75<br />
<br />
In EM articles, the term ''diopter ratio'' is often used interchangeably for left-right ''diopter gap''<ref>{{cite jake|https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/|The Diopter Ratio Trap: Don’t Favor One Eye}}</ref>, for example when talking about reducing a correction while keeping the ''gap'' the same. This can also be expressed as a [[wikipedia:Percent difference|percentage difference]] between the two diopter values<ref>{{cite jake|https://endmyopia.org/reducing-diopter-ratio-diy-patching-solution-pro-topic/|Reducing Diopter Ratio: DIY Patching Solution (PRO TOPIC)}}</ref> (e.g. the <tt>0.5 dpt</tt> difference between the right and left eyes here is equivalent to <tt>0.5 dpt / |-1.5 dpt| = 0.33</tt> or 33%).<br />
<br />
The general recommendation is that the left-right diopter gap is constant across all lenses being used. However, some old EM articles show successful cases where differentials are equalized but normalized have a 0.25 D gap.<ref>https://endmyopia.org/progress-improving-centimeter-62-90/ and https://endmyopia.org/saras-journey-truth-long-term-vision-improvement-potential/</ref><br />
<br />
Confusingly, diopter gap is also sometimes used to refer to the diff-norm gap, the difference between [[differentials]] and [[normalized]] or the [[spherical equivalent]] of that difference.<ref>https://endmyopia.org/pro-topic-managing-your-maximum-diopter-gap/</ref><br />
<br />
It is often useful to disambiguate what is being compared:<br />
* ''left-right gap'': left eye diopters minus right eye diopters, ignoring axis<br />
** In the example above, the left-right gap is +0.5 SPH -0.5 CYL.<br />
** The axis is ignored, and the cylinder powers are subtracted without using [[Diopters#Adding/Combining Lenses|lens combination calculations]].<br />
* ''diff-norm gap'': differentials diopter minus normalized diopters, ignoring axis<br />
** For example, if normalized is -2 SPH -0.5 CYL, and differentials are -0.75 SPH, the diff-norm gap is 1.25 SPH 0.5 CYL or 1.5 SPH equivalent.** The axis is ignored.<br />
** This quantity is generally positive, as more plus sphere is needed for [[close-up]] than [[distance vision]].<br />
<br />
==Technical Details==<br />
This section is for the math-savvy people. It explains concepts in more detail, but knowledge of it is not strictly necessary to use the EM method.<br />
<br />
===Thin Lens Equation===<br />
The focal length of a lens is given by the lensmaker's equation. By assuming the lens is much thinner than the radius of curvature, therefore assuming lens thickness is zero, we get a simplified version of the lensmaker's equation. We can do some further derivation, we arrive at the thin-lens equation:<ref>see derivations at https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses</ref><br />
<br />
<math>\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}</math><br />
<br />
According to the thin lens sign convention,<br />
* di is positive if it is a real image on the opposite side of the lens as the object, and it is negative if it is a virtual image on the same side of the lens as the object.<br />
* f is positive for converging lens and negative for diverging.<br />
<br />
This is also sometimes presented in the Newtonian form:<br />
<br />
<math>\left(d_o-f\right)\left(d_i-f\right)=f^2</math><br />
<br />
====Examples====<br />
"Full correction" takes an object at infinity and produces a virtual image at your far point distance d:<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{-d}=-\frac{1}{d}</math><br />
<br />
<br />
This is the resulting equation at the beginning of the article. It also explains why the focal power is increased for objects at closer distances: mainstream optometry calls this the "add" for presbyopia, although they typically use the minimum amount required for you to see at 40 cm with full distance correction using accommodation. For example, if you choose 80 cm as the working distance for your [[differentials]] (resulting in a +1.25 dpt "add"), and your blur horizon is 50 cm (resulting in -2 dpt), the formula is<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{80\ cm}+\frac{1}{-50\ cm}=1.25\ dpt + \left(-2\ dpt\right) = -0.75\ dpt</math><br />
<br />
=== Cylinder ===<br />
A cylindrical lens of power F<sub>c</sub> has focal power F at angle θ from its axis:<br />
<br />
<math>F = F_{cyl} (\sin\theta)^2</math><br />
<br />
==== Transposition ====<br />
We can understand why there are two different ways to write a spherical and cylindrical lens combination, using the Pythagorean trigonometric identity and the complementary angle identity:<br />
<br />
<math>(\sin\theta)^2 + (\cos\theta)^2 = 1</math><br />
<br />
<math>\cos\theta = \sin{\left(90^{\circ} - \theta\right)} = -\sin{\left(\theta - 90^{\circ}\right)}</math><br />
<br />
<br />
<math>F = F_{cyl} \left( 1 - (\cos\theta)^2 \right) = F_{cyl} + \left(-F_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math><br />
<br />
We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (same as subtracting 90 degrees, since the axis is in modulo 180 degrees) to the axis, we get an equivalent combination.<br />
<br />
For example, -1 sph -1 cyl 1 axis is the same as -2 sph +1 cyl 91 axis.<br />
<br />
In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two forms are equivalent.<br />
<br />
==== Spherical Equivalent ====<br />
{{See also|Astigmatism#Spherical equivalent}}<br />
<br />
By calculating the average value over all angles using an integral, the result<ref>it is only necessary to integrate one or two periods: https://www.wolframalpha.com/input/?i=average+of+%28sin+x%29%5E2+from+0+to+2+pi</ref> is<br />
<br />
<math>F_{avg} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} F_{cyl} (\sin{t})^2 \,dt = \frac{1}{2} F_{cyl}</math><br />
<br />
This is why the spherical equivalent has power equal to half of the cylinder's power.<br />
<br />
==== Adding/Combining Lenses ====<br />
Multiple lens, each with spherical and cylindrical components (not necessarily at the same axis) can be added to form one lens with a spherical and cylindrical component.<br />
<br />
We can use the double angle formula to convert each cylindrical lens into a constant plus a cosine:<br />
<br />
<math>\cos{2\theta}=1-2(\sin\theta)^2</math><br />
<br />
<br />
<math>F = F_{cyl} (\sin{\left(\theta + \phi\right)})^2 = F_{cyl} \left( \frac{1-\cos{\left(2\theta + 2\phi\right)}}{2} \right) = \frac{1}{2} F_{cyl} + \frac{-F_{cyl}}{2} \cos{\left(2\theta + 2\phi\right)}</math><br />
<br />
The constant parts are added with the spherical components. The cosines can be added by converting them to [https://en.wikipedia.org/wiki/Phasor phasors] and adding the phasors together. The resulting phasor corresponds to one of two cylindrical lenses (see the section on Transposition), and its corresponding spherical component must be subtracted from the total spherical component.<br />
<br />
There are implementations of this at<br />
* http://opticampus.opti.vision/tools/cylinders.php<br />
* http://billauer.co.il/simulator.html<br />
<br />
=== Decentration ===<br />
Induced prism can be calculated using Prentice's rule. Similar to Vertex Distance, decentration is less of an issue for smaller power lenses.<br />
<br />
The amount of prism P induced by decentration c of a lens of power f is<br />
<br />
<math>P=cf</math><br />
<br />
1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm, and f is in diopters, then P is in prism diopters.<br />
<br />
A prism with apex angle a and refractive index n results in angle of deviation of the light d, which is equal to P prism diopters:<br />
<br />
<math>d=(n-1)a</math><br />
<br />
<br />
<math>P=100\tan{d}=100\tan((n-1)a)</math><br />
<br />
=== Vertex Distance ===<br />
See [[Vertex distance#Calculation]]<br />
<br />
==References==<br />
{{reflist}}<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Diopters&diff=16550Diopters2022-03-28T16:11:28Z<p>User: /* Gap and ratio */</p>
<hr />
<div><br />
Diopter is a measure of the [https://en.wikipedia.org/wiki/Optical_power optical power] P of a [[lens]] (or mirror) and is equal to the reciprocal of [[focal length]] in meters. The most common unit symbol for diopters is dpt, D, or m<sup>-1</sup>.<br />
<br />
<math>P = \frac{1}{f} = -\frac{1}{d}</math><br />
<br />
* In [[EM]], we use the [[cm measurement]] to calculate diopters needed to correct [[refraction]] of the eye. If you can see 50 cm clearly, your diopters will be <math>-\frac{1}{0.50}=-2 dpt</math>.<br />
<br />
* Lenses in series add their powers: if you're wearing -2 diopter contacts ([[vertex distance|adjusted for glasses strength]]) and put +1 diopter reading glasses over the contacts you're in effect wearing -1 diopters.<br />
** There are some caveats such as vertex distance, since moving the lens away effectively gives you a weaker negative lens or stronger positive lens. There is also decentration, which induces prism when the lens is moved to the side. These effects become negligible for weaker lenses.<br />
* According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.<br />
** A lens with a negative diopter sign compensates for [[nearsightedness]] while a lens with a positive diopter sign compensates for [[farsightedness]].<br />
<br />
{| class="wikitable"<br />
|+ Approximate categorizations of myopia by [[spherical]] lens power:<br />
|-<br />
| 0.00 to -0.50 dpt || Not really considered myopic, probably don't need glasses<br />
|-<br />
| -0.50 to -1.00 dpt || Mild myopia, [[normalized]] sometimes not needed<br />
|-<br />
| -1.00 to -2.50 dpt || Mild myopia, [[differentials]] possibly not needed<br />
|-<br />
| -2.50 to -3.00 dpt || Mild myopia, differentials probably needed<br />
|-<br />
| -3.00 to -6.00 dpt || Moderate myopia, glasses always needed<br />
|-<br />
| -6.00 to -10.00 dpt || High myopia<br />
|-<br />
| -10.00+ dpt || Very high myopia. Field of view significantly reduced.<br />
|}<br />
<br />
==Gap and ratio==<br />
<br />
Comparisons between two diopters is typically expressed using one of these terms:<br />
<br />
* ''diopter gap'' (or ''diopter difference''): absolute difference in diopters between two values<br />
* ''diopter ratio'': ratio of one diopter value to another (such as right eye / left eye)<br />
<br />
For example, consider the following correction:<br />
<br />
OD: -1.5 SPH / -1.5 CYL<br />
OS: -1.0 SPH / -2.0 CYL<br />
<br />
It can be expressed as a 0.5 dpt gap in both SPH and CYL, a 1.5 ratio in SPH and a 0.75 ratio in CYL:<br />
<br />
|(-1.5 dpt) - (-1.0 dpt)| = 0.5 dpt<br />
|(-1.5 dpt) - (-2.0 dpt)| = 0.5 dpt<br />
(-1.5 dpt) / (-1.0 dpt) = 1.5<br />
(-1.5 dpt) / (-2.0 dpt) = 0.75<br />
<br />
In EM articles, the term ''diopter ratio'' is often used interchangeably for left-right ''diopter gap''<ref>{{cite jake|https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/|The Diopter Ratio Trap: Don’t Favor One Eye}}</ref>, for example when talking about reducing a correction while keeping the ''gap'' the same. This can also be expressed as a [[wikipedia:Percent difference|percentage difference]] between the two diopter values<ref>{{cite jake|https://endmyopia.org/reducing-diopter-ratio-diy-patching-solution-pro-topic/|Reducing Diopter Ratio: DIY Patching Solution (PRO TOPIC)}}</ref> (e.g. the <tt>0.5 dpt</tt> difference between the right and left eyes here is equivalent to <tt>0.5 dpt / |-1.5 dpt| = 0.33</tt> or 33%).<br />
<br />
The general recommendation is that the left-right diopter gap is constant across all lenses being used. However, some old EM articles show successful cases where differentials are equalized but normalized have a 0.25 D gap.<ref>https://endmyopia.org/progress-improving-centimeter-62-90/ and https://endmyopia.org/saras-journey-truth-long-term-vision-improvement-potential/</ref><br />
<br />
Confusingly, diopter gap is also sometimes used to refer to the diff-norm gap, the difference between [[differentials]] and [[normalized]] or the [[spherical equivalent]] of that difference.<ref>https://endmyopia.org/pro-topic-managing-your-maximum-diopter-gap/</ref><br />
<br />
It is often useful to disambiguate what is being compared:<br />
* ''left-right gap'': left eye diopters minus right eye diopters, ignoring axis<br />
** In the example above, the left-right gap is +0.5 SPH -0.5 CYL.<br />
** The axis is ignored, and the cylinder powers are subtracted without using [[Diopters#Adding/Combining Lenses|lens combination calculations]].<br />
* ''diff-norm gap'': differentials diopter minus normalized diopters, ignoring axis<br />
** For example, if normalized is -2 SPH -0.5 CYL, and differentials are -0.75 SPH, the diff-norm gap is 1.25 SPH 0.5 CYL or 1.5 SPH equivalent.<br />
** This quantity is generally positive, as more plus sphere is needed for [[close-up]] than [[distance vision]].<br />
** The axis is ignored.<br />
<br />
==Technical Details==<br />
This section is for the math-savvy people. It explains concepts in more detail, but knowledge of it is not strictly necessary to use the EM method.<br />
<br />
===Thin Lens Equation===<br />
The focal length of a lens is given by the lensmaker's equation. By assuming the lens is much thinner than the radius of curvature, therefore assuming lens thickness is zero, we get a simplified version of the lensmaker's equation. We can do some further derivation, we arrive at the thin-lens equation:<ref>see derivations at https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses</ref><br />
<br />
<math>\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}</math><br />
<br />
According to the thin lens sign convention,<br />
* di is positive if it is a real image on the opposite side of the lens as the object, and it is negative if it is a virtual image on the same side of the lens as the object.<br />
* f is positive for converging lens and negative for diverging.<br />
<br />
This is also sometimes presented in the Newtonian form:<br />
<br />
<math>\left(d_o-f\right)\left(d_i-f\right)=f^2</math><br />
<br />
====Examples====<br />
"Full correction" takes an object at infinity and produces a virtual image at your far point distance d:<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{-d}=-\frac{1}{d}</math><br />
<br />
<br />
This is the resulting equation at the beginning of the article. It also explains why the focal power is increased for objects at closer distances: mainstream optometry calls this the "add" for presbyopia, although they typically use the minimum amount required for you to see at 40 cm with full distance correction using accommodation. For example, if you choose 80 cm as the working distance for your [[differentials]] (resulting in a +1.25 dpt "add"), and your blur horizon is 50 cm (resulting in -2 dpt), the formula is<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{80\ cm}+\frac{1}{-50\ cm}=1.25\ dpt + \left(-2\ dpt\right) = -0.75\ dpt</math><br />
<br />
=== Cylinder ===<br />
A cylindrical lens of power F<sub>c</sub> has focal power F at angle θ from its axis:<br />
<br />
<math>F = F_{cyl} (\sin\theta)^2</math><br />
<br />
==== Transposition ====<br />
We can understand why there are two different ways to write a spherical and cylindrical lens combination, using the Pythagorean trigonometric identity and the complementary angle identity:<br />
<br />
<math>(\sin\theta)^2 + (\cos\theta)^2 = 1</math><br />
<br />
<math>\cos\theta = \sin{\left(90^{\circ} - \theta\right)} = -\sin{\left(\theta - 90^{\circ}\right)}</math><br />
<br />
<br />
<math>F = F_{cyl} \left( 1 - (\cos\theta)^2 \right) = F_{cyl} + \left(-F_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math><br />
<br />
We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (same as subtracting 90 degrees, since the axis is in modulo 180 degrees) to the axis, we get an equivalent combination.<br />
<br />
For example, -1 sph -1 cyl 1 axis is the same as -2 sph +1 cyl 91 axis.<br />
<br />
In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two forms are equivalent.<br />
<br />
==== Spherical Equivalent ====<br />
{{See also|Astigmatism#Spherical equivalent}}<br />
<br />
By calculating the average value over all angles using an integral, the result<ref>it is only necessary to integrate one or two periods: https://www.wolframalpha.com/input/?i=average+of+%28sin+x%29%5E2+from+0+to+2+pi</ref> is<br />
<br />
<math>F_{avg} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} F_{cyl} (\sin{t})^2 \,dt = \frac{1}{2} F_{cyl}</math><br />
<br />
This is why the spherical equivalent has power equal to half of the cylinder's power.<br />
<br />
==== Adding/Combining Lenses ====<br />
Multiple lens, each with spherical and cylindrical components (not necessarily at the same axis) can be added to form one lens with a spherical and cylindrical component.<br />
<br />
We can use the double angle formula to convert each cylindrical lens into a constant plus a cosine:<br />
<br />
<math>\cos{2\theta}=1-2(\sin\theta)^2</math><br />
<br />
<br />
<math>F = F_{cyl} (\sin{\left(\theta + \phi\right)})^2 = F_{cyl} \left( \frac{1-\cos{\left(2\theta + 2\phi\right)}}{2} \right) = \frac{1}{2} F_{cyl} + \frac{-F_{cyl}}{2} \cos{\left(2\theta + 2\phi\right)}</math><br />
<br />
The constant parts are added with the spherical components. The cosines can be added by converting them to [https://en.wikipedia.org/wiki/Phasor phasors] and adding the phasors together. The resulting phasor corresponds to one of two cylindrical lenses (see the section on Transposition), and its corresponding spherical component must be subtracted from the total spherical component.<br />
<br />
There are implementations of this at<br />
* http://opticampus.opti.vision/tools/cylinders.php<br />
* http://billauer.co.il/simulator.html<br />
<br />
=== Decentration ===<br />
Induced prism can be calculated using Prentice's rule. Similar to Vertex Distance, decentration is less of an issue for smaller power lenses.<br />
<br />
The amount of prism P induced by decentration c of a lens of power f is<br />
<br />
<math>P=cf</math><br />
<br />
1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm, and f is in diopters, then P is in prism diopters.<br />
<br />
A prism with apex angle a and refractive index n results in angle of deviation of the light d, which is equal to P prism diopters:<br />
<br />
<math>d=(n-1)a</math><br />
<br />
<br />
<math>P=100\tan{d}=100\tan((n-1)a)</math><br />
<br />
=== Vertex Distance ===<br />
See [[Vertex distance#Calculation]]<br />
<br />
==References==<br />
{{reflist}}<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Guide:Reducing_lens_complexity&diff=16549Guide:Reducing lens complexity2022-03-28T16:08:49Z<p>User: /* How to reduce lens complexity */</p>
<hr />
<div><br />
<br />
TODO: this article needs to be expanded for edge cases like already low diopters.<br />
<br />
==When to reduce lens complexity==<br />
<br />
[[Lens complexity]] is best reduced before getting into the [[low diopters]] range. Ideally, both eyes would be equal before the normalized correction reaches -1.5 [[diopters]].{{citation needed}}<br />
<br />
==How to reduce lens complexity==<br />
<br />
'''Make your first reduction or two simple and [[spherical]]. This will teach you the basics of the [[EndMyopia]] methods.'''<br />
<br />
There are two types of reductions:<br />
<br />
* <div>A ''simple reduction'' or ''binocular reduction'' is drop in lens powers for both eyes, simultaneously</div><br />
* <div>An ''equalizing reduction'' or ''monocular reduction'' is drop in lens power for one eye, the eye with greater correction (more negative)</div><br />
<br />
An [[equalizing]] reduction is done to bring the eyes closer to having the same level of correction. Jake said that "...if you do reduce the ratio, you should have at least 2 regular spherical reductions in between."<ref>https://community.endmyopia.org/t/key-to-patching-successfully-reducing-diopter-ratio/333/6</ref> This is not always possible, especially when [[Guide:High diopter gap|high anisometropia]] is involved.<br />
<br />
There are three types of reductions with respect to the power change:<br />
* a 0.25 [[diopter|D]] drop to [[spherical]] power<br />
* a 0.25 D drop to [[cylindrical]] power<br />
* a trade of 0.5 D cylindrical power for 0.25 D spherical power<br />
<br />
'''There are four rules for reducing complexity:'''<br />
# <div>Alternate types of reductions. Have one (Simple > Equalizing > Simple > Equalizing...) or two (Simple > Simple > Equalizing > Simple > Simple > Equalizing...) simple drops between equalizing drops.</div><br />
# <div>Change only spherical or only cylindrical and never both simultaneously.</div><br />
# <div>For an equalizing reduction, change both differential lenses and normalized lenses simultaneously to keep the [[focal planes]] in sync.</div><br />
# <div>For a simple reduction, change differential lenses a few weeks after normalized lenses to keep changes to [[focal planes]] to a minimum.</div><br />
<br />
<br />
'''A note on rule 3 and rule 4:''' Keeping focal planes in sync is a higher priority than keeping changes to focal planes to a minimum, thus rule 3 exists.<br />
<br />
{| class="wikitable" style="text-align:center;"<br />
|+ Example Spherical Reduction Schedule<br />
|-<br />
! style="text-align:left;" | Reduction Type<br />
! colspan="2" | Normalized<br />
! colspan="2" | Differentials<br />
! style="text-align:left;" | Explanation<br />
|-<br />
| style="text-align:left;" |<br />
| Left<br />
| Right<br />
| Left<br />
| Right<br />
| style="text-align:left;" |<br />
|-<br />
| rowspan="2" style="text-align:left;" |<br />
| -3.50<br />
| -4.00<br />
| -2.25<br />
| -2.75<br />
| style="text-align:left;" | This is the '''starting point'''.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 8 - 16 weeks<br />
|<br />
|-<br />
| rowspan="4" | Simple<br />
| -3.25<br />
| -3.75<br />
|<br />
|<br />
| style="text-align:left;" | Perform normalized reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
| (rule 4)<br />
|-<br />
|<br />
|<br />
| -2.00<br />
| -2.50<br />
| style="text-align:left;" | Perform differential reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
|<br />
|- style="font-weight:bold;"<br />
| rowspan="2" | Equalizing<br />
| -3.25<br />
| -3.50<br />
| -2.00<br />
| -2.25<br />
| style="text-align:left;" | Both norms and diffs are reduced simultaneously. (rule 3)<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center; font-weight:bold;" | wait 8 - 16 weeks<br />
|<br />
|-<br />
| rowspan="4" | Simple<br />
| -3.00<br />
| -3.25<br />
|<br />
|<br />
| style="text-align:left;" | Perform normalized reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
| (rule 4)<br />
|-<br />
|<br />
|<br />
| -1.75<br />
| -2.00<br />
| style="text-align:left;" | Perform differential reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
|<br />
|- style="font-weight:bold;"<br />
| rowspan="2" | Equalizing<br />
| -3.00<br />
| -3.00<br />
| -1.75<br />
| -1.75<br />
| style="text-align:left;" | Both norms and diffs are reduced simultaneously. (rule 3)<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center; font-weight:bold;" | wait 8 - 16 weeks<br />
|<br />
|}<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
==See also==<br />
* [[Equalizing]]<br />
<br />
* [[Guide:Resolving double vision | Resolving double vision]]<br />
<br />
* [[reduction | Reduction]]<br />
<br />
[[Category:Guides]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Guide:Reducing_lens_complexity&diff=16548Guide:Reducing lens complexity2022-03-28T16:08:19Z<p>User: /* How to reduce lens complexity */</p>
<hr />
<div><br />
<br />
TODO: this article needs to be expanded for edge cases like already low diopters.<br />
<br />
==When to reduce lens complexity==<br />
<br />
[[Lens complexity]] is best reduced before getting into the [[low diopters]] range. Ideally, both eyes would be equal before the normalized correction reaches -1.5 [[diopters]].{{citation needed}}<br />
<br />
==How to reduce lens complexity==<br />
<br />
'''Make your first reduction or two simple and [[spherical]]. This will teach you the basics of the [[EndMyopia]] methods.'''<br />
<br />
There are two types of reductions:<br />
<br />
* <div>A simple reduction or binocular reduction is drop in lens powers for both eyes, simultaneously</div><br />
* <div>An equalizing reduction or monocular reduction is drop in lens power for one eye, the eye with greater correction (more negative)</div><br />
<br />
An [[equalizing]] reduction is done to bring the eyes closer to having the same level of correction. Jake said that "...if you do reduce the ratio, you should have at least 2 regular spherical reductions in between."<ref>https://community.endmyopia.org/t/key-to-patching-successfully-reducing-diopter-ratio/333/6</ref> This is not always possible, especially when [[Guide:High diopter gap|high anisometropia]] is involved.<br />
<br />
There are three types of reductions with respect to the power change:<br />
* a 0.25 [[diopter|D]] drop to [[spherical]] power<br />
* a 0.25 D drop to [[cylindrical]] power<br />
* a trade of 0.5 D cylindrical power for 0.25 D spherical power<br />
<br />
'''There are four rules for reducing complexity:'''<br />
# <div>Alternate types of reductions. Have one (Simple > Equalizing > Simple > Equalizing...) or two (Simple > Simple > Equalizing > Simple > Simple > Equalizing...) simple drops between equalizing drops.</div><br />
# <div>Change only spherical or only cylindrical and never both simultaneously.</div><br />
# <div>For an equalizing reduction, change both differential lenses and normalized lenses simultaneously to keep the [[focal planes]] in sync.</div><br />
# <div>For a simple reduction, change differential lenses a few weeks after normalized lenses to keep changes to [[focal planes]] to a minimum.</div><br />
<br />
<br />
'''A note on rule 3 and rule 4:''' Keeping focal planes in sync is a higher priority than keeping changes to focal planes to a minimum, thus rule 3 exists.<br />
<br />
{| class="wikitable" style="text-align:center;"<br />
|+ Example Spherical Reduction Schedule<br />
|-<br />
! style="text-align:left;" | Reduction Type<br />
! colspan="2" | Normalized<br />
! colspan="2" | Differentials<br />
! style="text-align:left;" | Explanation<br />
|-<br />
| style="text-align:left;" |<br />
| Left<br />
| Right<br />
| Left<br />
| Right<br />
| style="text-align:left;" |<br />
|-<br />
| rowspan="2" style="text-align:left;" |<br />
| -3.50<br />
| -4.00<br />
| -2.25<br />
| -2.75<br />
| style="text-align:left;" | This is the '''starting point'''.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 8 - 16 weeks<br />
|<br />
|-<br />
| rowspan="4" | Simple<br />
| -3.25<br />
| -3.75<br />
|<br />
|<br />
| style="text-align:left;" | Perform normalized reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
| (rule 4)<br />
|-<br />
|<br />
|<br />
| -2.00<br />
| -2.50<br />
| style="text-align:left;" | Perform differential reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
|<br />
|- style="font-weight:bold;"<br />
| rowspan="2" | Equalizing<br />
| -3.25<br />
| -3.50<br />
| -2.00<br />
| -2.25<br />
| style="text-align:left;" | Both norms and diffs are reduced simultaneously. (rule 3)<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center; font-weight:bold;" | wait 8 - 16 weeks<br />
|<br />
|-<br />
| rowspan="4" | Simple<br />
| -3.00<br />
| -3.25<br />
|<br />
|<br />
| style="text-align:left;" | Perform normalized reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
| (rule 4)<br />
|-<br />
|<br />
|<br />
| -1.75<br />
| -2.00<br />
| style="text-align:left;" | Perform differential reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
|<br />
|- style="font-weight:bold;"<br />
| rowspan="2" | Equalizing<br />
| -3.00<br />
| -3.00<br />
| -1.75<br />
| -1.75<br />
| style="text-align:left;" | Both norms and diffs are reduced simultaneously. (rule 3)<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center; font-weight:bold;" | wait 8 - 16 weeks<br />
|<br />
|}<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
==See also==<br />
* [[Equalizing]]<br />
<br />
* [[Guide:Resolving double vision | Resolving double vision]]<br />
<br />
* [[reduction | Reduction]]<br />
<br />
[[Category:Guides]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Guide:Reducing_lens_complexity&diff=16547Guide:Reducing lens complexity2022-03-28T16:07:26Z<p>User: /* How to reduce lens complexity */</p>
<hr />
<div><br />
<br />
TODO: this article needs to be expanded for edge cases like already low diopters.<br />
<br />
==When to reduce lens complexity==<br />
<br />
[[Lens complexity]] is best reduced before getting into the [[low diopters]] range. Ideally, both eyes would be equal before the normalized correction reaches -1.5 [[diopters]].{{citation needed}}<br />
<br />
==How to reduce lens complexity==<br />
<br />
'''Make your first reduction a simple [[spherical]] reduction. This will teach you the basics of the [[EndMyopia]] methods.'''<br />
<br />
There are two types of reductions:<br />
<br />
* <div>A simple reduction or binocular reduction is drop in lens powers for both eyes, simultaneously</div><br />
* <div>An equalizing reduction or monocular reduction is drop in lens power for one eye, the eye with greater correction (more negative)</div><br />
<br />
An [[equalizing]] reduction is done to bring the eyes closer to having the same level of correction. Jake said that "...if you do reduce the ratio, you should have at least 2 regular spherical reductions in between."<ref>https://community.endmyopia.org/t/key-to-patching-successfully-reducing-diopter-ratio/333/6</ref> This is not always possible, especially when [[Guide:High diopter gap|high anisometropia]] is involved.<br />
<br />
There are three types of reductions with respect to the power change:<br />
* a 0.25 [[diopter|D]] drop to [[spherical]] power<br />
* a 0.25 D drop to [[cylindrical]] power<br />
* a trade of 0.5 D cylindrical power for 0.25 D spherical power<br />
<br />
'''There are four rules for reducing complexity:'''<br />
# <div>Alternate types of reductions. Have one (Simple > Equalizing > Simple > Equalizing...) or two (Simple > Simple > Equalizing > Simple > Simple > Equalizing...) simple drops between equalizing drops.</div><br />
# <div>Change only spherical or only cylindrical and never both simultaneously.</div><br />
# <div>For an equalizing reduction, change both differential lenses and normalized lenses simultaneously to keep the [[focal planes]] in sync.</div><br />
# <div>For a simple reduction, change differential lenses a few weeks after normalized lenses to keep changes to [[focal planes]] to a minimum.</div><br />
<br />
<br />
'''A note on rule 3 and rule 4:''' Keeping focal planes in sync is a higher priority than keeping changes to focal planes to a minimum, thus rule 3 exists.<br />
<br />
{| class="wikitable" style="text-align:center;"<br />
|+ Example Spherical Reduction Schedule<br />
|-<br />
! style="text-align:left;" | Reduction Type<br />
! colspan="2" | Normalized<br />
! colspan="2" | Differentials<br />
! style="text-align:left;" | Explanation<br />
|-<br />
| style="text-align:left;" |<br />
| Left<br />
| Right<br />
| Left<br />
| Right<br />
| style="text-align:left;" |<br />
|-<br />
| rowspan="2" style="text-align:left;" |<br />
| -3.50<br />
| -4.00<br />
| -2.25<br />
| -2.75<br />
| style="text-align:left;" | This is the '''starting point'''.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 8 - 16 weeks<br />
|<br />
|-<br />
| rowspan="4" | Simple<br />
| -3.25<br />
| -3.75<br />
|<br />
|<br />
| style="text-align:left;" | Perform normalized reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
| (rule 4)<br />
|-<br />
|<br />
|<br />
| -2.00<br />
| -2.50<br />
| style="text-align:left;" | Perform differential reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
|<br />
|- style="font-weight:bold;"<br />
| rowspan="2" | Equalizing<br />
| -3.25<br />
| -3.50<br />
| -2.00<br />
| -2.25<br />
| style="text-align:left;" | Both norms and diffs are reduced simultaneously. (rule 3)<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center; font-weight:bold;" | wait 8 - 16 weeks<br />
|<br />
|-<br />
| rowspan="4" | Simple<br />
| -3.00<br />
| -3.25<br />
|<br />
|<br />
| style="text-align:left;" | Perform normalized reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
| (rule 4)<br />
|-<br />
|<br />
|<br />
| -1.75<br />
| -2.00<br />
| style="text-align:left;" | Perform differential reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
|<br />
|- style="font-weight:bold;"<br />
| rowspan="2" | Equalizing<br />
| -3.00<br />
| -3.00<br />
| -1.75<br />
| -1.75<br />
| style="text-align:left;" | Both norms and diffs are reduced simultaneously. (rule 3)<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center; font-weight:bold;" | wait 8 - 16 weeks<br />
|<br />
|}<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
==See also==<br />
* [[Equalizing]]<br />
<br />
* [[Guide:Resolving double vision | Resolving double vision]]<br />
<br />
* [[reduction | Reduction]]<br />
<br />
[[Category:Guides]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Guide:Reducing_lens_complexity&diff=16546Guide:Reducing lens complexity2022-03-28T16:05:53Z<p>User: /* How to reduce lens complexity */</p>
<hr />
<div><br />
<br />
TODO: this article needs to be expanded for edge cases like already low diopters.<br />
<br />
==When to reduce lens complexity==<br />
<br />
[[Lens complexity]] is best reduced before getting into the [[low diopters]] range. Ideally, both eyes would be equal before the normalized correction reaches -1.5 [[diopters]].{{citation needed}}<br />
<br />
==How to reduce lens complexity==<br />
<br />
'''Make your first reduction a simple [[spherical]] reduction. This will teach you the basics of the [[EndMyopia]] methods.'''<br />
<br />
There are two types of reductions:<br />
<br />
* <div>A simple reduction or binocular reduction is drop in lens powers for both eyes, simultaneously</div><br />
* <div>An equalizing reduction or monocular reduction is drop in lens power for one eye, the eye with greater correction (more negative)</div><br />
<br />
An [[equalizing]] reduction is done to bring the eyes closer to having the same level of correction. Jake said that "...if you do reduce the ratio, you should have at least 2 regular spherical reductions in between."<ref>https://community.endmyopia.org/t/key-to-patching-successfully-reducing-diopter-ratio/333/6</ref> This is not always possible, especially when [[Guide:High diopter gap|high anisometropia]] is involved.<br />
<br />
There are three types of reductions with respect to the power change:<br />
* a 0.25 [[diopter|D]] drop to [[spherical]] power<br />
* a 0.25 D drop to [[cylindrical]] power<br />
* a trade of 0.5 D cylindrical power for 0.25 D spherical power<br />
<br />
'''There are four rules for reducing complexity:'''<br />
# <div>Alternate types of reductions. Simple > Equalizing > Simple > Equalizing...</div><br />
# <div>Change only spherical or only cylindrical and never both simultaneously.</div><br />
# <div>For an equalizing reduction, change both differential lenses and normalized lenses simultaneously to keep the [[focal planes]] in sync.</div><br />
# <div>For a simple reduction, change differential lenses a few weeks after normalized lenses to keep changes to [[focal planes]] to a minimum.</div><br />
<br />
<br />
'''A note on rule 3 and rule 4:''' Keeping focal planes in sync is a higher priority than keeping changes to focal planes to a minimum, thus rule 3 exists.<br />
<br />
{| class="wikitable" style="text-align:center;"<br />
|+ Example Spherical Reduction Schedule<br />
|-<br />
! style="text-align:left;" | Reduction Type<br />
! colspan="2" | Normalized<br />
! colspan="2" | Differentials<br />
! style="text-align:left;" | Explanation<br />
|-<br />
| style="text-align:left;" |<br />
| Left<br />
| Right<br />
| Left<br />
| Right<br />
| style="text-align:left;" |<br />
|-<br />
| rowspan="2" style="text-align:left;" |<br />
| -3.50<br />
| -4.00<br />
| -2.25<br />
| -2.75<br />
| style="text-align:left;" | This is the '''starting point'''.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 8 - 16 weeks<br />
|<br />
|-<br />
| rowspan="4" | Simple<br />
| -3.25<br />
| -3.75<br />
|<br />
|<br />
| style="text-align:left;" | Perform normalized reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
| (rule 4)<br />
|-<br />
|<br />
|<br />
| -2.00<br />
| -2.50<br />
| style="text-align:left;" | Perform differential reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
|<br />
|- style="font-weight:bold;"<br />
| rowspan="2" | Equalizing<br />
| -3.25<br />
| -3.50<br />
| -2.00<br />
| -2.25<br />
| style="text-align:left;" | Both norms and diffs are reduced simultaneously. (rule 3)<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center; font-weight:bold;" | wait 8 - 16 weeks<br />
|<br />
|-<br />
| rowspan="4" | Simple<br />
| -3.00<br />
| -3.25<br />
|<br />
|<br />
| style="text-align:left;" | Perform normalized reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
| (rule 4)<br />
|-<br />
|<br />
|<br />
| -1.75<br />
| -2.00<br />
| style="text-align:left;" | Perform differential reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
|<br />
|- style="font-weight:bold;"<br />
| rowspan="2" | Equalizing<br />
| -3.00<br />
| -3.00<br />
| -1.75<br />
| -1.75<br />
| style="text-align:left;" | Both norms and diffs are reduced simultaneously. (rule 3)<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center; font-weight:bold;" | wait 8 - 16 weeks<br />
|<br />
|}<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
==See also==<br />
* [[Equalizing]]<br />
<br />
* [[Guide:Resolving double vision | Resolving double vision]]<br />
<br />
* [[reduction | Reduction]]<br />
<br />
[[Category:Guides]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Guide:Reducing_lens_complexity&diff=16545Guide:Reducing lens complexity2022-03-28T16:05:34Z<p>User: /* How to reduce lens complexity */</p>
<hr />
<div><br />
<br />
TODO: this article needs to be expanded for edge cases like already low diopters.<br />
<br />
==When to reduce lens complexity==<br />
<br />
[[Lens complexity]] is best reduced before getting into the [[low diopters]] range. Ideally, both eyes would be equal before the normalized correction reaches -1.5 [[diopters]].{{citation needed}}<br />
<br />
==How to reduce lens complexity==<br />
<br />
'''Make your first reduction a simple [[spherical]] reduction. This will teach you the basics of the [[EndMyopia]] methods.'''<br />
<br />
There are two types of reductions:<br />
<br />
* <div>A simple reduction or binocular reduction is drop in lens powers for both eyes, simultaneously</div><br />
* <div>An equalizing reduction or monocular reduction is drop in lens power for one eye, the eye with greater correction (more negative)</div><br />
<br />
An [[equalizing]] reduction is done to bring the eyes closer to having the same level of correction. Jake said that "...if you do reduce the ratio, you should have at least 2 regular spherical reductions in between."<ref>https://community.endmyopia.org/t/key-to-patching-successfully-reducing-diopter-ratio/333/6</ref> This is not always possible, especially when [[Guide:High diopter gap|high anisometropia]] is involved.<br />
<br />
There are three types of reductions with respect to the power change:<br />
* a 0.25 [[diopter]] drop to [[spherical]] power<br />
* a 0.25 D drop to [[cylindrical]] power<br />
* a trade of 0.5 D cylindrical power for 0.25 spherical power<br />
<br />
'''There are four rules for reducing complexity:'''<br />
# <div>Alternate types of reductions. Simple > Equalizing > Simple > Equalizing...</div><br />
# <div>Change only spherical or only cylindrical and never both simultaneously.</div><br />
# <div>For an equalizing reduction, change both differential lenses and normalized lenses simultaneously to keep the [[focal planes]] in sync.</div><br />
# <div>For a simple reduction, change differential lenses a few weeks after normalized lenses to keep changes to [[focal planes]] to a minimum.</div><br />
<br />
<br />
'''A note on rule 3 and rule 4:''' Keeping focal planes in sync is a higher priority than keeping changes to focal planes to a minimum, thus rule 3 exists.<br />
<br />
{| class="wikitable" style="text-align:center;"<br />
|+ Example Spherical Reduction Schedule<br />
|-<br />
! style="text-align:left;" | Reduction Type<br />
! colspan="2" | Normalized<br />
! colspan="2" | Differentials<br />
! style="text-align:left;" | Explanation<br />
|-<br />
| style="text-align:left;" |<br />
| Left<br />
| Right<br />
| Left<br />
| Right<br />
| style="text-align:left;" |<br />
|-<br />
| rowspan="2" style="text-align:left;" |<br />
| -3.50<br />
| -4.00<br />
| -2.25<br />
| -2.75<br />
| style="text-align:left;" | This is the '''starting point'''.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 8 - 16 weeks<br />
|<br />
|-<br />
| rowspan="4" | Simple<br />
| -3.25<br />
| -3.75<br />
|<br />
|<br />
| style="text-align:left;" | Perform normalized reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
| (rule 4)<br />
|-<br />
|<br />
|<br />
| -2.00<br />
| -2.50<br />
| style="text-align:left;" | Perform differential reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
|<br />
|- style="font-weight:bold;"<br />
| rowspan="2" | Equalizing<br />
| -3.25<br />
| -3.50<br />
| -2.00<br />
| -2.25<br />
| style="text-align:left;" | Both norms and diffs are reduced simultaneously. (rule 3)<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center; font-weight:bold;" | wait 8 - 16 weeks<br />
|<br />
|-<br />
| rowspan="4" | Simple<br />
| -3.00<br />
| -3.25<br />
|<br />
|<br />
| style="text-align:left;" | Perform normalized reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
| (rule 4)<br />
|-<br />
|<br />
|<br />
| -1.75<br />
| -2.00<br />
| style="text-align:left;" | Perform differential reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
|<br />
|- style="font-weight:bold;"<br />
| rowspan="2" | Equalizing<br />
| -3.00<br />
| -3.00<br />
| -1.75<br />
| -1.75<br />
| style="text-align:left;" | Both norms and diffs are reduced simultaneously. (rule 3)<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center; font-weight:bold;" | wait 8 - 16 weeks<br />
|<br />
|}<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
==See also==<br />
* [[Equalizing]]<br />
<br />
* [[Guide:Resolving double vision | Resolving double vision]]<br />
<br />
* [[reduction | Reduction]]<br />
<br />
[[Category:Guides]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Reduction&diff=16544Reduction2022-03-28T16:02:42Z<p>User: </p>
<hr />
<div>Your [[Normalized]] and [[Differentials]] [[Lenses]] power should steadily reduce in power over time. (+0.25 for myopes, -0.25 for hyperopes, moving towards 0)<br />
<br />
Generally, the [[correction]] should be a quarter diopter weaker than needed to see clearly, which provides a slight [[blur]] stimulus for change, although trading 0.5 cyl for 0.25 [[spherical equivalent|sph equivalent]] is also possible.<br />
<br />
==When to reduce==<br />
As your eyes improve, you will need to reduce again to maintain that slight blur. These reductions typically occur every 3-4 months for sphere and at least 6 months for cylinder. Alternate between differentials and normalized with 4-6 weeks of adjustment period between changes to your focal plane. Do not reduce your sphere and cylinder at the same time. It is important to be sure you are ready to reduce and that your measurements justify reduction. Reducing too soon is never a good idea (see [[blur adaptation]]). Ideally, you should be consistently (for a week or two) seeing 20/20 in your current correction, indoors, with reasonably good lighting, on a 20 foot or 6 meter chart. The 20/20 doesn't need to be ultra sharp, remember being able to identify half or better on a line is a pass, but make sure you are only giving yourself credit for letters you can actually see; preferably without [[active focus]].<br />
<br />
===Example reduction schedule===<br />
: ''See also:'' [[Guide:Reducing lens complexity]]<br />
<br />
If you work around 70 to 90 cm,<br />
* Reduce norm at 80cm through diff (gap of 1 D for first half of norm, second half of diff)<br />
* Reduce diff at 88.89 cm through old diff, 72.73 cm through new diff (gap of 1.25 D for second half of norm, first half of diff)<br />
{| class="wikitable" style="text-align:center;"<br />
! Normalized<br />
! Differentials<br />
|-<br />
| -2<br />
| -1<br />
<br />
|-<br />
| -2<br />
| -0.75<br />
|-<br />
| -1.75<br />
| -0.75<br />
|-<br />
| -1.75<br />
| -0.5<br />
|-<br />
| -1.5<br />
| -0.5<br />
|-<br />
| -1.5<br />
| -0.25<br />
|-<br />
| -1.25<br />
| -0.25<br />
|-<br />
| -1.25<br />
| 0<br />
|-<br />
<br />
| -1<br />
| 0<br />
|}<br />
<br />
This can be generalized to alternating a gap of <code>G-0.25 D</code> and <code>G</code>, with these properties:<br />
<br />
* Reduce norm at <code>1/G</code> through diff (gap of <code>G-0.25 D</code> for first half of norm, second half of diff)<br />
* Reduce diff at <code>1/(G-0.125 D)</code> through old diff, <code>1/(G+0.125 D)</code> through new diff (gap of <code>G</code> for second half of norm, first half of diff)<br />
* Norm always has 0 to 0.25 D of undercorrection.<br />
* Diff always gives cm within 0.125 D of <code>1/G</code>.<br />
<br />
==How to reduce==<br />
Once your measurements justify that reduction you want to start out with the new correction properly, which is why it is best to perform a "[[zero diopter reset]]".<br />
<br />
==Further Reading==<br />
<br />
===Blog===<br />
<br />
* [https://endmyopia.org/qa-can-reduce-1-2-diopter-get-moar-gains/ Can I Reduce More Diopters For More Gains?] (NO.)<br />
===Forum===<br />
<br />
* [https://community.endmyopia.org/t/ocular-dominance-why-your-eyes-each-dont-see-the-same-o-0/1401/60 halmadavid's simple, but concise description for reduction]<br />
* [https://community.endmyopia.org/t/are-my-normalized-too-weak/16037/2 BiancaK on a laid-back approach to reducing diffs & norms]<br />
* [https://endmyopia.org/how-fast-does-my-eyesight-improve-when-can-i-reduce-diopters/ STOP CARING ABOUT IMPROVING YOUR EYESIGHT]<br />
<br />
* [https://community.endmyopia.org/t/reducing-more-than-advised/4685 Endmyopia recommends reducing ones spherical correction by 0.25 diopters at a time, why is that?] by Laurens<br />
===Wiki===<br />
* [[Guide:How to measure your eyesight | How to measure your eyesight]]<br />
* [[Reduced_lenses | Reduced lenses]]<br />
* [[Guide:Reducing lens complexity | Reducing lens complexity]]<br />
* [[Guide:Reducing_differentials | Reducing differentials]]<br />
* [[Guide:Reducing normalized | Reducing normalized]]<br />
* [[Guide:Not_reducing_too_quickly | Take it slow]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Reduction&diff=16543Reduction2022-03-28T16:02:14Z<p>User: </p>
<hr />
<div>Your [[Normalized]] and [[Differentials]] [[Lenses]] power should steadily reduce in power over time. (+0.25 for myopes, -0.25 for hyperopes, moving towards 0)<br />
<br />
Generally, the [[correction]] should be a quarter diopter weaker than needed to see clearly, which provides a slight [[blur]] stimulus for change, although trading 0.5 cyl for 0.25 sph is also possible.<br />
<br />
==When to reduce==<br />
As your eyes improve, you will need to reduce again to maintain that slight blur. These reductions typically occur every 3-4 months for sphere and at least 6 months for cylinder. Alternate between differentials and normalized with 4-6 weeks of adjustment period between changes to your focal plane. Do not reduce your sphere and cylinder at the same time. It is important to be sure you are ready to reduce and that your measurements justify reduction. Reducing too soon is never a good idea (see [[blur adaptation]]). Ideally, you should be consistently (for a week or two) seeing 20/20 in your current correction, indoors, with reasonably good lighting, on a 20 foot or 6 meter chart. The 20/20 doesn't need to be ultra sharp, remember being able to identify half or better on a line is a pass, but make sure you are only giving yourself credit for letters you can actually see; preferably without [[active focus]].<br />
<br />
===Example reduction schedule===<br />
: ''See also:'' [[Guide:Reducing lens complexity]]<br />
<br />
If you work around 70 to 90 cm,<br />
* Reduce norm at 80cm through diff (gap of 1 D for first half of norm, second half of diff)<br />
* Reduce diff at 88.89 cm through old diff, 72.73 cm through new diff (gap of 1.25 D for second half of norm, first half of diff)<br />
{| class="wikitable" style="text-align:center;"<br />
! Normalized<br />
! Differentials<br />
|-<br />
| -2<br />
| -1<br />
<br />
|-<br />
| -2<br />
| -0.75<br />
|-<br />
| -1.75<br />
| -0.75<br />
|-<br />
| -1.75<br />
| -0.5<br />
|-<br />
| -1.5<br />
| -0.5<br />
|-<br />
| -1.5<br />
| -0.25<br />
|-<br />
| -1.25<br />
| -0.25<br />
|-<br />
| -1.25<br />
| 0<br />
|-<br />
<br />
| -1<br />
| 0<br />
|}<br />
<br />
This can be generalized to alternating a gap of <code>G-0.25 D</code> and <code>G</code>, with these properties:<br />
<br />
* Reduce norm at <code>1/G</code> through diff (gap of <code>G-0.25 D</code> for first half of norm, second half of diff)<br />
* Reduce diff at <code>1/(G-0.125 D)</code> through old diff, <code>1/(G+0.125 D)</code> through new diff (gap of <code>G</code> for second half of norm, first half of diff)<br />
* Norm always has 0 to 0.25 D of undercorrection.<br />
* Diff always gives cm within 0.125 D of <code>1/G</code>.<br />
<br />
==How to reduce==<br />
Once your measurements justify that reduction you want to start out with the new correction properly, which is why it is best to perform a "[[zero diopter reset]]".<br />
<br />
==Further Reading==<br />
<br />
===Blog===<br />
<br />
* [https://endmyopia.org/qa-can-reduce-1-2-diopter-get-moar-gains/ Can I Reduce More Diopters For More Gains?] (NO.)<br />
===Forum===<br />
<br />
* [https://community.endmyopia.org/t/ocular-dominance-why-your-eyes-each-dont-see-the-same-o-0/1401/60 halmadavid's simple, but concise description for reduction]<br />
* [https://community.endmyopia.org/t/are-my-normalized-too-weak/16037/2 BiancaK on a laid-back approach to reducing diffs & norms]<br />
* [https://endmyopia.org/how-fast-does-my-eyesight-improve-when-can-i-reduce-diopters/ STOP CARING ABOUT IMPROVING YOUR EYESIGHT]<br />
<br />
* [https://community.endmyopia.org/t/reducing-more-than-advised/4685 Endmyopia recommends reducing ones spherical correction by 0.25 diopters at a time, why is that?] by Laurens<br />
===Wiki===<br />
* [[Guide:How to measure your eyesight | How to measure your eyesight]]<br />
* [[Reduced_lenses | Reduced lenses]]<br />
* [[Guide:Reducing lens complexity | Reducing lens complexity]]<br />
* [[Guide:Reducing_differentials | Reducing differentials]]<br />
* [[Guide:Reducing normalized | Reducing normalized]]<br />
* [[Guide:Not_reducing_too_quickly | Take it slow]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Astigmatism&diff=16542Astigmatism2022-03-28T15:58:42Z<p>User: /* Spherical equivalent */</p>
<hr />
<div>'''Astigmatism''' is an eye condition that means you have blur in a specific direction, or [[axis]] (technically, depending on the notation used for your prescription, the axis may indicate the angle of the eye's meridian where you have the least focusing power, or the one where you have the most). Astigmatism is compensated with [[cylinder]] lenses. A cylinder lens adds power along one particular meridian of the eye.<br />
<br />
Astigmatism often reduces spontaneously as myopia is corrected.<br />
<br />
==Symptoms==<br />
Uncorrected and uncompensated astigmatism appears as ''directional blur'' or ''[[double vision]]''. [[Transient astigmatism]] also occurs when making spherical reductions. According to EM, the [[visual cortex]] compensates for irregularities in the cornea. If the [[double vision]] is just a little bit, the visual cortex can learn to fuse double vision and change the compensation.<br />
<br />
==Understanding astigmatism==<br />
<br />
Astigmatism is caused by an irregularly shaped cornea or lens. The first is called corneal astigmatism, which is the more common form, and the second is called lenticular astigmatism. "Regular" astigmatism is often described as having the cornea shaped like a rugby ball, rather than spherical like a basketball. The optics of an ''idealised'' lens of such a form would cause incoming light on different planes (corresponding to the two principal axes of the lens) to be focused at different offsets beyond the lens.<br />
<br />
[[File:Astigmatism.svg|Astigmatism]]<br />
<br />
Most diagrams of lenses show only a single vertical plane. In the real world, of course, there is a full cone of light arriving on the lens from the source object. This diagram shows two different cross-sections through the incident cone of light, aligned with the two axes. Rays in the horizontal cross-section (which contains the stronger curve) are focused earlier - at the label 'T' (for 'Tangential'). The rays in the vertical cross-section (the 'Saggital') are focused further behind, at 'S'. The other rays around the light cone are focused at points in between the two, giving an image smeared out along the axis.<br />
<br />
===Stenopaeic slit===<br />
<br />
The Stenopaeic slit is a simple tool which can be used in diagnosis / measurement of astigmatism. It is simply a disk with a narrow slit which can be rotated to find the clearest image. By reducing light coming in the "wrong" direction, the spherical correction on each axis can be measured directly.<br />
<br />
===Analogy with Chromatic Aberration===<br />
<br />
It may be simpler to picture the effect by comparing with [[Chromatic Aberration]]. In both cases, an extra variable means different parts of the light are focused differently.<br />
<br />
[[File:Chromatic aberration lens diagram.svg|Chromatic aberration lens diagram]]<br />
<br />
(Unfortunately the astigmatism diagram choose red and blue the wrong way round !)<br />
<br />
* If the red light is focused on the retina, the green/blue light is focused in front, and is blurred.<br />
* If the blue light is focused correctly, green and red are focused beyond the retina and is blurred.<br />
* It's not possible to get everything into focus using only spherical lenses.<br />
As a compromise, focusing the green light on the retina causes a little bit of myopic blue blur and hyperopic red blur. This corresponds to the "circle of least confusion" in astigmatism.<br />
<br />
On a prescription, there are two different conventions for specifying the cylinder. This corresponds to either quoting the spherical correction to focus red on the retina, and then the additional "minus" required to focus blue; or a spherical correction for blue, and then how much that can be reduced by for red. The average of the two, or the "spherical equivalence", is then the correction required to put green on the retina.<br />
<br />
The analogue of the Stenopaeic slit is this model is a simple coloured filter : by allowing only monochromatic light into the eye, the spherical correction for each colour can be measured separately.<br />
<br />
If the object is moved away, beyond your blur horizon, so that your eye can no longer keep the green light focused,<br />
all colours will suffer myopic blur, but blue will have the worst blur. This corresponds to the directional blur<br />
in astigmatism. Adding some spherical correction would allow you to push the green back into focus.<br />
<br />
Chromatic aberration could be treated by adding some material which applies the opposite chromatic error - bending the blue light out a bit more than the red light, to cancel the error introduced by the eye. This corresponds to cylinder correction. (But as with all analogies, it's starting to stretch a bit thin...)<br />
<br />
==Irregular Astigmatism==<br />
<br />
A real cornea, of course, doesn't conform to expectations. Being messier, it just has a bulge, which means that the image is not only smeared out along the axis, but is rotated, resulting in multiple (blurred) images being perceived on the retina.<br />
<br />
[[File:Astigmatism (Eye).png|Astigmatism (Eye)]]<br />
<br />
==Childhood Astigmatism==<br />
Astigmatism in young children often changes after they reach school age.<ref>{{Cite journal |last=Dobson |first=V. |last2=Fulton |first2=A. B. |last3=Sebris |first3=S. L. |date=1984-01-01 |title=Cycloplegic refractions of infants and young children: the axis of astigmatism. |url=https://iovs.arvojournals.org/article.aspx?articleid=2159731 |journal=Investigative Ophthalmology & Visual Science |language=en |volume=25 |issue=1 |pages=83–87 |issn=1552-5783}}</ref><br />
<br />
==Reducing astigmatism==<br />
As with myopia, astigmatism should be tackled in small steps when selecting lenses for [[differential]] or [[normalized]] glasses. If only a small amount of cylinder correction is present, say 0.25 [[diopters]], the cylinder correction can be dropped, with no other changes. Otherwise, cylinder should be reduced in small increments. If sphere is being reduced, cylinder should not be changed at the same time, and conversely, if cylinder is being reduced then sphere should not be changed. The only time that both sphere and cylinder should be changed, is when converting to the spherical equivalent.<br />
<br />
The link between astigmatism strength and visual acuity is weak. How your eyes and [[visual cortex]] respond to astigmatism is a greater factor in visual acuity than the number of dipoters.<ref>{{Cite journal |last=Remón |first=Laura |last2=Tornel |first2=Marta |last3=Furlan |first3=Walter D. |date=2006-05 |title=Visual Acuity in Simple Myopic Astigmatism: Influence of Cylinder Axis |url=https://journals.lww.com/optvissci/Abstract/2006/05000/Visual_Acuity_in_Simple_Myopic_Astigmatism_.11.aspx |journal=Optometry and Vision Science |language=en-US |volume=83 |issue=5 |pages=311–315 |doi=10.1097/01.opx.0000216099.29968.36 |issn=1538-9235}}</ref> If the standard advice for correcting astigmatism does not work for you, you may need a more gradual reduction. <br />
<br />
The average person with medium-to-high myopia should wait until having reduced norms/diffs twice each before reducing cylinder for the first time. Then wait a minimum of 8 weeks before introducing the next spherical reduction, and wait 6 months before introducing the next cylinder reduction.<br />
<br />
Regardless of how the myope reduces their lenses, the goal of each reduction is to have a small amount of "useful blur", to be cleared up with [[active focus]] and good habits.<br />
<br />
===Axis===<br />
{{Main|Axis}}<br />
When reducing cylinder value, you should never change the axis value if it has been consistent for some time. The axis only refers to the orientation in which the cylinder is affecting your eyes, and any reduction of cylinder will happen on this orientation.<br />
<br />
==Spherical equivalent==<br />
{{Main|Diopters#Spherical Equivalent}}<br />
The '''spherical equivalent''' of cylinder lenses may be useful, to simplify the reduced lens path. 0.50 cylinder means the power varies from 0D on one axis to 0.5D on the perpendicular axis. This can be substituted by the spherical power with the averaged value of 0.25D. For example, a full prescription of "-1.00 Sphere -1.50 Cylinder" could be converted to "-1.75 Sphere".<br />
<br />
A common [[reduction]] is to trade 0.5 cylinder to its spherical equivalent of 0.25 sphere (of the same sign).<br />
* For example, -2 sph -1 cyl (equivalently, -3 +1) is reduced to -2.25 -0.5 or -2.75 +0.5.<br />
<br />
The resulting spherical equivalent is not intended to compensate for the asymmetry of the lens, so it will introduce some directional blur.<br />
<br />
==Resources==<br />
<br />
* [[Astigmatism measurement]]<br />
* [https://endmyopia.org/the-definitive-guide-astigmatism/ EndMyopia Blog - The Definitive Guide: What Is Astigmatism] (2013)<br />
* [https://endmyopia.org/astigmatism-the-big-guide-summary/ EndMyopia Blog - Astigmatism: The Big Guide & Summary] (2021)<br />
* [https://endmyopia.org/tag/astigmatism-2/ EndMyopia Blog - all astigmatism articles]<br />
* [https://endmyopia.org/diy-tools-how-to-measure-your-astigmatism-diopters/ How To Measure Your Astigmatism Diopters]<br />
* [https://visiontools.netlify.app/ Vision tool]<br />
<!-- * [https://community.endmyopia.org/t/having-trouble-figuring-out-my-astigmatism/4843/6 Astigmatism Assasin's guide] forum access required; not a public link --><br />
* [https://www.youtube.com/watch?v=KDgU4AoFsA4 Fixing Astigmatism - Jake Steiner]<br />
* [https://drboulet.com/wp-content/uploads/2016/07/Forrest-a-new-model-of-functional-astigmatism.pdf Functional astigmatism]<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
[[Category:Articles]]<br />
[[Category:Eye conditions]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Diopters&diff=16541Diopters2022-03-28T15:56:11Z<p>User: /* Spherical Equivalent */</p>
<hr />
<div><br />
Diopter is a measure of the [https://en.wikipedia.org/wiki/Optical_power optical power] P of a [[lens]] (or mirror) and is equal to the reciprocal of [[focal length]] in meters. The most common unit symbol for diopters is dpt, D, or m<sup>-1</sup>.<br />
<br />
<math>P = \frac{1}{f} = -\frac{1}{d}</math><br />
<br />
* In [[EM]], we use the [[cm measurement]] to calculate diopters needed to correct [[refraction]] of the eye. If you can see 50 cm clearly, your diopters will be <math>-\frac{1}{0.50}=-2 dpt</math>.<br />
<br />
* Lenses in series add their powers: if you're wearing -2 diopter contacts ([[vertex distance|adjusted for glasses strength]]) and put +1 diopter reading glasses over the contacts you're in effect wearing -1 diopters.<br />
** There are some caveats such as vertex distance, since moving the lens away effectively gives you a weaker negative lens or stronger positive lens. There is also decentration, which induces prism when the lens is moved to the side. These effects become negligible for weaker lenses.<br />
* According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.<br />
** A lens with a negative diopter sign compensates for [[nearsightedness]] while a lens with a positive diopter sign compensates for [[farsightedness]].<br />
<br />
{| class="wikitable"<br />
|+ Approximate categorizations of myopia by [[spherical]] lens power:<br />
|-<br />
| 0.00 to -0.50 dpt || Not really considered myopic, probably don't need glasses<br />
|-<br />
| -0.50 to -1.00 dpt || Mild myopia, [[normalized]] sometimes not needed<br />
|-<br />
| -1.00 to -2.50 dpt || Mild myopia, [[differentials]] possibly not needed<br />
|-<br />
| -2.50 to -3.00 dpt || Mild myopia, differentials probably needed<br />
|-<br />
| -3.00 to -6.00 dpt || Moderate myopia, glasses always needed<br />
|-<br />
| -6.00 to -10.00 dpt || High myopia<br />
|-<br />
| -10.00+ dpt || Very high myopia. Field of view significantly reduced.<br />
|}<br />
<br />
==Gap and ratio==<br />
<br />
Comparisons between two diopters is typically expressed using one of these terms:<br />
<br />
* ''diopter gap'' (or ''diopter difference''): absolute difference in diopters between two values<br />
* ''diopter ratio'': ratio of one diopter value to another (such as right eye / left eye)<br />
<br />
For example, consider the following correction:<br />
<br />
OD: -1.5 SPH / -1.5 CYL<br />
OS: -1.0 SPH / -2.0 CYL<br />
<br />
It can be expressed as a 0.5 dpt gap in both SPH and CYL, a 1.5 ratio in SPH and a 0.75 ratio in CYL:<br />
<br />
|(-1.5 dpt) - (-1.0 dpt)| = 0.5 dpt<br />
|(-1.5 dpt) - (-2.0 dpt)| = 0.5 dpt<br />
(-1.5 dpt) / (-1.0 dpt) = 1.5<br />
(-1.5 dpt) / (-2.0 dpt) = 0.75<br />
<br />
In EM articles, the term ''diopter ratio'' is often used interchangeably for left-right ''diopter gap''<ref>{{cite jake|https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/|The Diopter Ratio Trap: Don’t Favor One Eye}}</ref>, for example when talking about reducing a correction while keeping the ''gap'' the same. This can also be expressed as a [[wikipedia:Percent difference|percentage difference]] between the two diopter values<ref>{{cite jake|https://endmyopia.org/reducing-diopter-ratio-diy-patching-solution-pro-topic/|Reducing Diopter Ratio: DIY Patching Solution (PRO TOPIC)}}</ref> (e.g. the <tt>0.5 dpt</tt> difference between the right and left eyes here is equivalent to <tt>0.5 dpt / |-1.5 dpt| = 0.33</tt> or 33%).<br />
<br />
The general recommendation is that the left-right diopter gap is constant across all lenses being used. However, some old EM articles show successful cases where differentials are equalized but normalized have a 0.25 D gap.<ref>https://endmyopia.org/progress-improving-centimeter-62-90/ and https://endmyopia.org/saras-journey-truth-long-term-vision-improvement-potential/</ref><br />
<br />
Confusingly, diopter gap is also sometimes used to refer to the diff-norm gap, the difference between [[differentials]] and [[normalized]] or the [[spherical equivalent]] of that difference.<ref>https://endmyopia.org/pro-topic-managing-your-maximum-diopter-gap/</ref><br />
<br />
It is often useful to disambiguate what is being compared:<br />
* ''left-right gap'': left eye diopters minus right eye diopters, ignoring axis<br />
** In the example above, the left-right gap is +0.5 SPH -0.5 CYL.<br />
** The axis is ignored, and the cylinder powers are subtracted without using [[Diopters#Adding/Combining Lenses|lens combination calculations]].<br />
* ''diff-norm gap'': differentials diopter minus normalized diopters, ignoring axis<br />
** For example, if normalized is -2 SPH -0.5 CYL, and differentials are -0.75 SPH, the diff-norm gap is 1.25 SPH 0.5 CYL or 1.5 SPH equivalent.<br />
** The axis is ignored.<br />
<br />
==Technical Details==<br />
This section is for the math-savvy people. It explains concepts in more detail, but knowledge of it is not strictly necessary to use the EM method.<br />
<br />
===Thin Lens Equation===<br />
The focal length of a lens is given by the lensmaker's equation. By assuming the lens is much thinner than the radius of curvature, therefore assuming lens thickness is zero, we get a simplified version of the lensmaker's equation. We can do some further derivation, we arrive at the thin-lens equation:<ref>see derivations at https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses</ref><br />
<br />
<math>\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}</math><br />
<br />
According to the thin lens sign convention,<br />
* di is positive if it is a real image on the opposite side of the lens as the object, and it is negative if it is a virtual image on the same side of the lens as the object.<br />
* f is positive for converging lens and negative for diverging.<br />
<br />
This is also sometimes presented in the Newtonian form:<br />
<br />
<math>\left(d_o-f\right)\left(d_i-f\right)=f^2</math><br />
<br />
====Examples====<br />
"Full correction" takes an object at infinity and produces a virtual image at your far point distance d:<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{-d}=-\frac{1}{d}</math><br />
<br />
<br />
This is the resulting equation at the beginning of the article. It also explains why the focal power is increased for objects at closer distances: mainstream optometry calls this the "add" for presbyopia, although they typically use the minimum amount required for you to see at 40 cm with full distance correction using accommodation. For example, if you choose 80 cm as the working distance for your [[differentials]] (resulting in a +1.25 dpt "add"), and your blur horizon is 50 cm (resulting in -2 dpt), the formula is<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{80\ cm}+\frac{1}{-50\ cm}=1.25\ dpt + \left(-2\ dpt\right) = -0.75\ dpt</math><br />
<br />
=== Cylinder ===<br />
A cylindrical lens of power F<sub>c</sub> has focal power F at angle θ from its axis:<br />
<br />
<math>F = F_{cyl} (\sin\theta)^2</math><br />
<br />
==== Transposition ====<br />
We can understand why there are two different ways to write a spherical and cylindrical lens combination, using the Pythagorean trigonometric identity and the complementary angle identity:<br />
<br />
<math>(\sin\theta)^2 + (\cos\theta)^2 = 1</math><br />
<br />
<math>\cos\theta = \sin{\left(90^{\circ} - \theta\right)} = -\sin{\left(\theta - 90^{\circ}\right)}</math><br />
<br />
<br />
<math>F = F_{cyl} \left( 1 - (\cos\theta)^2 \right) = F_{cyl} + \left(-F_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math><br />
<br />
We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (same as subtracting 90 degrees, since the axis is in modulo 180 degrees) to the axis, we get an equivalent combination.<br />
<br />
For example, -1 sph -1 cyl 1 axis is the same as -2 sph +1 cyl 91 axis.<br />
<br />
In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two forms are equivalent.<br />
<br />
==== Spherical Equivalent ====<br />
{{See also|Astigmatism#Spherical equivalent}}<br />
<br />
By calculating the average value over all angles using an integral, the result<ref>it is only necessary to integrate one or two periods: https://www.wolframalpha.com/input/?i=average+of+%28sin+x%29%5E2+from+0+to+2+pi</ref> is<br />
<br />
<math>F_{avg} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} F_{cyl} (\sin{t})^2 \,dt = \frac{1}{2} F_{cyl}</math><br />
<br />
This is why the spherical equivalent has power equal to half of the cylinder's power.<br />
<br />
==== Adding/Combining Lenses ====<br />
Multiple lens, each with spherical and cylindrical components (not necessarily at the same axis) can be added to form one lens with a spherical and cylindrical component.<br />
<br />
We can use the double angle formula to convert each cylindrical lens into a constant plus a cosine:<br />
<br />
<math>\cos{2\theta}=1-2(\sin\theta)^2</math><br />
<br />
<br />
<math>F = F_{cyl} (\sin{\left(\theta + \phi\right)})^2 = F_{cyl} \left( \frac{1-\cos{\left(2\theta + 2\phi\right)}}{2} \right) = \frac{1}{2} F_{cyl} + \frac{-F_{cyl}}{2} \cos{\left(2\theta + 2\phi\right)}</math><br />
<br />
The constant parts are added with the spherical components. The cosines can be added by converting them to [https://en.wikipedia.org/wiki/Phasor phasors] and adding the phasors together. The resulting phasor corresponds to one of two cylindrical lenses (see the section on Transposition), and its corresponding spherical component must be subtracted from the total spherical component.<br />
<br />
There are implementations of this at<br />
* http://opticampus.opti.vision/tools/cylinders.php<br />
* http://billauer.co.il/simulator.html<br />
<br />
=== Decentration ===<br />
Induced prism can be calculated using Prentice's rule. Similar to Vertex Distance, decentration is less of an issue for smaller power lenses.<br />
<br />
The amount of prism P induced by decentration c of a lens of power f is<br />
<br />
<math>P=cf</math><br />
<br />
1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm, and f is in diopters, then P is in prism diopters.<br />
<br />
A prism with apex angle a and refractive index n results in angle of deviation of the light d, which is equal to P prism diopters:<br />
<br />
<math>d=(n-1)a</math><br />
<br />
<br />
<math>P=100\tan{d}=100\tan((n-1)a)</math><br />
<br />
=== Vertex Distance ===<br />
See [[Vertex distance#Calculation]]<br />
<br />
==References==<br />
{{reflist}}<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Diopters&diff=16540Diopters2022-03-28T15:55:22Z<p>User: /* Spherical Equivalent */</p>
<hr />
<div><br />
Diopter is a measure of the [https://en.wikipedia.org/wiki/Optical_power optical power] P of a [[lens]] (or mirror) and is equal to the reciprocal of [[focal length]] in meters. The most common unit symbol for diopters is dpt, D, or m<sup>-1</sup>.<br />
<br />
<math>P = \frac{1}{f} = -\frac{1}{d}</math><br />
<br />
* In [[EM]], we use the [[cm measurement]] to calculate diopters needed to correct [[refraction]] of the eye. If you can see 50 cm clearly, your diopters will be <math>-\frac{1}{0.50}=-2 dpt</math>.<br />
<br />
* Lenses in series add their powers: if you're wearing -2 diopter contacts ([[vertex distance|adjusted for glasses strength]]) and put +1 diopter reading glasses over the contacts you're in effect wearing -1 diopters.<br />
** There are some caveats such as vertex distance, since moving the lens away effectively gives you a weaker negative lens or stronger positive lens. There is also decentration, which induces prism when the lens is moved to the side. These effects become negligible for weaker lenses.<br />
* According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.<br />
** A lens with a negative diopter sign compensates for [[nearsightedness]] while a lens with a positive diopter sign compensates for [[farsightedness]].<br />
<br />
{| class="wikitable"<br />
|+ Approximate categorizations of myopia by [[spherical]] lens power:<br />
|-<br />
| 0.00 to -0.50 dpt || Not really considered myopic, probably don't need glasses<br />
|-<br />
| -0.50 to -1.00 dpt || Mild myopia, [[normalized]] sometimes not needed<br />
|-<br />
| -1.00 to -2.50 dpt || Mild myopia, [[differentials]] possibly not needed<br />
|-<br />
| -2.50 to -3.00 dpt || Mild myopia, differentials probably needed<br />
|-<br />
| -3.00 to -6.00 dpt || Moderate myopia, glasses always needed<br />
|-<br />
| -6.00 to -10.00 dpt || High myopia<br />
|-<br />
| -10.00+ dpt || Very high myopia. Field of view significantly reduced.<br />
|}<br />
<br />
==Gap and ratio==<br />
<br />
Comparisons between two diopters is typically expressed using one of these terms:<br />
<br />
* ''diopter gap'' (or ''diopter difference''): absolute difference in diopters between two values<br />
* ''diopter ratio'': ratio of one diopter value to another (such as right eye / left eye)<br />
<br />
For example, consider the following correction:<br />
<br />
OD: -1.5 SPH / -1.5 CYL<br />
OS: -1.0 SPH / -2.0 CYL<br />
<br />
It can be expressed as a 0.5 dpt gap in both SPH and CYL, a 1.5 ratio in SPH and a 0.75 ratio in CYL:<br />
<br />
|(-1.5 dpt) - (-1.0 dpt)| = 0.5 dpt<br />
|(-1.5 dpt) - (-2.0 dpt)| = 0.5 dpt<br />
(-1.5 dpt) / (-1.0 dpt) = 1.5<br />
(-1.5 dpt) / (-2.0 dpt) = 0.75<br />
<br />
In EM articles, the term ''diopter ratio'' is often used interchangeably for left-right ''diopter gap''<ref>{{cite jake|https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/|The Diopter Ratio Trap: Don’t Favor One Eye}}</ref>, for example when talking about reducing a correction while keeping the ''gap'' the same. This can also be expressed as a [[wikipedia:Percent difference|percentage difference]] between the two diopter values<ref>{{cite jake|https://endmyopia.org/reducing-diopter-ratio-diy-patching-solution-pro-topic/|Reducing Diopter Ratio: DIY Patching Solution (PRO TOPIC)}}</ref> (e.g. the <tt>0.5 dpt</tt> difference between the right and left eyes here is equivalent to <tt>0.5 dpt / |-1.5 dpt| = 0.33</tt> or 33%).<br />
<br />
The general recommendation is that the left-right diopter gap is constant across all lenses being used. However, some old EM articles show successful cases where differentials are equalized but normalized have a 0.25 D gap.<ref>https://endmyopia.org/progress-improving-centimeter-62-90/ and https://endmyopia.org/saras-journey-truth-long-term-vision-improvement-potential/</ref><br />
<br />
Confusingly, diopter gap is also sometimes used to refer to the diff-norm gap, the difference between [[differentials]] and [[normalized]] or the [[spherical equivalent]] of that difference.<ref>https://endmyopia.org/pro-topic-managing-your-maximum-diopter-gap/</ref><br />
<br />
It is often useful to disambiguate what is being compared:<br />
* ''left-right gap'': left eye diopters minus right eye diopters, ignoring axis<br />
** In the example above, the left-right gap is +0.5 SPH -0.5 CYL.<br />
** The axis is ignored, and the cylinder powers are subtracted without using [[Diopters#Adding/Combining Lenses|lens combination calculations]].<br />
* ''diff-norm gap'': differentials diopter minus normalized diopters, ignoring axis<br />
** For example, if normalized is -2 SPH -0.5 CYL, and differentials are -0.75 SPH, the diff-norm gap is 1.25 SPH 0.5 CYL or 1.5 SPH equivalent.<br />
** The axis is ignored.<br />
<br />
==Technical Details==<br />
This section is for the math-savvy people. It explains concepts in more detail, but knowledge of it is not strictly necessary to use the EM method.<br />
<br />
===Thin Lens Equation===<br />
The focal length of a lens is given by the lensmaker's equation. By assuming the lens is much thinner than the radius of curvature, therefore assuming lens thickness is zero, we get a simplified version of the lensmaker's equation. We can do some further derivation, we arrive at the thin-lens equation:<ref>see derivations at https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses</ref><br />
<br />
<math>\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}</math><br />
<br />
According to the thin lens sign convention,<br />
* di is positive if it is a real image on the opposite side of the lens as the object, and it is negative if it is a virtual image on the same side of the lens as the object.<br />
* f is positive for converging lens and negative for diverging.<br />
<br />
This is also sometimes presented in the Newtonian form:<br />
<br />
<math>\left(d_o-f\right)\left(d_i-f\right)=f^2</math><br />
<br />
====Examples====<br />
"Full correction" takes an object at infinity and produces a virtual image at your far point distance d:<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{-d}=-\frac{1}{d}</math><br />
<br />
<br />
This is the resulting equation at the beginning of the article. It also explains why the focal power is increased for objects at closer distances: mainstream optometry calls this the "add" for presbyopia, although they typically use the minimum amount required for you to see at 40 cm with full distance correction using accommodation. For example, if you choose 80 cm as the working distance for your [[differentials]] (resulting in a +1.25 dpt "add"), and your blur horizon is 50 cm (resulting in -2 dpt), the formula is<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{80\ cm}+\frac{1}{-50\ cm}=1.25\ dpt + \left(-2\ dpt\right) = -0.75\ dpt</math><br />
<br />
=== Cylinder ===<br />
A cylindrical lens of power F<sub>c</sub> has focal power F at angle θ from its axis:<br />
<br />
<math>F = F_{cyl} (\sin\theta)^2</math><br />
<br />
==== Transposition ====<br />
We can understand why there are two different ways to write a spherical and cylindrical lens combination, using the Pythagorean trigonometric identity and the complementary angle identity:<br />
<br />
<math>(\sin\theta)^2 + (\cos\theta)^2 = 1</math><br />
<br />
<math>\cos\theta = \sin{\left(90^{\circ} - \theta\right)} = -\sin{\left(\theta - 90^{\circ}\right)}</math><br />
<br />
<br />
<math>F = F_{cyl} \left( 1 - (\cos\theta)^2 \right) = F_{cyl} + \left(-F_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math><br />
<br />
We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (same as subtracting 90 degrees, since the axis is in modulo 180 degrees) to the axis, we get an equivalent combination.<br />
<br />
For example, -1 sph -1 cyl 1 axis is the same as -2 sph +1 cyl 91 axis.<br />
<br />
In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two forms are equivalent.<br />
<br />
==== Spherical Equivalent ====<br />
:See also: [[Astigmatism#Spherical equivalent|Astigmatism § Spherical equivalent]]<br />
By calculating the average value over all angles using an integral, the result<ref>it is only necessary to integrate one or two periods: https://www.wolframalpha.com/input/?i=average+of+%28sin+x%29%5E2+from+0+to+2+pi</ref> is<br />
<br />
<math>F_{avg} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} F_{cyl} (\sin{t})^2 \,dt = \frac{1}{2} F_{cyl}</math><br />
<br />
This is why the spherical equivalent has power equal to half of the cylinder's power.<br />
<br />
==== Adding/Combining Lenses ====<br />
Multiple lens, each with spherical and cylindrical components (not necessarily at the same axis) can be added to form one lens with a spherical and cylindrical component.<br />
<br />
We can use the double angle formula to convert each cylindrical lens into a constant plus a cosine:<br />
<br />
<math>\cos{2\theta}=1-2(\sin\theta)^2</math><br />
<br />
<br />
<math>F = F_{cyl} (\sin{\left(\theta + \phi\right)})^2 = F_{cyl} \left( \frac{1-\cos{\left(2\theta + 2\phi\right)}}{2} \right) = \frac{1}{2} F_{cyl} + \frac{-F_{cyl}}{2} \cos{\left(2\theta + 2\phi\right)}</math><br />
<br />
The constant parts are added with the spherical components. The cosines can be added by converting them to [https://en.wikipedia.org/wiki/Phasor phasors] and adding the phasors together. The resulting phasor corresponds to one of two cylindrical lenses (see the section on Transposition), and its corresponding spherical component must be subtracted from the total spherical component.<br />
<br />
There are implementations of this at<br />
* http://opticampus.opti.vision/tools/cylinders.php<br />
* http://billauer.co.il/simulator.html<br />
<br />
=== Decentration ===<br />
Induced prism can be calculated using Prentice's rule. Similar to Vertex Distance, decentration is less of an issue for smaller power lenses.<br />
<br />
The amount of prism P induced by decentration c of a lens of power f is<br />
<br />
<math>P=cf</math><br />
<br />
1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm, and f is in diopters, then P is in prism diopters.<br />
<br />
A prism with apex angle a and refractive index n results in angle of deviation of the light d, which is equal to P prism diopters:<br />
<br />
<math>d=(n-1)a</math><br />
<br />
<br />
<math>P=100\tan{d}=100\tan((n-1)a)</math><br />
<br />
=== Vertex Distance ===<br />
See [[Vertex distance#Calculation]]<br />
<br />
==References==<br />
{{reflist}}<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Diopters&diff=16539Diopters2022-03-28T15:55:14Z<p>User: /* Spherical Equivalent */</p>
<hr />
<div><br />
Diopter is a measure of the [https://en.wikipedia.org/wiki/Optical_power optical power] P of a [[lens]] (or mirror) and is equal to the reciprocal of [[focal length]] in meters. The most common unit symbol for diopters is dpt, D, or m<sup>-1</sup>.<br />
<br />
<math>P = \frac{1}{f} = -\frac{1}{d}</math><br />
<br />
* In [[EM]], we use the [[cm measurement]] to calculate diopters needed to correct [[refraction]] of the eye. If you can see 50 cm clearly, your diopters will be <math>-\frac{1}{0.50}=-2 dpt</math>.<br />
<br />
* Lenses in series add their powers: if you're wearing -2 diopter contacts ([[vertex distance|adjusted for glasses strength]]) and put +1 diopter reading glasses over the contacts you're in effect wearing -1 diopters.<br />
** There are some caveats such as vertex distance, since moving the lens away effectively gives you a weaker negative lens or stronger positive lens. There is also decentration, which induces prism when the lens is moved to the side. These effects become negligible for weaker lenses.<br />
* According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.<br />
** A lens with a negative diopter sign compensates for [[nearsightedness]] while a lens with a positive diopter sign compensates for [[farsightedness]].<br />
<br />
{| class="wikitable"<br />
|+ Approximate categorizations of myopia by [[spherical]] lens power:<br />
|-<br />
| 0.00 to -0.50 dpt || Not really considered myopic, probably don't need glasses<br />
|-<br />
| -0.50 to -1.00 dpt || Mild myopia, [[normalized]] sometimes not needed<br />
|-<br />
| -1.00 to -2.50 dpt || Mild myopia, [[differentials]] possibly not needed<br />
|-<br />
| -2.50 to -3.00 dpt || Mild myopia, differentials probably needed<br />
|-<br />
| -3.00 to -6.00 dpt || Moderate myopia, glasses always needed<br />
|-<br />
| -6.00 to -10.00 dpt || High myopia<br />
|-<br />
| -10.00+ dpt || Very high myopia. Field of view significantly reduced.<br />
|}<br />
<br />
==Gap and ratio==<br />
<br />
Comparisons between two diopters is typically expressed using one of these terms:<br />
<br />
* ''diopter gap'' (or ''diopter difference''): absolute difference in diopters between two values<br />
* ''diopter ratio'': ratio of one diopter value to another (such as right eye / left eye)<br />
<br />
For example, consider the following correction:<br />
<br />
OD: -1.5 SPH / -1.5 CYL<br />
OS: -1.0 SPH / -2.0 CYL<br />
<br />
It can be expressed as a 0.5 dpt gap in both SPH and CYL, a 1.5 ratio in SPH and a 0.75 ratio in CYL:<br />
<br />
|(-1.5 dpt) - (-1.0 dpt)| = 0.5 dpt<br />
|(-1.5 dpt) - (-2.0 dpt)| = 0.5 dpt<br />
(-1.5 dpt) / (-1.0 dpt) = 1.5<br />
(-1.5 dpt) / (-2.0 dpt) = 0.75<br />
<br />
In EM articles, the term ''diopter ratio'' is often used interchangeably for left-right ''diopter gap''<ref>{{cite jake|https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/|The Diopter Ratio Trap: Don’t Favor One Eye}}</ref>, for example when talking about reducing a correction while keeping the ''gap'' the same. This can also be expressed as a [[wikipedia:Percent difference|percentage difference]] between the two diopter values<ref>{{cite jake|https://endmyopia.org/reducing-diopter-ratio-diy-patching-solution-pro-topic/|Reducing Diopter Ratio: DIY Patching Solution (PRO TOPIC)}}</ref> (e.g. the <tt>0.5 dpt</tt> difference between the right and left eyes here is equivalent to <tt>0.5 dpt / |-1.5 dpt| = 0.33</tt> or 33%).<br />
<br />
The general recommendation is that the left-right diopter gap is constant across all lenses being used. However, some old EM articles show successful cases where differentials are equalized but normalized have a 0.25 D gap.<ref>https://endmyopia.org/progress-improving-centimeter-62-90/ and https://endmyopia.org/saras-journey-truth-long-term-vision-improvement-potential/</ref><br />
<br />
Confusingly, diopter gap is also sometimes used to refer to the diff-norm gap, the difference between [[differentials]] and [[normalized]] or the [[spherical equivalent]] of that difference.<ref>https://endmyopia.org/pro-topic-managing-your-maximum-diopter-gap/</ref><br />
<br />
It is often useful to disambiguate what is being compared:<br />
* ''left-right gap'': left eye diopters minus right eye diopters, ignoring axis<br />
** In the example above, the left-right gap is +0.5 SPH -0.5 CYL.<br />
** The axis is ignored, and the cylinder powers are subtracted without using [[Diopters#Adding/Combining Lenses|lens combination calculations]].<br />
* ''diff-norm gap'': differentials diopter minus normalized diopters, ignoring axis<br />
** For example, if normalized is -2 SPH -0.5 CYL, and differentials are -0.75 SPH, the diff-norm gap is 1.25 SPH 0.5 CYL or 1.5 SPH equivalent.<br />
** The axis is ignored.<br />
<br />
==Technical Details==<br />
This section is for the math-savvy people. It explains concepts in more detail, but knowledge of it is not strictly necessary to use the EM method.<br />
<br />
===Thin Lens Equation===<br />
The focal length of a lens is given by the lensmaker's equation. By assuming the lens is much thinner than the radius of curvature, therefore assuming lens thickness is zero, we get a simplified version of the lensmaker's equation. We can do some further derivation, we arrive at the thin-lens equation:<ref>see derivations at https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses</ref><br />
<br />
<math>\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}</math><br />
<br />
According to the thin lens sign convention,<br />
* di is positive if it is a real image on the opposite side of the lens as the object, and it is negative if it is a virtual image on the same side of the lens as the object.<br />
* f is positive for converging lens and negative for diverging.<br />
<br />
This is also sometimes presented in the Newtonian form:<br />
<br />
<math>\left(d_o-f\right)\left(d_i-f\right)=f^2</math><br />
<br />
====Examples====<br />
"Full correction" takes an object at infinity and produces a virtual image at your far point distance d:<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{-d}=-\frac{1}{d}</math><br />
<br />
<br />
This is the resulting equation at the beginning of the article. It also explains why the focal power is increased for objects at closer distances: mainstream optometry calls this the "add" for presbyopia, although they typically use the minimum amount required for you to see at 40 cm with full distance correction using accommodation. For example, if you choose 80 cm as the working distance for your [[differentials]] (resulting in a +1.25 dpt "add"), and your blur horizon is 50 cm (resulting in -2 dpt), the formula is<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{80\ cm}+\frac{1}{-50\ cm}=1.25\ dpt + \left(-2\ dpt\right) = -0.75\ dpt</math><br />
<br />
=== Cylinder ===<br />
A cylindrical lens of power F<sub>c</sub> has focal power F at angle θ from its axis:<br />
<br />
<math>F = F_{cyl} (\sin\theta)^2</math><br />
<br />
==== Transposition ====<br />
We can understand why there are two different ways to write a spherical and cylindrical lens combination, using the Pythagorean trigonometric identity and the complementary angle identity:<br />
<br />
<math>(\sin\theta)^2 + (\cos\theta)^2 = 1</math><br />
<br />
<math>\cos\theta = \sin{\left(90^{\circ} - \theta\right)} = -\sin{\left(\theta - 90^{\circ}\right)}</math><br />
<br />
<br />
<math>F = F_{cyl} \left( 1 - (\cos\theta)^2 \right) = F_{cyl} + \left(-F_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math><br />
<br />
We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (same as subtracting 90 degrees, since the axis is in modulo 180 degrees) to the axis, we get an equivalent combination.<br />
<br />
For example, -1 sph -1 cyl 1 axis is the same as -2 sph +1 cyl 91 axis.<br />
<br />
In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two forms are equivalent.<br />
<br />
==== Spherical Equivalent ====<br />
:See also: [[Astigmatism#Spherical equivalent||Astigmatism § Spherical equivalent]]<br />
By calculating the average value over all angles using an integral, the result<ref>it is only necessary to integrate one or two periods: https://www.wolframalpha.com/input/?i=average+of+%28sin+x%29%5E2+from+0+to+2+pi</ref> is<br />
<br />
<math>F_{avg} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} F_{cyl} (\sin{t})^2 \,dt = \frac{1}{2} F_{cyl}</math><br />
<br />
This is why the spherical equivalent has power equal to half of the cylinder's power.<br />
<br />
==== Adding/Combining Lenses ====<br />
Multiple lens, each with spherical and cylindrical components (not necessarily at the same axis) can be added to form one lens with a spherical and cylindrical component.<br />
<br />
We can use the double angle formula to convert each cylindrical lens into a constant plus a cosine:<br />
<br />
<math>\cos{2\theta}=1-2(\sin\theta)^2</math><br />
<br />
<br />
<math>F = F_{cyl} (\sin{\left(\theta + \phi\right)})^2 = F_{cyl} \left( \frac{1-\cos{\left(2\theta + 2\phi\right)}}{2} \right) = \frac{1}{2} F_{cyl} + \frac{-F_{cyl}}{2} \cos{\left(2\theta + 2\phi\right)}</math><br />
<br />
The constant parts are added with the spherical components. The cosines can be added by converting them to [https://en.wikipedia.org/wiki/Phasor phasors] and adding the phasors together. The resulting phasor corresponds to one of two cylindrical lenses (see the section on Transposition), and its corresponding spherical component must be subtracted from the total spherical component.<br />
<br />
There are implementations of this at<br />
* http://opticampus.opti.vision/tools/cylinders.php<br />
* http://billauer.co.il/simulator.html<br />
<br />
=== Decentration ===<br />
Induced prism can be calculated using Prentice's rule. Similar to Vertex Distance, decentration is less of an issue for smaller power lenses.<br />
<br />
The amount of prism P induced by decentration c of a lens of power f is<br />
<br />
<math>P=cf</math><br />
<br />
1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm, and f is in diopters, then P is in prism diopters.<br />
<br />
A prism with apex angle a and refractive index n results in angle of deviation of the light d, which is equal to P prism diopters:<br />
<br />
<math>d=(n-1)a</math><br />
<br />
<br />
<math>P=100\tan{d}=100\tan((n-1)a)</math><br />
<br />
=== Vertex Distance ===<br />
See [[Vertex distance#Calculation]]<br />
<br />
==References==<br />
{{reflist}}<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Diopters&diff=16538Diopters2022-03-28T15:54:56Z<p>User: /* Spherical Equivalent */</p>
<hr />
<div><br />
Diopter is a measure of the [https://en.wikipedia.org/wiki/Optical_power optical power] P of a [[lens]] (or mirror) and is equal to the reciprocal of [[focal length]] in meters. The most common unit symbol for diopters is dpt, D, or m<sup>-1</sup>.<br />
<br />
<math>P = \frac{1}{f} = -\frac{1}{d}</math><br />
<br />
* In [[EM]], we use the [[cm measurement]] to calculate diopters needed to correct [[refraction]] of the eye. If you can see 50 cm clearly, your diopters will be <math>-\frac{1}{0.50}=-2 dpt</math>.<br />
<br />
* Lenses in series add their powers: if you're wearing -2 diopter contacts ([[vertex distance|adjusted for glasses strength]]) and put +1 diopter reading glasses over the contacts you're in effect wearing -1 diopters.<br />
** There are some caveats such as vertex distance, since moving the lens away effectively gives you a weaker negative lens or stronger positive lens. There is also decentration, which induces prism when the lens is moved to the side. These effects become negligible for weaker lenses.<br />
* According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.<br />
** A lens with a negative diopter sign compensates for [[nearsightedness]] while a lens with a positive diopter sign compensates for [[farsightedness]].<br />
<br />
{| class="wikitable"<br />
|+ Approximate categorizations of myopia by [[spherical]] lens power:<br />
|-<br />
| 0.00 to -0.50 dpt || Not really considered myopic, probably don't need glasses<br />
|-<br />
| -0.50 to -1.00 dpt || Mild myopia, [[normalized]] sometimes not needed<br />
|-<br />
| -1.00 to -2.50 dpt || Mild myopia, [[differentials]] possibly not needed<br />
|-<br />
| -2.50 to -3.00 dpt || Mild myopia, differentials probably needed<br />
|-<br />
| -3.00 to -6.00 dpt || Moderate myopia, glasses always needed<br />
|-<br />
| -6.00 to -10.00 dpt || High myopia<br />
|-<br />
| -10.00+ dpt || Very high myopia. Field of view significantly reduced.<br />
|}<br />
<br />
==Gap and ratio==<br />
<br />
Comparisons between two diopters is typically expressed using one of these terms:<br />
<br />
* ''diopter gap'' (or ''diopter difference''): absolute difference in diopters between two values<br />
* ''diopter ratio'': ratio of one diopter value to another (such as right eye / left eye)<br />
<br />
For example, consider the following correction:<br />
<br />
OD: -1.5 SPH / -1.5 CYL<br />
OS: -1.0 SPH / -2.0 CYL<br />
<br />
It can be expressed as a 0.5 dpt gap in both SPH and CYL, a 1.5 ratio in SPH and a 0.75 ratio in CYL:<br />
<br />
|(-1.5 dpt) - (-1.0 dpt)| = 0.5 dpt<br />
|(-1.5 dpt) - (-2.0 dpt)| = 0.5 dpt<br />
(-1.5 dpt) / (-1.0 dpt) = 1.5<br />
(-1.5 dpt) / (-2.0 dpt) = 0.75<br />
<br />
In EM articles, the term ''diopter ratio'' is often used interchangeably for left-right ''diopter gap''<ref>{{cite jake|https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/|The Diopter Ratio Trap: Don’t Favor One Eye}}</ref>, for example when talking about reducing a correction while keeping the ''gap'' the same. This can also be expressed as a [[wikipedia:Percent difference|percentage difference]] between the two diopter values<ref>{{cite jake|https://endmyopia.org/reducing-diopter-ratio-diy-patching-solution-pro-topic/|Reducing Diopter Ratio: DIY Patching Solution (PRO TOPIC)}}</ref> (e.g. the <tt>0.5 dpt</tt> difference between the right and left eyes here is equivalent to <tt>0.5 dpt / |-1.5 dpt| = 0.33</tt> or 33%).<br />
<br />
The general recommendation is that the left-right diopter gap is constant across all lenses being used. However, some old EM articles show successful cases where differentials are equalized but normalized have a 0.25 D gap.<ref>https://endmyopia.org/progress-improving-centimeter-62-90/ and https://endmyopia.org/saras-journey-truth-long-term-vision-improvement-potential/</ref><br />
<br />
Confusingly, diopter gap is also sometimes used to refer to the diff-norm gap, the difference between [[differentials]] and [[normalized]] or the [[spherical equivalent]] of that difference.<ref>https://endmyopia.org/pro-topic-managing-your-maximum-diopter-gap/</ref><br />
<br />
It is often useful to disambiguate what is being compared:<br />
* ''left-right gap'': left eye diopters minus right eye diopters, ignoring axis<br />
** In the example above, the left-right gap is +0.5 SPH -0.5 CYL.<br />
** The axis is ignored, and the cylinder powers are subtracted without using [[Diopters#Adding/Combining Lenses|lens combination calculations]].<br />
* ''diff-norm gap'': differentials diopter minus normalized diopters, ignoring axis<br />
** For example, if normalized is -2 SPH -0.5 CYL, and differentials are -0.75 SPH, the diff-norm gap is 1.25 SPH 0.5 CYL or 1.5 SPH equivalent.<br />
** The axis is ignored.<br />
<br />
==Technical Details==<br />
This section is for the math-savvy people. It explains concepts in more detail, but knowledge of it is not strictly necessary to use the EM method.<br />
<br />
===Thin Lens Equation===<br />
The focal length of a lens is given by the lensmaker's equation. By assuming the lens is much thinner than the radius of curvature, therefore assuming lens thickness is zero, we get a simplified version of the lensmaker's equation. We can do some further derivation, we arrive at the thin-lens equation:<ref>see derivations at https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses</ref><br />
<br />
<math>\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}</math><br />
<br />
According to the thin lens sign convention,<br />
* di is positive if it is a real image on the opposite side of the lens as the object, and it is negative if it is a virtual image on the same side of the lens as the object.<br />
* f is positive for converging lens and negative for diverging.<br />
<br />
This is also sometimes presented in the Newtonian form:<br />
<br />
<math>\left(d_o-f\right)\left(d_i-f\right)=f^2</math><br />
<br />
====Examples====<br />
"Full correction" takes an object at infinity and produces a virtual image at your far point distance d:<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{-d}=-\frac{1}{d}</math><br />
<br />
<br />
This is the resulting equation at the beginning of the article. It also explains why the focal power is increased for objects at closer distances: mainstream optometry calls this the "add" for presbyopia, although they typically use the minimum amount required for you to see at 40 cm with full distance correction using accommodation. For example, if you choose 80 cm as the working distance for your [[differentials]] (resulting in a +1.25 dpt "add"), and your blur horizon is 50 cm (resulting in -2 dpt), the formula is<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{80\ cm}+\frac{1}{-50\ cm}=1.25\ dpt + \left(-2\ dpt\right) = -0.75\ dpt</math><br />
<br />
=== Cylinder ===<br />
A cylindrical lens of power F<sub>c</sub> has focal power F at angle θ from its axis:<br />
<br />
<math>F = F_{cyl} (\sin\theta)^2</math><br />
<br />
==== Transposition ====<br />
We can understand why there are two different ways to write a spherical and cylindrical lens combination, using the Pythagorean trigonometric identity and the complementary angle identity:<br />
<br />
<math>(\sin\theta)^2 + (\cos\theta)^2 = 1</math><br />
<br />
<math>\cos\theta = \sin{\left(90^{\circ} - \theta\right)} = -\sin{\left(\theta - 90^{\circ}\right)}</math><br />
<br />
<br />
<math>F = F_{cyl} \left( 1 - (\cos\theta)^2 \right) = F_{cyl} + \left(-F_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math><br />
<br />
We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (same as subtracting 90 degrees, since the axis is in modulo 180 degrees) to the axis, we get an equivalent combination.<br />
<br />
For example, -1 sph -1 cyl 1 axis is the same as -2 sph +1 cyl 91 axis.<br />
<br />
In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two forms are equivalent.<br />
<br />
==== Spherical Equivalent ====<br />
:See also: [[Astigmatism#Spherical Equivalent|Astigmatism § Spherical Equivalent]]<br />
By calculating the average value over all angles using an integral, the result<ref>it is only necessary to integrate one or two periods: https://www.wolframalpha.com/input/?i=average+of+%28sin+x%29%5E2+from+0+to+2+pi</ref> is<br />
<br />
<math>F_{avg} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} F_{cyl} (\sin{t})^2 \,dt = \frac{1}{2} F_{cyl}</math><br />
<br />
This is why the spherical equivalent has power equal to half of the cylinder's power.<br />
<br />
==== Adding/Combining Lenses ====<br />
Multiple lens, each with spherical and cylindrical components (not necessarily at the same axis) can be added to form one lens with a spherical and cylindrical component.<br />
<br />
We can use the double angle formula to convert each cylindrical lens into a constant plus a cosine:<br />
<br />
<math>\cos{2\theta}=1-2(\sin\theta)^2</math><br />
<br />
<br />
<math>F = F_{cyl} (\sin{\left(\theta + \phi\right)})^2 = F_{cyl} \left( \frac{1-\cos{\left(2\theta + 2\phi\right)}}{2} \right) = \frac{1}{2} F_{cyl} + \frac{-F_{cyl}}{2} \cos{\left(2\theta + 2\phi\right)}</math><br />
<br />
The constant parts are added with the spherical components. The cosines can be added by converting them to [https://en.wikipedia.org/wiki/Phasor phasors] and adding the phasors together. The resulting phasor corresponds to one of two cylindrical lenses (see the section on Transposition), and its corresponding spherical component must be subtracted from the total spherical component.<br />
<br />
There are implementations of this at<br />
* http://opticampus.opti.vision/tools/cylinders.php<br />
* http://billauer.co.il/simulator.html<br />
<br />
=== Decentration ===<br />
Induced prism can be calculated using Prentice's rule. Similar to Vertex Distance, decentration is less of an issue for smaller power lenses.<br />
<br />
The amount of prism P induced by decentration c of a lens of power f is<br />
<br />
<math>P=cf</math><br />
<br />
1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm, and f is in diopters, then P is in prism diopters.<br />
<br />
A prism with apex angle a and refractive index n results in angle of deviation of the light d, which is equal to P prism diopters:<br />
<br />
<math>d=(n-1)a</math><br />
<br />
<br />
<math>P=100\tan{d}=100\tan((n-1)a)</math><br />
<br />
=== Vertex Distance ===<br />
See [[Vertex distance#Calculation]]<br />
<br />
==References==<br />
{{reflist}}<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Diopters&diff=16537Diopters2022-03-28T15:53:51Z<p>User: /* Gap and ratio */</p>
<hr />
<div><br />
Diopter is a measure of the [https://en.wikipedia.org/wiki/Optical_power optical power] P of a [[lens]] (or mirror) and is equal to the reciprocal of [[focal length]] in meters. The most common unit symbol for diopters is dpt, D, or m<sup>-1</sup>.<br />
<br />
<math>P = \frac{1}{f} = -\frac{1}{d}</math><br />
<br />
* In [[EM]], we use the [[cm measurement]] to calculate diopters needed to correct [[refraction]] of the eye. If you can see 50 cm clearly, your diopters will be <math>-\frac{1}{0.50}=-2 dpt</math>.<br />
<br />
* Lenses in series add their powers: if you're wearing -2 diopter contacts ([[vertex distance|adjusted for glasses strength]]) and put +1 diopter reading glasses over the contacts you're in effect wearing -1 diopters.<br />
** There are some caveats such as vertex distance, since moving the lens away effectively gives you a weaker negative lens or stronger positive lens. There is also decentration, which induces prism when the lens is moved to the side. These effects become negligible for weaker lenses.<br />
* According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.<br />
** A lens with a negative diopter sign compensates for [[nearsightedness]] while a lens with a positive diopter sign compensates for [[farsightedness]].<br />
<br />
{| class="wikitable"<br />
|+ Approximate categorizations of myopia by [[spherical]] lens power:<br />
|-<br />
| 0.00 to -0.50 dpt || Not really considered myopic, probably don't need glasses<br />
|-<br />
| -0.50 to -1.00 dpt || Mild myopia, [[normalized]] sometimes not needed<br />
|-<br />
| -1.00 to -2.50 dpt || Mild myopia, [[differentials]] possibly not needed<br />
|-<br />
| -2.50 to -3.00 dpt || Mild myopia, differentials probably needed<br />
|-<br />
| -3.00 to -6.00 dpt || Moderate myopia, glasses always needed<br />
|-<br />
| -6.00 to -10.00 dpt || High myopia<br />
|-<br />
| -10.00+ dpt || Very high myopia. Field of view significantly reduced.<br />
|}<br />
<br />
==Gap and ratio==<br />
<br />
Comparisons between two diopters is typically expressed using one of these terms:<br />
<br />
* ''diopter gap'' (or ''diopter difference''): absolute difference in diopters between two values<br />
* ''diopter ratio'': ratio of one diopter value to another (such as right eye / left eye)<br />
<br />
For example, consider the following correction:<br />
<br />
OD: -1.5 SPH / -1.5 CYL<br />
OS: -1.0 SPH / -2.0 CYL<br />
<br />
It can be expressed as a 0.5 dpt gap in both SPH and CYL, a 1.5 ratio in SPH and a 0.75 ratio in CYL:<br />
<br />
|(-1.5 dpt) - (-1.0 dpt)| = 0.5 dpt<br />
|(-1.5 dpt) - (-2.0 dpt)| = 0.5 dpt<br />
(-1.5 dpt) / (-1.0 dpt) = 1.5<br />
(-1.5 dpt) / (-2.0 dpt) = 0.75<br />
<br />
In EM articles, the term ''diopter ratio'' is often used interchangeably for left-right ''diopter gap''<ref>{{cite jake|https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/|The Diopter Ratio Trap: Don’t Favor One Eye}}</ref>, for example when talking about reducing a correction while keeping the ''gap'' the same. This can also be expressed as a [[wikipedia:Percent difference|percentage difference]] between the two diopter values<ref>{{cite jake|https://endmyopia.org/reducing-diopter-ratio-diy-patching-solution-pro-topic/|Reducing Diopter Ratio: DIY Patching Solution (PRO TOPIC)}}</ref> (e.g. the <tt>0.5 dpt</tt> difference between the right and left eyes here is equivalent to <tt>0.5 dpt / |-1.5 dpt| = 0.33</tt> or 33%).<br />
<br />
The general recommendation is that the left-right diopter gap is constant across all lenses being used. However, some old EM articles show successful cases where differentials are equalized but normalized have a 0.25 D gap.<ref>https://endmyopia.org/progress-improving-centimeter-62-90/ and https://endmyopia.org/saras-journey-truth-long-term-vision-improvement-potential/</ref><br />
<br />
Confusingly, diopter gap is also sometimes used to refer to the diff-norm gap, the difference between [[differentials]] and [[normalized]] or the [[spherical equivalent]] of that difference.<ref>https://endmyopia.org/pro-topic-managing-your-maximum-diopter-gap/</ref><br />
<br />
It is often useful to disambiguate what is being compared:<br />
* ''left-right gap'': left eye diopters minus right eye diopters, ignoring axis<br />
** In the example above, the left-right gap is +0.5 SPH -0.5 CYL.<br />
** The axis is ignored, and the cylinder powers are subtracted without using [[Diopters#Adding/Combining Lenses|lens combination calculations]].<br />
* ''diff-norm gap'': differentials diopter minus normalized diopters, ignoring axis<br />
** For example, if normalized is -2 SPH -0.5 CYL, and differentials are -0.75 SPH, the diff-norm gap is 1.25 SPH 0.5 CYL or 1.5 SPH equivalent.<br />
** The axis is ignored.<br />
<br />
==Technical Details==<br />
This section is for the math-savvy people. It explains concepts in more detail, but knowledge of it is not strictly necessary to use the EM method.<br />
<br />
===Thin Lens Equation===<br />
The focal length of a lens is given by the lensmaker's equation. By assuming the lens is much thinner than the radius of curvature, therefore assuming lens thickness is zero, we get a simplified version of the lensmaker's equation. We can do some further derivation, we arrive at the thin-lens equation:<ref>see derivations at https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses</ref><br />
<br />
<math>\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}</math><br />
<br />
According to the thin lens sign convention,<br />
* di is positive if it is a real image on the opposite side of the lens as the object, and it is negative if it is a virtual image on the same side of the lens as the object.<br />
* f is positive for converging lens and negative for diverging.<br />
<br />
This is also sometimes presented in the Newtonian form:<br />
<br />
<math>\left(d_o-f\right)\left(d_i-f\right)=f^2</math><br />
<br />
====Examples====<br />
"Full correction" takes an object at infinity and produces a virtual image at your far point distance d:<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{-d}=-\frac{1}{d}</math><br />
<br />
<br />
This is the resulting equation at the beginning of the article. It also explains why the focal power is increased for objects at closer distances: mainstream optometry calls this the "add" for presbyopia, although they typically use the minimum amount required for you to see at 40 cm with full distance correction using accommodation. For example, if you choose 80 cm as the working distance for your [[differentials]] (resulting in a +1.25 dpt "add"), and your blur horizon is 50 cm (resulting in -2 dpt), the formula is<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{80\ cm}+\frac{1}{-50\ cm}=1.25\ dpt + \left(-2\ dpt\right) = -0.75\ dpt</math><br />
<br />
=== Cylinder ===<br />
A cylindrical lens of power F<sub>c</sub> has focal power F at angle θ from its axis:<br />
<br />
<math>F = F_{cyl} (\sin\theta)^2</math><br />
<br />
==== Transposition ====<br />
We can understand why there are two different ways to write a spherical and cylindrical lens combination, using the Pythagorean trigonometric identity and the complementary angle identity:<br />
<br />
<math>(\sin\theta)^2 + (\cos\theta)^2 = 1</math><br />
<br />
<math>\cos\theta = \sin{\left(90^{\circ} - \theta\right)} = -\sin{\left(\theta - 90^{\circ}\right)}</math><br />
<br />
<br />
<math>F = F_{cyl} \left( 1 - (\cos\theta)^2 \right) = F_{cyl} + \left(-F_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math><br />
<br />
We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (same as subtracting 90 degrees, since the axis is in modulo 180 degrees) to the axis, we get an equivalent combination.<br />
<br />
For example, -1 sph -1 cyl 1 axis is the same as -2 sph +1 cyl 91 axis.<br />
<br />
In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two forms are equivalent.<br />
<br />
==== Spherical Equivalent ====<br />
By calculating the average value over all angles using an integral, the result<ref>it is only necessary to integrate one or two periods: https://www.wolframalpha.com/input/?i=average+of+%28sin+x%29%5E2+from+0+to+2+pi</ref> is<br />
<br />
<math>F_{avg} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} F_{cyl} (\sin{t})^2 \,dt = \frac{1}{2} F_{cyl}</math><br />
<br />
This is why the spherical equivalent has power equal to half of the cylinder's power.<br />
<br />
==== Adding/Combining Lenses ====<br />
Multiple lens, each with spherical and cylindrical components (not necessarily at the same axis) can be added to form one lens with a spherical and cylindrical component.<br />
<br />
We can use the double angle formula to convert each cylindrical lens into a constant plus a cosine:<br />
<br />
<math>\cos{2\theta}=1-2(\sin\theta)^2</math><br />
<br />
<br />
<math>F = F_{cyl} (\sin{\left(\theta + \phi\right)})^2 = F_{cyl} \left( \frac{1-\cos{\left(2\theta + 2\phi\right)}}{2} \right) = \frac{1}{2} F_{cyl} + \frac{-F_{cyl}}{2} \cos{\left(2\theta + 2\phi\right)}</math><br />
<br />
The constant parts are added with the spherical components. The cosines can be added by converting them to [https://en.wikipedia.org/wiki/Phasor phasors] and adding the phasors together. The resulting phasor corresponds to one of two cylindrical lenses (see the section on Transposition), and its corresponding spherical component must be subtracted from the total spherical component.<br />
<br />
There are implementations of this at<br />
* http://opticampus.opti.vision/tools/cylinders.php<br />
* http://billauer.co.il/simulator.html<br />
<br />
=== Decentration ===<br />
Induced prism can be calculated using Prentice's rule. Similar to Vertex Distance, decentration is less of an issue for smaller power lenses.<br />
<br />
The amount of prism P induced by decentration c of a lens of power f is<br />
<br />
<math>P=cf</math><br />
<br />
1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm, and f is in diopters, then P is in prism diopters.<br />
<br />
A prism with apex angle a and refractive index n results in angle of deviation of the light d, which is equal to P prism diopters:<br />
<br />
<math>d=(n-1)a</math><br />
<br />
<br />
<math>P=100\tan{d}=100\tan((n-1)a)</math><br />
<br />
=== Vertex Distance ===<br />
See [[Vertex distance#Calculation]]<br />
<br />
==References==<br />
{{reflist}}<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Diopters&diff=16536Diopters2022-03-28T15:53:20Z<p>User: /* Gap and ratio */</p>
<hr />
<div><br />
Diopter is a measure of the [https://en.wikipedia.org/wiki/Optical_power optical power] P of a [[lens]] (or mirror) and is equal to the reciprocal of [[focal length]] in meters. The most common unit symbol for diopters is dpt, D, or m<sup>-1</sup>.<br />
<br />
<math>P = \frac{1}{f} = -\frac{1}{d}</math><br />
<br />
* In [[EM]], we use the [[cm measurement]] to calculate diopters needed to correct [[refraction]] of the eye. If you can see 50 cm clearly, your diopters will be <math>-\frac{1}{0.50}=-2 dpt</math>.<br />
<br />
* Lenses in series add their powers: if you're wearing -2 diopter contacts ([[vertex distance|adjusted for glasses strength]]) and put +1 diopter reading glasses over the contacts you're in effect wearing -1 diopters.<br />
** There are some caveats such as vertex distance, since moving the lens away effectively gives you a weaker negative lens or stronger positive lens. There is also decentration, which induces prism when the lens is moved to the side. These effects become negligible for weaker lenses.<br />
* According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.<br />
** A lens with a negative diopter sign compensates for [[nearsightedness]] while a lens with a positive diopter sign compensates for [[farsightedness]].<br />
<br />
{| class="wikitable"<br />
|+ Approximate categorizations of myopia by [[spherical]] lens power:<br />
|-<br />
| 0.00 to -0.50 dpt || Not really considered myopic, probably don't need glasses<br />
|-<br />
| -0.50 to -1.00 dpt || Mild myopia, [[normalized]] sometimes not needed<br />
|-<br />
| -1.00 to -2.50 dpt || Mild myopia, [[differentials]] possibly not needed<br />
|-<br />
| -2.50 to -3.00 dpt || Mild myopia, differentials probably needed<br />
|-<br />
| -3.00 to -6.00 dpt || Moderate myopia, glasses always needed<br />
|-<br />
| -6.00 to -10.00 dpt || High myopia<br />
|-<br />
| -10.00+ dpt || Very high myopia. Field of view significantly reduced.<br />
|}<br />
<br />
==Gap and ratio==<br />
<br />
Comparisons between two diopters is typically expressed using one of these terms:<br />
<br />
* ''diopter gap'' (or ''diopter difference''): absolute difference in diopters between two values<br />
* ''diopter ratio'': ratio of one diopter value to another (such as right eye / left eye)<br />
<br />
For example, consider the following correction:<br />
<br />
OD: -1.5 SPH / -1.5 CYL<br />
OS: -1.0 SPH / -2.0 CYL<br />
<br />
It can be expressed as a 0.5 dpt gap in both SPH and CYL, a 1.5 ratio in SPH and a 0.75 ratio in CYL:<br />
<br />
|(-1.5 dpt) - (-1.0 dpt)| = 0.5 dpt<br />
|(-1.5 dpt) - (-2.0 dpt)| = 0.5 dpt<br />
(-1.5 dpt) / (-1.0 dpt) = 1.5<br />
(-1.5 dpt) / (-2.0 dpt) = 0.75<br />
<br />
In EM articles, the term ''diopter ratio'' is often used interchangeably for left-right ''diopter gap''<ref>{{cite jake|https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/|The Diopter Ratio Trap: Don’t Favor One Eye}}</ref>, for example when talking about reducing a correction while keeping the ''gap'' the same. This can also be expressed as a [[wikipedia:Percent difference|percentage difference]] between the two diopter values<ref>{{cite jake|https://endmyopia.org/reducing-diopter-ratio-diy-patching-solution-pro-topic/|Reducing Diopter Ratio: DIY Patching Solution (PRO TOPIC)}}</ref> (e.g. the <tt>0.5 dpt</tt> difference between the right and left eyes here is equivalent to <tt>0.5 dpt / |-1.5 dpt| = 0.33</tt> or 33%).<br />
<br />
The general recommendation is that the left-right diopter gap is constant across all lenses being used. However, some old EM articles show successful cases where differentials are equalized but normalized have a 0.25 D gap.<ref>https://endmyopia.org/progress-improving-centimeter-62-90/ and https://endmyopia.org/saras-journey-truth-long-term-vision-improvement-potential/</ref><br />
<br />
Confusingly, diopter gap is also sometimes used to refer to the diff-norm gap, the difference between [[differentials]] and [[normalized]] or the [[spherical equivalent]] of that difference.<ref>https://endmyopia.org/pro-topic-managing-your-maximum-diopter-gap/</ref><br />
<br />
It is often useful to disambiguate what is being compared:<br />
* ''left-right gap'': left eye diopters minus right eye diopters, ignoring axis<br />
** In the example above, the left-right gap is +0.5 SPH -0.5 CYL.<br />
* ''diff-norm gap'': differentials diopter minus normalized diopters, ignoring axis<br />
** For example, if normalized is -2 SPH -0.5 CYL, and differentials are -0.75 SPH, the diff-norm gap is 1.25 SPH 0.5 CYL or 1.5 SPH equivalent.<br />
** The axis is ignored, and the cylinder powers are subtracted without using [[Diopters#Adding/Combining Lenses|lens combination calculations]].<br />
<br />
==Technical Details==<br />
This section is for the math-savvy people. It explains concepts in more detail, but knowledge of it is not strictly necessary to use the EM method.<br />
<br />
===Thin Lens Equation===<br />
The focal length of a lens is given by the lensmaker's equation. By assuming the lens is much thinner than the radius of curvature, therefore assuming lens thickness is zero, we get a simplified version of the lensmaker's equation. We can do some further derivation, we arrive at the thin-lens equation:<ref>see derivations at https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses</ref><br />
<br />
<math>\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}</math><br />
<br />
According to the thin lens sign convention,<br />
* di is positive if it is a real image on the opposite side of the lens as the object, and it is negative if it is a virtual image on the same side of the lens as the object.<br />
* f is positive for converging lens and negative for diverging.<br />
<br />
This is also sometimes presented in the Newtonian form:<br />
<br />
<math>\left(d_o-f\right)\left(d_i-f\right)=f^2</math><br />
<br />
====Examples====<br />
"Full correction" takes an object at infinity and produces a virtual image at your far point distance d:<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{-d}=-\frac{1}{d}</math><br />
<br />
<br />
This is the resulting equation at the beginning of the article. It also explains why the focal power is increased for objects at closer distances: mainstream optometry calls this the "add" for presbyopia, although they typically use the minimum amount required for you to see at 40 cm with full distance correction using accommodation. For example, if you choose 80 cm as the working distance for your [[differentials]] (resulting in a +1.25 dpt "add"), and your blur horizon is 50 cm (resulting in -2 dpt), the formula is<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{80\ cm}+\frac{1}{-50\ cm}=1.25\ dpt + \left(-2\ dpt\right) = -0.75\ dpt</math><br />
<br />
=== Cylinder ===<br />
A cylindrical lens of power F<sub>c</sub> has focal power F at angle θ from its axis:<br />
<br />
<math>F = F_{cyl} (\sin\theta)^2</math><br />
<br />
==== Transposition ====<br />
We can understand why there are two different ways to write a spherical and cylindrical lens combination, using the Pythagorean trigonometric identity and the complementary angle identity:<br />
<br />
<math>(\sin\theta)^2 + (\cos\theta)^2 = 1</math><br />
<br />
<math>\cos\theta = \sin{\left(90^{\circ} - \theta\right)} = -\sin{\left(\theta - 90^{\circ}\right)}</math><br />
<br />
<br />
<math>F = F_{cyl} \left( 1 - (\cos\theta)^2 \right) = F_{cyl} + \left(-F_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math><br />
<br />
We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (same as subtracting 90 degrees, since the axis is in modulo 180 degrees) to the axis, we get an equivalent combination.<br />
<br />
For example, -1 sph -1 cyl 1 axis is the same as -2 sph +1 cyl 91 axis.<br />
<br />
In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two forms are equivalent.<br />
<br />
==== Spherical Equivalent ====<br />
By calculating the average value over all angles using an integral, the result<ref>it is only necessary to integrate one or two periods: https://www.wolframalpha.com/input/?i=average+of+%28sin+x%29%5E2+from+0+to+2+pi</ref> is<br />
<br />
<math>F_{avg} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} F_{cyl} (\sin{t})^2 \,dt = \frac{1}{2} F_{cyl}</math><br />
<br />
This is why the spherical equivalent has power equal to half of the cylinder's power.<br />
<br />
==== Adding/Combining Lenses ====<br />
Multiple lens, each with spherical and cylindrical components (not necessarily at the same axis) can be added to form one lens with a spherical and cylindrical component.<br />
<br />
We can use the double angle formula to convert each cylindrical lens into a constant plus a cosine:<br />
<br />
<math>\cos{2\theta}=1-2(\sin\theta)^2</math><br />
<br />
<br />
<math>F = F_{cyl} (\sin{\left(\theta + \phi\right)})^2 = F_{cyl} \left( \frac{1-\cos{\left(2\theta + 2\phi\right)}}{2} \right) = \frac{1}{2} F_{cyl} + \frac{-F_{cyl}}{2} \cos{\left(2\theta + 2\phi\right)}</math><br />
<br />
The constant parts are added with the spherical components. The cosines can be added by converting them to [https://en.wikipedia.org/wiki/Phasor phasors] and adding the phasors together. The resulting phasor corresponds to one of two cylindrical lenses (see the section on Transposition), and its corresponding spherical component must be subtracted from the total spherical component.<br />
<br />
There are implementations of this at<br />
* http://opticampus.opti.vision/tools/cylinders.php<br />
* http://billauer.co.il/simulator.html<br />
<br />
=== Decentration ===<br />
Induced prism can be calculated using Prentice's rule. Similar to Vertex Distance, decentration is less of an issue for smaller power lenses.<br />
<br />
The amount of prism P induced by decentration c of a lens of power f is<br />
<br />
<math>P=cf</math><br />
<br />
1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm, and f is in diopters, then P is in prism diopters.<br />
<br />
A prism with apex angle a and refractive index n results in angle of deviation of the light d, which is equal to P prism diopters:<br />
<br />
<math>d=(n-1)a</math><br />
<br />
<br />
<math>P=100\tan{d}=100\tan((n-1)a)</math><br />
<br />
=== Vertex Distance ===<br />
See [[Vertex distance#Calculation]]<br />
<br />
==References==<br />
{{reflist}}<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Diopters&diff=16535Diopters2022-03-28T15:53:04Z<p>User: /* Gap and ratio */</p>
<hr />
<div><br />
Diopter is a measure of the [https://en.wikipedia.org/wiki/Optical_power optical power] P of a [[lens]] (or mirror) and is equal to the reciprocal of [[focal length]] in meters. The most common unit symbol for diopters is dpt, D, or m<sup>-1</sup>.<br />
<br />
<math>P = \frac{1}{f} = -\frac{1}{d}</math><br />
<br />
* In [[EM]], we use the [[cm measurement]] to calculate diopters needed to correct [[refraction]] of the eye. If you can see 50 cm clearly, your diopters will be <math>-\frac{1}{0.50}=-2 dpt</math>.<br />
<br />
* Lenses in series add their powers: if you're wearing -2 diopter contacts ([[vertex distance|adjusted for glasses strength]]) and put +1 diopter reading glasses over the contacts you're in effect wearing -1 diopters.<br />
** There are some caveats such as vertex distance, since moving the lens away effectively gives you a weaker negative lens or stronger positive lens. There is also decentration, which induces prism when the lens is moved to the side. These effects become negligible for weaker lenses.<br />
* According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.<br />
** A lens with a negative diopter sign compensates for [[nearsightedness]] while a lens with a positive diopter sign compensates for [[farsightedness]].<br />
<br />
{| class="wikitable"<br />
|+ Approximate categorizations of myopia by [[spherical]] lens power:<br />
|-<br />
| 0.00 to -0.50 dpt || Not really considered myopic, probably don't need glasses<br />
|-<br />
| -0.50 to -1.00 dpt || Mild myopia, [[normalized]] sometimes not needed<br />
|-<br />
| -1.00 to -2.50 dpt || Mild myopia, [[differentials]] possibly not needed<br />
|-<br />
| -2.50 to -3.00 dpt || Mild myopia, differentials probably needed<br />
|-<br />
| -3.00 to -6.00 dpt || Moderate myopia, glasses always needed<br />
|-<br />
| -6.00 to -10.00 dpt || High myopia<br />
|-<br />
| -10.00+ dpt || Very high myopia. Field of view significantly reduced.<br />
|}<br />
<br />
==Gap and ratio==<br />
<br />
Comparisons between two diopters is typically expressed using one of these terms:<br />
<br />
* ''diopter gap'' (or ''diopter difference''): absolute difference in diopters between two values<br />
* ''diopter ratio'': ratio of one diopter value to another (such as right eye / left eye)<br />
<br />
For example, consider the following correction:<br />
<br />
OD: -1.5 SPH / -1.5 CYL<br />
OS: -1.0 SPH / -2.0 CYL<br />
<br />
It can be expressed as a 0.5 dpt gap in both SPH and CYL, a 1.5 ratio in SPH and a 0.75 ratio in CYL:<br />
<br />
|(-1.5 dpt) - (-1.0 dpt)| = 0.5 dpt<br />
|(-1.5 dpt) - (-2.0 dpt)| = 0.5 dpt<br />
(-1.5 dpt) / (-1.0 dpt) = 1.5<br />
(-1.5 dpt) / (-2.0 dpt) = 0.75<br />
<br />
In EM articles, the term ''diopter ratio'' is often used interchangeably for left-right ''diopter gap''<ref>{{cite jake|https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/|The Diopter Ratio Trap: Don’t Favor One Eye}}</ref>, for example when talking about reducing a correction while keeping the ''gap'' the same. This can also be expressed as a [[wikipedia:Percent difference|percentage difference]] between the two diopter values<ref>{{cite jake|https://endmyopia.org/reducing-diopter-ratio-diy-patching-solution-pro-topic/|Reducing Diopter Ratio: DIY Patching Solution (PRO TOPIC)}}</ref> (e.g. the <tt>0.5 dpt</tt> difference between the right and left eyes here is equivalent to <tt>0.5 dpt / |-1.5 dpt| = 0.33</tt> or 33%).<br />
<br />
The general recommendation is that the left-right diopter gap is constant across all lenses being used. However, some old EM articles show successful cases where differentials are equalized but normalized have a 0.25 D gap.<ref>https://endmyopia.org/progress-improving-centimeter-62-90/ and https://endmyopia.org/saras-journey-truth-long-term-vision-improvement-potential/</ref><br />
<br />
Confusingly, diopter gap is also sometimes used to refer to the diff-norm gap, the difference between [[differentials]] and [[normalized]] or the [[spherical equivalent]] of that difference.<ref>https://endmyopia.org/pro-topic-managing-your-maximum-diopter-gap/</ref><br />
<br />
It is often useful to disambiguate what is being compared:<br />
* ''left-right gap'': left eye diopters minus right eye diopters, ignoring axis<br />
** In the example above, the left-right gap is +0.5 SPH -0.5 CYL.<br />
* ''diff-norm gap'': differentials diopter minus normalized diopters, ignoring axis<br />
** For example, if normalized is -2 SPH -0.5 CYL, and differentials are -0.75 SPH, the diff-norm gap is 1.25 SPH 0.5 CYL or 1.5 SPH equivalent.<br />
** The axis is ignored, and the cylinder powers are subtracted without using [[Diopters#Adding/Combining Lenses]].<br />
<br />
==Technical Details==<br />
This section is for the math-savvy people. It explains concepts in more detail, but knowledge of it is not strictly necessary to use the EM method.<br />
<br />
===Thin Lens Equation===<br />
The focal length of a lens is given by the lensmaker's equation. By assuming the lens is much thinner than the radius of curvature, therefore assuming lens thickness is zero, we get a simplified version of the lensmaker's equation. We can do some further derivation, we arrive at the thin-lens equation:<ref>see derivations at https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses</ref><br />
<br />
<math>\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}</math><br />
<br />
According to the thin lens sign convention,<br />
* di is positive if it is a real image on the opposite side of the lens as the object, and it is negative if it is a virtual image on the same side of the lens as the object.<br />
* f is positive for converging lens and negative for diverging.<br />
<br />
This is also sometimes presented in the Newtonian form:<br />
<br />
<math>\left(d_o-f\right)\left(d_i-f\right)=f^2</math><br />
<br />
====Examples====<br />
"Full correction" takes an object at infinity and produces a virtual image at your far point distance d:<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{-d}=-\frac{1}{d}</math><br />
<br />
<br />
This is the resulting equation at the beginning of the article. It also explains why the focal power is increased for objects at closer distances: mainstream optometry calls this the "add" for presbyopia, although they typically use the minimum amount required for you to see at 40 cm with full distance correction using accommodation. For example, if you choose 80 cm as the working distance for your [[differentials]] (resulting in a +1.25 dpt "add"), and your blur horizon is 50 cm (resulting in -2 dpt), the formula is<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{80\ cm}+\frac{1}{-50\ cm}=1.25\ dpt + \left(-2\ dpt\right) = -0.75\ dpt</math><br />
<br />
=== Cylinder ===<br />
A cylindrical lens of power F<sub>c</sub> has focal power F at angle θ from its axis:<br />
<br />
<math>F = F_{cyl} (\sin\theta)^2</math><br />
<br />
==== Transposition ====<br />
We can understand why there are two different ways to write a spherical and cylindrical lens combination, using the Pythagorean trigonometric identity and the complementary angle identity:<br />
<br />
<math>(\sin\theta)^2 + (\cos\theta)^2 = 1</math><br />
<br />
<math>\cos\theta = \sin{\left(90^{\circ} - \theta\right)} = -\sin{\left(\theta - 90^{\circ}\right)}</math><br />
<br />
<br />
<math>F = F_{cyl} \left( 1 - (\cos\theta)^2 \right) = F_{cyl} + \left(-F_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math><br />
<br />
We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (same as subtracting 90 degrees, since the axis is in modulo 180 degrees) to the axis, we get an equivalent combination.<br />
<br />
For example, -1 sph -1 cyl 1 axis is the same as -2 sph +1 cyl 91 axis.<br />
<br />
In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two forms are equivalent.<br />
<br />
==== Spherical Equivalent ====<br />
By calculating the average value over all angles using an integral, the result<ref>it is only necessary to integrate one or two periods: https://www.wolframalpha.com/input/?i=average+of+%28sin+x%29%5E2+from+0+to+2+pi</ref> is<br />
<br />
<math>F_{avg} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} F_{cyl} (\sin{t})^2 \,dt = \frac{1}{2} F_{cyl}</math><br />
<br />
This is why the spherical equivalent has power equal to half of the cylinder's power.<br />
<br />
==== Adding/Combining Lenses ====<br />
Multiple lens, each with spherical and cylindrical components (not necessarily at the same axis) can be added to form one lens with a spherical and cylindrical component.<br />
<br />
We can use the double angle formula to convert each cylindrical lens into a constant plus a cosine:<br />
<br />
<math>\cos{2\theta}=1-2(\sin\theta)^2</math><br />
<br />
<br />
<math>F = F_{cyl} (\sin{\left(\theta + \phi\right)})^2 = F_{cyl} \left( \frac{1-\cos{\left(2\theta + 2\phi\right)}}{2} \right) = \frac{1}{2} F_{cyl} + \frac{-F_{cyl}}{2} \cos{\left(2\theta + 2\phi\right)}</math><br />
<br />
The constant parts are added with the spherical components. The cosines can be added by converting them to [https://en.wikipedia.org/wiki/Phasor phasors] and adding the phasors together. The resulting phasor corresponds to one of two cylindrical lenses (see the section on Transposition), and its corresponding spherical component must be subtracted from the total spherical component.<br />
<br />
There are implementations of this at<br />
* http://opticampus.opti.vision/tools/cylinders.php<br />
* http://billauer.co.il/simulator.html<br />
<br />
=== Decentration ===<br />
Induced prism can be calculated using Prentice's rule. Similar to Vertex Distance, decentration is less of an issue for smaller power lenses.<br />
<br />
The amount of prism P induced by decentration c of a lens of power f is<br />
<br />
<math>P=cf</math><br />
<br />
1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm, and f is in diopters, then P is in prism diopters.<br />
<br />
A prism with apex angle a and refractive index n results in angle of deviation of the light d, which is equal to P prism diopters:<br />
<br />
<math>d=(n-1)a</math><br />
<br />
<br />
<math>P=100\tan{d}=100\tan((n-1)a)</math><br />
<br />
=== Vertex Distance ===<br />
See [[Vertex distance#Calculation]]<br />
<br />
==References==<br />
{{reflist}}<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Diopters&diff=16534Diopters2022-03-28T15:52:55Z<p>User: /* Gap and ratio */</p>
<hr />
<div><br />
Diopter is a measure of the [https://en.wikipedia.org/wiki/Optical_power optical power] P of a [[lens]] (or mirror) and is equal to the reciprocal of [[focal length]] in meters. The most common unit symbol for diopters is dpt, D, or m<sup>-1</sup>.<br />
<br />
<math>P = \frac{1}{f} = -\frac{1}{d}</math><br />
<br />
* In [[EM]], we use the [[cm measurement]] to calculate diopters needed to correct [[refraction]] of the eye. If you can see 50 cm clearly, your diopters will be <math>-\frac{1}{0.50}=-2 dpt</math>.<br />
<br />
* Lenses in series add their powers: if you're wearing -2 diopter contacts ([[vertex distance|adjusted for glasses strength]]) and put +1 diopter reading glasses over the contacts you're in effect wearing -1 diopters.<br />
** There are some caveats such as vertex distance, since moving the lens away effectively gives you a weaker negative lens or stronger positive lens. There is also decentration, which induces prism when the lens is moved to the side. These effects become negligible for weaker lenses.<br />
* According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.<br />
** A lens with a negative diopter sign compensates for [[nearsightedness]] while a lens with a positive diopter sign compensates for [[farsightedness]].<br />
<br />
{| class="wikitable"<br />
|+ Approximate categorizations of myopia by [[spherical]] lens power:<br />
|-<br />
| 0.00 to -0.50 dpt || Not really considered myopic, probably don't need glasses<br />
|-<br />
| -0.50 to -1.00 dpt || Mild myopia, [[normalized]] sometimes not needed<br />
|-<br />
| -1.00 to -2.50 dpt || Mild myopia, [[differentials]] possibly not needed<br />
|-<br />
| -2.50 to -3.00 dpt || Mild myopia, differentials probably needed<br />
|-<br />
| -3.00 to -6.00 dpt || Moderate myopia, glasses always needed<br />
|-<br />
| -6.00 to -10.00 dpt || High myopia<br />
|-<br />
| -10.00+ dpt || Very high myopia. Field of view significantly reduced.<br />
|}<br />
<br />
==Gap and ratio==<br />
<br />
Comparisons between two diopters is typically expressed using one of these terms:<br />
<br />
* ''diopter gap'' (or ''diopter difference''): absolute difference in diopters between two values<br />
* ''diopter ratio'': ratio of one diopter value to another (such as right eye / left eye)<br />
<br />
For example, consider the following correction:<br />
<br />
OD: -1.5 SPH / -1.5 CYL<br />
OS: -1.0 SPH / -2.0 CYL<br />
<br />
It can be expressed as a 0.5 dpt gap in both SPH and CYL, a 1.5 ratio in SPH and a 0.75 ratio in CYL:<br />
<br />
|(-1.5 dpt) - (-1.0 dpt)| = 0.5 dpt<br />
|(-1.5 dpt) - (-2.0 dpt)| = 0.5 dpt<br />
(-1.5 dpt) / (-1.0 dpt) = 1.5<br />
(-1.5 dpt) / (-2.0 dpt) = 0.75<br />
<br />
In EM articles, the term ''diopter ratio'' is often used interchangeably for left-right ''diopter gap''<ref>{{cite jake|https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/|The Diopter Ratio Trap: Don’t Favor One Eye}}</ref>, for example when talking about reducing a correction while keeping the ''gap'' the same. This can also be expressed as a [[wikipedia:Percent difference|percentage difference]] between the two diopter values<ref>{{cite jake|https://endmyopia.org/reducing-diopter-ratio-diy-patching-solution-pro-topic/|Reducing Diopter Ratio: DIY Patching Solution (PRO TOPIC)}}</ref> (e.g. the <tt>0.5 dpt</tt> difference between the right and left eyes here is equivalent to <tt>0.5 dpt / |-1.5 dpt| = 0.33</tt> or 33%).<br />
<br />
The general recommendation is that the left-right diopter gap is constant across all lenses being used. However, some old EM articles show successful cases where differentials are equalized but normalized have a 0.25 D gap.<ref>https://endmyopia.org/progress-improving-centimeter-62-90/ and https://endmyopia.org/saras-journey-truth-long-term-vision-improvement-potential/</ref><br />
<br />
Confusingly, diopter gap is also sometimes used to refer to the diff-norm gap, the difference between [[differentials]] and [[normalized]] or the [[spherical equivalent]] of that difference.<ref>https://endmyopia.org/pro-topic-managing-your-maximum-diopter-gap/</ref><br />
<br />
It is often useful to disambiguate what is being compared:<br />
* ''left-right gap'': left eye diopters minus right eye diopters, ignoring axis<br />
** In the example above, the left-right gap is +0.5 SPH -0.5 CYL.<br />
* ''diff-norm gap'': differentials diopter minus normalized diopters, ignoring axis<br />
** For example, if normalized is -2 SPH -0.5 CYL, and differentials are -0.75 SPH, the diff-norm gap is 1.25 SPH 0.5 CYL or 1.5 SPH equivalent.<br />
** The axis is ignored, and the cylinder powers are subtracted without using [[#Adding/Combining Lenses]].<br />
<br />
==Technical Details==<br />
This section is for the math-savvy people. It explains concepts in more detail, but knowledge of it is not strictly necessary to use the EM method.<br />
<br />
===Thin Lens Equation===<br />
The focal length of a lens is given by the lensmaker's equation. By assuming the lens is much thinner than the radius of curvature, therefore assuming lens thickness is zero, we get a simplified version of the lensmaker's equation. We can do some further derivation, we arrive at the thin-lens equation:<ref>see derivations at https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses</ref><br />
<br />
<math>\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}</math><br />
<br />
According to the thin lens sign convention,<br />
* di is positive if it is a real image on the opposite side of the lens as the object, and it is negative if it is a virtual image on the same side of the lens as the object.<br />
* f is positive for converging lens and negative for diverging.<br />
<br />
This is also sometimes presented in the Newtonian form:<br />
<br />
<math>\left(d_o-f\right)\left(d_i-f\right)=f^2</math><br />
<br />
====Examples====<br />
"Full correction" takes an object at infinity and produces a virtual image at your far point distance d:<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{-d}=-\frac{1}{d}</math><br />
<br />
<br />
This is the resulting equation at the beginning of the article. It also explains why the focal power is increased for objects at closer distances: mainstream optometry calls this the "add" for presbyopia, although they typically use the minimum amount required for you to see at 40 cm with full distance correction using accommodation. For example, if you choose 80 cm as the working distance for your [[differentials]] (resulting in a +1.25 dpt "add"), and your blur horizon is 50 cm (resulting in -2 dpt), the formula is<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{80\ cm}+\frac{1}{-50\ cm}=1.25\ dpt + \left(-2\ dpt\right) = -0.75\ dpt</math><br />
<br />
=== Cylinder ===<br />
A cylindrical lens of power F<sub>c</sub> has focal power F at angle θ from its axis:<br />
<br />
<math>F = F_{cyl} (\sin\theta)^2</math><br />
<br />
==== Transposition ====<br />
We can understand why there are two different ways to write a spherical and cylindrical lens combination, using the Pythagorean trigonometric identity and the complementary angle identity:<br />
<br />
<math>(\sin\theta)^2 + (\cos\theta)^2 = 1</math><br />
<br />
<math>\cos\theta = \sin{\left(90^{\circ} - \theta\right)} = -\sin{\left(\theta - 90^{\circ}\right)}</math><br />
<br />
<br />
<math>F = F_{cyl} \left( 1 - (\cos\theta)^2 \right) = F_{cyl} + \left(-F_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math><br />
<br />
We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (same as subtracting 90 degrees, since the axis is in modulo 180 degrees) to the axis, we get an equivalent combination.<br />
<br />
For example, -1 sph -1 cyl 1 axis is the same as -2 sph +1 cyl 91 axis.<br />
<br />
In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two forms are equivalent.<br />
<br />
==== Spherical Equivalent ====<br />
By calculating the average value over all angles using an integral, the result<ref>it is only necessary to integrate one or two periods: https://www.wolframalpha.com/input/?i=average+of+%28sin+x%29%5E2+from+0+to+2+pi</ref> is<br />
<br />
<math>F_{avg} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} F_{cyl} (\sin{t})^2 \,dt = \frac{1}{2} F_{cyl}</math><br />
<br />
This is why the spherical equivalent has power equal to half of the cylinder's power.<br />
<br />
==== Adding/Combining Lenses ====<br />
Multiple lens, each with spherical and cylindrical components (not necessarily at the same axis) can be added to form one lens with a spherical and cylindrical component.<br />
<br />
We can use the double angle formula to convert each cylindrical lens into a constant plus a cosine:<br />
<br />
<math>\cos{2\theta}=1-2(\sin\theta)^2</math><br />
<br />
<br />
<math>F = F_{cyl} (\sin{\left(\theta + \phi\right)})^2 = F_{cyl} \left( \frac{1-\cos{\left(2\theta + 2\phi\right)}}{2} \right) = \frac{1}{2} F_{cyl} + \frac{-F_{cyl}}{2} \cos{\left(2\theta + 2\phi\right)}</math><br />
<br />
The constant parts are added with the spherical components. The cosines can be added by converting them to [https://en.wikipedia.org/wiki/Phasor phasors] and adding the phasors together. The resulting phasor corresponds to one of two cylindrical lenses (see the section on Transposition), and its corresponding spherical component must be subtracted from the total spherical component.<br />
<br />
There are implementations of this at<br />
* http://opticampus.opti.vision/tools/cylinders.php<br />
* http://billauer.co.il/simulator.html<br />
<br />
=== Decentration ===<br />
Induced prism can be calculated using Prentice's rule. Similar to Vertex Distance, decentration is less of an issue for smaller power lenses.<br />
<br />
The amount of prism P induced by decentration c of a lens of power f is<br />
<br />
<math>P=cf</math><br />
<br />
1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm, and f is in diopters, then P is in prism diopters.<br />
<br />
A prism with apex angle a and refractive index n results in angle of deviation of the light d, which is equal to P prism diopters:<br />
<br />
<math>d=(n-1)a</math><br />
<br />
<br />
<math>P=100\tan{d}=100\tan((n-1)a)</math><br />
<br />
=== Vertex Distance ===<br />
See [[Vertex distance#Calculation]]<br />
<br />
==References==<br />
{{reflist}}<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Diopters&diff=16533Diopters2022-03-28T15:51:28Z<p>User: /* Gap and ratio */</p>
<hr />
<div><br />
Diopter is a measure of the [https://en.wikipedia.org/wiki/Optical_power optical power] P of a [[lens]] (or mirror) and is equal to the reciprocal of [[focal length]] in meters. The most common unit symbol for diopters is dpt, D, or m<sup>-1</sup>.<br />
<br />
<math>P = \frac{1}{f} = -\frac{1}{d}</math><br />
<br />
* In [[EM]], we use the [[cm measurement]] to calculate diopters needed to correct [[refraction]] of the eye. If you can see 50 cm clearly, your diopters will be <math>-\frac{1}{0.50}=-2 dpt</math>.<br />
<br />
* Lenses in series add their powers: if you're wearing -2 diopter contacts ([[vertex distance|adjusted for glasses strength]]) and put +1 diopter reading glasses over the contacts you're in effect wearing -1 diopters.<br />
** There are some caveats such as vertex distance, since moving the lens away effectively gives you a weaker negative lens or stronger positive lens. There is also decentration, which induces prism when the lens is moved to the side. These effects become negligible for weaker lenses.<br />
* According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.<br />
** A lens with a negative diopter sign compensates for [[nearsightedness]] while a lens with a positive diopter sign compensates for [[farsightedness]].<br />
<br />
{| class="wikitable"<br />
|+ Approximate categorizations of myopia by [[spherical]] lens power:<br />
|-<br />
| 0.00 to -0.50 dpt || Not really considered myopic, probably don't need glasses<br />
|-<br />
| -0.50 to -1.00 dpt || Mild myopia, [[normalized]] sometimes not needed<br />
|-<br />
| -1.00 to -2.50 dpt || Mild myopia, [[differentials]] possibly not needed<br />
|-<br />
| -2.50 to -3.00 dpt || Mild myopia, differentials probably needed<br />
|-<br />
| -3.00 to -6.00 dpt || Moderate myopia, glasses always needed<br />
|-<br />
| -6.00 to -10.00 dpt || High myopia<br />
|-<br />
| -10.00+ dpt || Very high myopia. Field of view significantly reduced.<br />
|}<br />
<br />
==Gap and ratio==<br />
<br />
Comparisons between two diopters is typically expressed using one of these terms:<br />
<br />
* ''diopter gap'' (or ''diopter difference''): absolute difference in diopters between two values<br />
* ''diopter ratio'': ratio of one diopter value to another (such as right eye / left eye)<br />
<br />
For example, consider the following correction:<br />
<br />
OD: -1.5 SPH / -1.5 CYL<br />
OS: -1.0 SPH / -2.0 CYL<br />
<br />
It can be expressed as a 0.5 dpt gap in both SPH and CYL, a 1.5 ratio in SPH and a 0.75 ratio in CYL:<br />
<br />
|(-1.5 dpt) - (-1.0 dpt)| = 0.5 dpt<br />
|(-1.5 dpt) - (-2.0 dpt)| = 0.5 dpt<br />
(-1.5 dpt) / (-1.0 dpt) = 1.5<br />
(-1.5 dpt) / (-2.0 dpt) = 0.75<br />
<br />
In EM articles, the term ''diopter ratio'' is often used interchangeably for left-right ''diopter gap''<ref>{{cite jake|https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/|The Diopter Ratio Trap: Don’t Favor One Eye}}</ref>, for example when talking about reducing a correction while keeping the ''gap'' the same. This can also be expressed as a [[wikipedia:Percent difference|percentage difference]] between the two diopter values<ref>{{cite jake|https://endmyopia.org/reducing-diopter-ratio-diy-patching-solution-pro-topic/|Reducing Diopter Ratio: DIY Patching Solution (PRO TOPIC)}}</ref> (e.g. the <tt>0.5 dpt</tt> difference between the right and left eyes here is equivalent to <tt>0.5 dpt / |-1.5 dpt| = 0.33</tt> or 33%).<br />
<br />
The general recommendation is that the left-right diopter gap is constant across all lenses being used. However, some old EM articles show successful cases where differentials are equalized but normalized have a 0.25 D gap.<ref>https://endmyopia.org/progress-improving-centimeter-62-90/ and https://endmyopia.org/saras-journey-truth-long-term-vision-improvement-potential/</ref><br />
<br />
Confusingly, diopter gap is also sometimes used to refer to the diff-norm gap, the difference between [[differentials]] and [[normalized]] or the [[spherical equivalent]] of that difference.<ref>https://endmyopia.org/pro-topic-managing-your-maximum-diopter-gap/</ref><br />
<br />
It is often useful to disambiguate what is being compared:<br />
* ''left-right gap'': left eye diopters minus right eye diopters, ignoring axis<br />
** In the example above, the left-right gap is +0.5 SPH -0.5 CYL.<br />
* ''diff-norm gap'': differentials diopter minus normalized diopters, ignoring axis<br />
** For example, if normalized is -2 SPH -0.5 CYL, and differentials are -0.75 SPH, the diff-norm gap is 1.25 SPH 0.5 CYL or 1.5 SPH equivalent.<br />
<br />
==Technical Details==<br />
This section is for the math-savvy people. It explains concepts in more detail, but knowledge of it is not strictly necessary to use the EM method.<br />
<br />
===Thin Lens Equation===<br />
The focal length of a lens is given by the lensmaker's equation. By assuming the lens is much thinner than the radius of curvature, therefore assuming lens thickness is zero, we get a simplified version of the lensmaker's equation. We can do some further derivation, we arrive at the thin-lens equation:<ref>see derivations at https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses</ref><br />
<br />
<math>\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}</math><br />
<br />
According to the thin lens sign convention,<br />
* di is positive if it is a real image on the opposite side of the lens as the object, and it is negative if it is a virtual image on the same side of the lens as the object.<br />
* f is positive for converging lens and negative for diverging.<br />
<br />
This is also sometimes presented in the Newtonian form:<br />
<br />
<math>\left(d_o-f\right)\left(d_i-f\right)=f^2</math><br />
<br />
====Examples====<br />
"Full correction" takes an object at infinity and produces a virtual image at your far point distance d:<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{-d}=-\frac{1}{d}</math><br />
<br />
<br />
This is the resulting equation at the beginning of the article. It also explains why the focal power is increased for objects at closer distances: mainstream optometry calls this the "add" for presbyopia, although they typically use the minimum amount required for you to see at 40 cm with full distance correction using accommodation. For example, if you choose 80 cm as the working distance for your [[differentials]] (resulting in a +1.25 dpt "add"), and your blur horizon is 50 cm (resulting in -2 dpt), the formula is<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{80\ cm}+\frac{1}{-50\ cm}=1.25\ dpt + \left(-2\ dpt\right) = -0.75\ dpt</math><br />
<br />
=== Cylinder ===<br />
A cylindrical lens of power F<sub>c</sub> has focal power F at angle θ from its axis:<br />
<br />
<math>F = F_{cyl} (\sin\theta)^2</math><br />
<br />
==== Transposition ====<br />
We can understand why there are two different ways to write a spherical and cylindrical lens combination, using the Pythagorean trigonometric identity and the complementary angle identity:<br />
<br />
<math>(\sin\theta)^2 + (\cos\theta)^2 = 1</math><br />
<br />
<math>\cos\theta = \sin{\left(90^{\circ} - \theta\right)} = -\sin{\left(\theta - 90^{\circ}\right)}</math><br />
<br />
<br />
<math>F = F_{cyl} \left( 1 - (\cos\theta)^2 \right) = F_{cyl} + \left(-F_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math><br />
<br />
We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (same as subtracting 90 degrees, since the axis is in modulo 180 degrees) to the axis, we get an equivalent combination.<br />
<br />
For example, -1 sph -1 cyl 1 axis is the same as -2 sph +1 cyl 91 axis.<br />
<br />
In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two forms are equivalent.<br />
<br />
==== Spherical Equivalent ====<br />
By calculating the average value over all angles using an integral, the result<ref>it is only necessary to integrate one or two periods: https://www.wolframalpha.com/input/?i=average+of+%28sin+x%29%5E2+from+0+to+2+pi</ref> is<br />
<br />
<math>F_{avg} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} F_{cyl} (\sin{t})^2 \,dt = \frac{1}{2} F_{cyl}</math><br />
<br />
This is why the spherical equivalent has power equal to half of the cylinder's power.<br />
<br />
==== Adding/Combining Lenses ====<br />
Multiple lens, each with spherical and cylindrical components (not necessarily at the same axis) can be added to form one lens with a spherical and cylindrical component.<br />
<br />
We can use the double angle formula to convert each cylindrical lens into a constant plus a cosine:<br />
<br />
<math>\cos{2\theta}=1-2(\sin\theta)^2</math><br />
<br />
<br />
<math>F = F_{cyl} (\sin{\left(\theta + \phi\right)})^2 = F_{cyl} \left( \frac{1-\cos{\left(2\theta + 2\phi\right)}}{2} \right) = \frac{1}{2} F_{cyl} + \frac{-F_{cyl}}{2} \cos{\left(2\theta + 2\phi\right)}</math><br />
<br />
The constant parts are added with the spherical components. The cosines can be added by converting them to [https://en.wikipedia.org/wiki/Phasor phasors] and adding the phasors together. The resulting phasor corresponds to one of two cylindrical lenses (see the section on Transposition), and its corresponding spherical component must be subtracted from the total spherical component.<br />
<br />
There are implementations of this at<br />
* http://opticampus.opti.vision/tools/cylinders.php<br />
* http://billauer.co.il/simulator.html<br />
<br />
=== Decentration ===<br />
Induced prism can be calculated using Prentice's rule. Similar to Vertex Distance, decentration is less of an issue for smaller power lenses.<br />
<br />
The amount of prism P induced by decentration c of a lens of power f is<br />
<br />
<math>P=cf</math><br />
<br />
1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm, and f is in diopters, then P is in prism diopters.<br />
<br />
A prism with apex angle a and refractive index n results in angle of deviation of the light d, which is equal to P prism diopters:<br />
<br />
<math>d=(n-1)a</math><br />
<br />
<br />
<math>P=100\tan{d}=100\tan((n-1)a)</math><br />
<br />
=== Vertex Distance ===<br />
See [[Vertex distance#Calculation]]<br />
<br />
==References==<br />
{{reflist}}<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Diopters&diff=16532Diopters2022-03-28T15:51:09Z<p>User: /* Gap and ratio */</p>
<hr />
<div><br />
Diopter is a measure of the [https://en.wikipedia.org/wiki/Optical_power optical power] P of a [[lens]] (or mirror) and is equal to the reciprocal of [[focal length]] in meters. The most common unit symbol for diopters is dpt, D, or m<sup>-1</sup>.<br />
<br />
<math>P = \frac{1}{f} = -\frac{1}{d}</math><br />
<br />
* In [[EM]], we use the [[cm measurement]] to calculate diopters needed to correct [[refraction]] of the eye. If you can see 50 cm clearly, your diopters will be <math>-\frac{1}{0.50}=-2 dpt</math>.<br />
<br />
* Lenses in series add their powers: if you're wearing -2 diopter contacts ([[vertex distance|adjusted for glasses strength]]) and put +1 diopter reading glasses over the contacts you're in effect wearing -1 diopters.<br />
** There are some caveats such as vertex distance, since moving the lens away effectively gives you a weaker negative lens or stronger positive lens. There is also decentration, which induces prism when the lens is moved to the side. These effects become negligible for weaker lenses.<br />
* According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.<br />
** A lens with a negative diopter sign compensates for [[nearsightedness]] while a lens with a positive diopter sign compensates for [[farsightedness]].<br />
<br />
{| class="wikitable"<br />
|+ Approximate categorizations of myopia by [[spherical]] lens power:<br />
|-<br />
| 0.00 to -0.50 dpt || Not really considered myopic, probably don't need glasses<br />
|-<br />
| -0.50 to -1.00 dpt || Mild myopia, [[normalized]] sometimes not needed<br />
|-<br />
| -1.00 to -2.50 dpt || Mild myopia, [[differentials]] possibly not needed<br />
|-<br />
| -2.50 to -3.00 dpt || Mild myopia, differentials probably needed<br />
|-<br />
| -3.00 to -6.00 dpt || Moderate myopia, glasses always needed<br />
|-<br />
| -6.00 to -10.00 dpt || High myopia<br />
|-<br />
| -10.00+ dpt || Very high myopia. Field of view significantly reduced.<br />
|}<br />
<br />
==Gap and ratio==<br />
<br />
Comparisons between two diopters is typically expressed using one of these terms:<br />
<br />
* ''diopter gap'' (or ''diopter difference''): absolute difference in diopters between two values<br />
* ''diopter ratio'': ratio of one diopter value to another (such as right eye / left eye)<br />
<br />
For example, consider the following correction:<br />
<br />
OD: -1.5 SPH / -1.5 CYL<br />
OS: -1.0 SPH / -2.0 CYL<br />
<br />
It can be expressed as a 0.5 dpt gap in both SPH and CYL, a 1.5 ratio in SPH and a 0.75 ratio in CYL:<br />
<br />
|(-1.5 dpt) - (-1.0 dpt)| = 0.5 dpt<br />
|(-1.5 dpt) - (-2.0 dpt)| = 0.5 dpt<br />
(-1.5 dpt) / (-1.0 dpt) = 1.5<br />
(-1.5 dpt) / (-2.0 dpt) = 0.75<br />
<br />
In EM articles, the term ''diopter ratio'' is often used interchangeably for left-right ''diopter gap''<ref>{{cite jake|https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/|The Diopter Ratio Trap: Don’t Favor One Eye}}</ref>, for example when talking about reducing a correction while keeping the ''gap'' the same. This can also be expressed as a [[wikipedia:Percent difference|percentage difference]] between the two diopter values<ref>{{cite jake|https://endmyopia.org/reducing-diopter-ratio-diy-patching-solution-pro-topic/|Reducing Diopter Ratio: DIY Patching Solution (PRO TOPIC)}}</ref> (e.g. the <tt>0.5 dpt</tt> difference between the right and left eyes here is equivalent to <tt>0.5 dpt / |-1.5 dpt| = 0.33</tt> or 33%).<br />
<br />
The general recommendation is that the left-right diopter gap is constant across all lenses being used. However, some old EM articles show successful cases where differentials are equalized but normalized have a 0.25 D gap.<ref>https://endmyopia.org/progress-improving-centimeter-62-90/ and https://endmyopia.org/saras-journey-truth-long-term-vision-improvement-potential/</ref><br />
<br />
Confusingly, diopter gap is also sometimes used to refer to the diff-norm gap, the difference between [[differentials]] and [[normalized]] or the [[spherical equivalent]] of that difference.<ref>https://endmyopia.org/pro-topic-managing-your-maximum-diopter-gap/</ref><br />
<br />
It is often useful to disambiguate what is being compared:<br />
* ''left-right gap'': left eye diopters minus right eye diopters, ignoring axis<br />
* In the example above, the left-right gap is +0.5 SPH -0.5 CYL.<br />
* ''diff-norm gap'': differentials diopter minus normalized diopters, ignoring axis<br />
* As an example, if normalized is -2 SPH -0.5 CYL, and differentials are -0.75 SPH, the diff-norm gap is 1.25 SPH 0.5 CYL or 1.5 SPH equivalent.<br />
<br />
==Technical Details==<br />
This section is for the math-savvy people. It explains concepts in more detail, but knowledge of it is not strictly necessary to use the EM method.<br />
<br />
===Thin Lens Equation===<br />
The focal length of a lens is given by the lensmaker's equation. By assuming the lens is much thinner than the radius of curvature, therefore assuming lens thickness is zero, we get a simplified version of the lensmaker's equation. We can do some further derivation, we arrive at the thin-lens equation:<ref>see derivations at https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses</ref><br />
<br />
<math>\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}</math><br />
<br />
According to the thin lens sign convention,<br />
* di is positive if it is a real image on the opposite side of the lens as the object, and it is negative if it is a virtual image on the same side of the lens as the object.<br />
* f is positive for converging lens and negative for diverging.<br />
<br />
This is also sometimes presented in the Newtonian form:<br />
<br />
<math>\left(d_o-f\right)\left(d_i-f\right)=f^2</math><br />
<br />
====Examples====<br />
"Full correction" takes an object at infinity and produces a virtual image at your far point distance d:<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{-d}=-\frac{1}{d}</math><br />
<br />
<br />
This is the resulting equation at the beginning of the article. It also explains why the focal power is increased for objects at closer distances: mainstream optometry calls this the "add" for presbyopia, although they typically use the minimum amount required for you to see at 40 cm with full distance correction using accommodation. For example, if you choose 80 cm as the working distance for your [[differentials]] (resulting in a +1.25 dpt "add"), and your blur horizon is 50 cm (resulting in -2 dpt), the formula is<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{80\ cm}+\frac{1}{-50\ cm}=1.25\ dpt + \left(-2\ dpt\right) = -0.75\ dpt</math><br />
<br />
=== Cylinder ===<br />
A cylindrical lens of power F<sub>c</sub> has focal power F at angle θ from its axis:<br />
<br />
<math>F = F_{cyl} (\sin\theta)^2</math><br />
<br />
==== Transposition ====<br />
We can understand why there are two different ways to write a spherical and cylindrical lens combination, using the Pythagorean trigonometric identity and the complementary angle identity:<br />
<br />
<math>(\sin\theta)^2 + (\cos\theta)^2 = 1</math><br />
<br />
<math>\cos\theta = \sin{\left(90^{\circ} - \theta\right)} = -\sin{\left(\theta - 90^{\circ}\right)}</math><br />
<br />
<br />
<math>F = F_{cyl} \left( 1 - (\cos\theta)^2 \right) = F_{cyl} + \left(-F_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math><br />
<br />
We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (same as subtracting 90 degrees, since the axis is in modulo 180 degrees) to the axis, we get an equivalent combination.<br />
<br />
For example, -1 sph -1 cyl 1 axis is the same as -2 sph +1 cyl 91 axis.<br />
<br />
In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two forms are equivalent.<br />
<br />
==== Spherical Equivalent ====<br />
By calculating the average value over all angles using an integral, the result<ref>it is only necessary to integrate one or two periods: https://www.wolframalpha.com/input/?i=average+of+%28sin+x%29%5E2+from+0+to+2+pi</ref> is<br />
<br />
<math>F_{avg} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} F_{cyl} (\sin{t})^2 \,dt = \frac{1}{2} F_{cyl}</math><br />
<br />
This is why the spherical equivalent has power equal to half of the cylinder's power.<br />
<br />
==== Adding/Combining Lenses ====<br />
Multiple lens, each with spherical and cylindrical components (not necessarily at the same axis) can be added to form one lens with a spherical and cylindrical component.<br />
<br />
We can use the double angle formula to convert each cylindrical lens into a constant plus a cosine:<br />
<br />
<math>\cos{2\theta}=1-2(\sin\theta)^2</math><br />
<br />
<br />
<math>F = F_{cyl} (\sin{\left(\theta + \phi\right)})^2 = F_{cyl} \left( \frac{1-\cos{\left(2\theta + 2\phi\right)}}{2} \right) = \frac{1}{2} F_{cyl} + \frac{-F_{cyl}}{2} \cos{\left(2\theta + 2\phi\right)}</math><br />
<br />
The constant parts are added with the spherical components. The cosines can be added by converting them to [https://en.wikipedia.org/wiki/Phasor phasors] and adding the phasors together. The resulting phasor corresponds to one of two cylindrical lenses (see the section on Transposition), and its corresponding spherical component must be subtracted from the total spherical component.<br />
<br />
There are implementations of this at<br />
* http://opticampus.opti.vision/tools/cylinders.php<br />
* http://billauer.co.il/simulator.html<br />
<br />
=== Decentration ===<br />
Induced prism can be calculated using Prentice's rule. Similar to Vertex Distance, decentration is less of an issue for smaller power lenses.<br />
<br />
The amount of prism P induced by decentration c of a lens of power f is<br />
<br />
<math>P=cf</math><br />
<br />
1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm, and f is in diopters, then P is in prism diopters.<br />
<br />
A prism with apex angle a and refractive index n results in angle of deviation of the light d, which is equal to P prism diopters:<br />
<br />
<math>d=(n-1)a</math><br />
<br />
<br />
<math>P=100\tan{d}=100\tan((n-1)a)</math><br />
<br />
=== Vertex Distance ===<br />
See [[Vertex distance#Calculation]]<br />
<br />
==References==<br />
{{reflist}}<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Diopters&diff=16531Diopters2022-03-28T15:47:19Z<p>User: /* Gap and ratio */</p>
<hr />
<div><br />
Diopter is a measure of the [https://en.wikipedia.org/wiki/Optical_power optical power] P of a [[lens]] (or mirror) and is equal to the reciprocal of [[focal length]] in meters. The most common unit symbol for diopters is dpt, D, or m<sup>-1</sup>.<br />
<br />
<math>P = \frac{1}{f} = -\frac{1}{d}</math><br />
<br />
* In [[EM]], we use the [[cm measurement]] to calculate diopters needed to correct [[refraction]] of the eye. If you can see 50 cm clearly, your diopters will be <math>-\frac{1}{0.50}=-2 dpt</math>.<br />
<br />
* Lenses in series add their powers: if you're wearing -2 diopter contacts ([[vertex distance|adjusted for glasses strength]]) and put +1 diopter reading glasses over the contacts you're in effect wearing -1 diopters.<br />
** There are some caveats such as vertex distance, since moving the lens away effectively gives you a weaker negative lens or stronger positive lens. There is also decentration, which induces prism when the lens is moved to the side. These effects become negligible for weaker lenses.<br />
* According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.<br />
** A lens with a negative diopter sign compensates for [[nearsightedness]] while a lens with a positive diopter sign compensates for [[farsightedness]].<br />
<br />
{| class="wikitable"<br />
|+ Approximate categorizations of myopia by [[spherical]] lens power:<br />
|-<br />
| 0.00 to -0.50 dpt || Not really considered myopic, probably don't need glasses<br />
|-<br />
| -0.50 to -1.00 dpt || Mild myopia, [[normalized]] sometimes not needed<br />
|-<br />
| -1.00 to -2.50 dpt || Mild myopia, [[differentials]] possibly not needed<br />
|-<br />
| -2.50 to -3.00 dpt || Mild myopia, differentials probably needed<br />
|-<br />
| -3.00 to -6.00 dpt || Moderate myopia, glasses always needed<br />
|-<br />
| -6.00 to -10.00 dpt || High myopia<br />
|-<br />
| -10.00+ dpt || Very high myopia. Field of view significantly reduced.<br />
|}<br />
<br />
==Gap and ratio==<br />
<br />
Comparisons between two diopters is typically expressed using one of these terms:<br />
<br />
* ''diopter gap'' (or ''diopter difference''): absolute difference in diopters between two values<br />
* ''diopter ratio'': ratio of one diopter value to another (such as right eye / left eye)<br />
<br />
For example, consider the following correction:<br />
<br />
OD: -1.5 SPH / -1.5 CYL<br />
OS: -1.0 SPH / -2.0 CYL<br />
<br />
It can be expressed as a 0.5 dpt gap in both SPH and CYL, a 1.5 ratio in SPH and a 0.75 ratio in CYL:<br />
<br />
|(-1.5 dpt) - (-1.0 dpt)| = 0.5 dpt<br />
|(-1.5 dpt) - (-2.0 dpt)| = 0.5 dpt<br />
(-1.5 dpt) / (-1.0 dpt) = 1.5<br />
(-1.5 dpt) / (-2.0 dpt) = 0.75<br />
<br />
In EM articles, the term ''diopter ratio'' is often used interchangeably for left-right ''diopter gap''<ref>{{cite jake|https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/|The Diopter Ratio Trap: Don’t Favor One Eye}}</ref>, for example when talking about reducing a correction while keeping the ''gap'' the same. This can also be expressed as a [[wikipedia:Percent difference|percentage difference]] between the two diopter values<ref>{{cite jake|https://endmyopia.org/reducing-diopter-ratio-diy-patching-solution-pro-topic/|Reducing Diopter Ratio: DIY Patching Solution (PRO TOPIC)}}</ref> (e.g. the <tt>0.5 dpt</tt> difference between the right and left eyes here is equivalent to <tt>0.5 dpt / |-1.5 dpt| = 0.33</tt> or 33%).<br />
<br />
The general recommendation is that the left-right diopter gap is constant across all lenses being used. However, some old EM articles show successful cases where differentials are equalized but normalized have a 0.25 D gap.<ref>https://endmyopia.org/progress-improving-centimeter-62-90/ and https://endmyopia.org/saras-journey-truth-long-term-vision-improvement-potential/</ref><br />
<br />
Confusingly, diopter gap is also sometimes used to refer to the diff-norm gap, the difference between [[differentials]] and [[normalized]] or the [[spherical equivalent]] of that difference.<ref>https://endmyopia.org/pro-topic-managing-your-maximum-diopter-gap/</ref><br />
<br />
==Technical Details==<br />
This section is for the math-savvy people. It explains concepts in more detail, but knowledge of it is not strictly necessary to use the EM method.<br />
<br />
===Thin Lens Equation===<br />
The focal length of a lens is given by the lensmaker's equation. By assuming the lens is much thinner than the radius of curvature, therefore assuming lens thickness is zero, we get a simplified version of the lensmaker's equation. We can do some further derivation, we arrive at the thin-lens equation:<ref>see derivations at https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses</ref><br />
<br />
<math>\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}</math><br />
<br />
According to the thin lens sign convention,<br />
* di is positive if it is a real image on the opposite side of the lens as the object, and it is negative if it is a virtual image on the same side of the lens as the object.<br />
* f is positive for converging lens and negative for diverging.<br />
<br />
This is also sometimes presented in the Newtonian form:<br />
<br />
<math>\left(d_o-f\right)\left(d_i-f\right)=f^2</math><br />
<br />
====Examples====<br />
"Full correction" takes an object at infinity and produces a virtual image at your far point distance d:<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{-d}=-\frac{1}{d}</math><br />
<br />
<br />
This is the resulting equation at the beginning of the article. It also explains why the focal power is increased for objects at closer distances: mainstream optometry calls this the "add" for presbyopia, although they typically use the minimum amount required for you to see at 40 cm with full distance correction using accommodation. For example, if you choose 80 cm as the working distance for your [[differentials]] (resulting in a +1.25 dpt "add"), and your blur horizon is 50 cm (resulting in -2 dpt), the formula is<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{80\ cm}+\frac{1}{-50\ cm}=1.25\ dpt + \left(-2\ dpt\right) = -0.75\ dpt</math><br />
<br />
=== Cylinder ===<br />
A cylindrical lens of power F<sub>c</sub> has focal power F at angle θ from its axis:<br />
<br />
<math>F = F_{cyl} (\sin\theta)^2</math><br />
<br />
==== Transposition ====<br />
We can understand why there are two different ways to write a spherical and cylindrical lens combination, using the Pythagorean trigonometric identity and the complementary angle identity:<br />
<br />
<math>(\sin\theta)^2 + (\cos\theta)^2 = 1</math><br />
<br />
<math>\cos\theta = \sin{\left(90^{\circ} - \theta\right)} = -\sin{\left(\theta - 90^{\circ}\right)}</math><br />
<br />
<br />
<math>F = F_{cyl} \left( 1 - (\cos\theta)^2 \right) = F_{cyl} + \left(-F_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math><br />
<br />
We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (same as subtracting 90 degrees, since the axis is in modulo 180 degrees) to the axis, we get an equivalent combination.<br />
<br />
For example, -1 sph -1 cyl 1 axis is the same as -2 sph +1 cyl 91 axis.<br />
<br />
In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two forms are equivalent.<br />
<br />
==== Spherical Equivalent ====<br />
By calculating the average value over all angles using an integral, the result<ref>it is only necessary to integrate one or two periods: https://www.wolframalpha.com/input/?i=average+of+%28sin+x%29%5E2+from+0+to+2+pi</ref> is<br />
<br />
<math>F_{avg} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} F_{cyl} (\sin{t})^2 \,dt = \frac{1}{2} F_{cyl}</math><br />
<br />
This is why the spherical equivalent has power equal to half of the cylinder's power.<br />
<br />
==== Adding/Combining Lenses ====<br />
Multiple lens, each with spherical and cylindrical components (not necessarily at the same axis) can be added to form one lens with a spherical and cylindrical component.<br />
<br />
We can use the double angle formula to convert each cylindrical lens into a constant plus a cosine:<br />
<br />
<math>\cos{2\theta}=1-2(\sin\theta)^2</math><br />
<br />
<br />
<math>F = F_{cyl} (\sin{\left(\theta + \phi\right)})^2 = F_{cyl} \left( \frac{1-\cos{\left(2\theta + 2\phi\right)}}{2} \right) = \frac{1}{2} F_{cyl} + \frac{-F_{cyl}}{2} \cos{\left(2\theta + 2\phi\right)}</math><br />
<br />
The constant parts are added with the spherical components. The cosines can be added by converting them to [https://en.wikipedia.org/wiki/Phasor phasors] and adding the phasors together. The resulting phasor corresponds to one of two cylindrical lenses (see the section on Transposition), and its corresponding spherical component must be subtracted from the total spherical component.<br />
<br />
There are implementations of this at<br />
* http://opticampus.opti.vision/tools/cylinders.php<br />
* http://billauer.co.il/simulator.html<br />
<br />
=== Decentration ===<br />
Induced prism can be calculated using Prentice's rule. Similar to Vertex Distance, decentration is less of an issue for smaller power lenses.<br />
<br />
The amount of prism P induced by decentration c of a lens of power f is<br />
<br />
<math>P=cf</math><br />
<br />
1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm, and f is in diopters, then P is in prism diopters.<br />
<br />
A prism with apex angle a and refractive index n results in angle of deviation of the light d, which is equal to P prism diopters:<br />
<br />
<math>d=(n-1)a</math><br />
<br />
<br />
<math>P=100\tan{d}=100\tan((n-1)a)</math><br />
<br />
=== Vertex Distance ===<br />
See [[Vertex distance#Calculation]]<br />
<br />
==References==<br />
{{reflist}}<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Diopters&diff=16530Diopters2022-03-28T15:34:46Z<p>User: /* Gap and ratio */</p>
<hr />
<div><br />
Diopter is a measure of the [https://en.wikipedia.org/wiki/Optical_power optical power] P of a [[lens]] (or mirror) and is equal to the reciprocal of [[focal length]] in meters. The most common unit symbol for diopters is dpt, D, or m<sup>-1</sup>.<br />
<br />
<math>P = \frac{1}{f} = -\frac{1}{d}</math><br />
<br />
* In [[EM]], we use the [[cm measurement]] to calculate diopters needed to correct [[refraction]] of the eye. If you can see 50 cm clearly, your diopters will be <math>-\frac{1}{0.50}=-2 dpt</math>.<br />
<br />
* Lenses in series add their powers: if you're wearing -2 diopter contacts ([[vertex distance|adjusted for glasses strength]]) and put +1 diopter reading glasses over the contacts you're in effect wearing -1 diopters.<br />
** There are some caveats such as vertex distance, since moving the lens away effectively gives you a weaker negative lens or stronger positive lens. There is also decentration, which induces prism when the lens is moved to the side. These effects become negligible for weaker lenses.<br />
* According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.<br />
** A lens with a negative diopter sign compensates for [[nearsightedness]] while a lens with a positive diopter sign compensates for [[farsightedness]].<br />
<br />
{| class="wikitable"<br />
|+ Approximate categorizations of myopia by [[spherical]] lens power:<br />
|-<br />
| 0.00 to -0.50 dpt || Not really considered myopic, probably don't need glasses<br />
|-<br />
| -0.50 to -1.00 dpt || Mild myopia, [[normalized]] sometimes not needed<br />
|-<br />
| -1.00 to -2.50 dpt || Mild myopia, [[differentials]] possibly not needed<br />
|-<br />
| -2.50 to -3.00 dpt || Mild myopia, differentials probably needed<br />
|-<br />
| -3.00 to -6.00 dpt || Moderate myopia, glasses always needed<br />
|-<br />
| -6.00 to -10.00 dpt || High myopia<br />
|-<br />
| -10.00+ dpt || Very high myopia. Field of view significantly reduced.<br />
|}<br />
<br />
==Gap and ratio==<br />
<br />
Comparisons between two diopters is typically expressed using one of these terms:<br />
<br />
* ''diopter gap'' (or ''diopter difference''): absolute difference in diopters between the values of the two eyes<br />
* ''diopter ratio'': ratio of the diopters in one eye over the other one (right eye / left eye)<br />
<br />
For example,the following correction:<br />
<br />
OD: -1.5 SPH / -1.5 CYL<br />
OS: -1.0 SPH / -2.0 CYL<br />
<br />
can be expressed as a 0.5 dpt gap in both SPH and CYL, a 1.5 ratio in SPH and a 0.75 ratio in CYL:<br />
<br />
|(-1.5 dpt) - (-1.0 dpt)| = 0.5 dpt<br />
|(-1.5 dpt) - (-2.0 dpt)| = 0.5 dpt<br />
(-1.5 dpt) / (-1.0 dpt) = 1.5<br />
(-1.5 dpt) / (-2.0 dpt) = 0.75<br />
<br />
Note that the term ''diopter ratio'' is often used interchangeably for ''diopter gap''<ref>{{cite jake|https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/|The Diopter Ratio Trap: Don’t Favor One Eye}}</ref>, for example when talking about reducing a correction while keeping the ''gap'' the same. This can also be expressed as a [[wikipedia:Percent difference|percentage difference]] between the two diopter values<ref>{{cite jake|https://endmyopia.org/reducing-diopter-ratio-diy-patching-solution-pro-topic/|Reducing Diopter Ratio: DIY Patching Solution (PRO TOPIC)}}</ref> (e.g. the <tt>0.5 dpt</tt> difference between the right and left eyes here is equivalent to <tt>0.5 dpt / |-1.5 dpt| = 0.33</tt> or 33%).<br />
<br />
The general recommendation is that the diopter gap is constant across all lenses being used. However, some old EM articles show successful cases where differentials are equalized but normalized have a 0.25 D gap.<ref>https://endmyopia.org/progress-improving-centimeter-62-90/ and https://endmyopia.org/saras-journey-truth-long-term-vision-improvement-potential/</ref><br />
<br />
Confusingly, diopter gap is also sometimes used to refer to the [[spherical equivalent]] difference between [[differentials]] and [[normalized]].<ref>https://endmyopia.org/pro-topic-managing-your-maximum-diopter-gap/</ref><br />
<br />
==Technical Details==<br />
This section is for the math-savvy people. It explains concepts in more detail, but knowledge of it is not strictly necessary to use the EM method.<br />
<br />
===Thin Lens Equation===<br />
The focal length of a lens is given by the lensmaker's equation. By assuming the lens is much thinner than the radius of curvature, therefore assuming lens thickness is zero, we get a simplified version of the lensmaker's equation. We can do some further derivation, we arrive at the thin-lens equation:<ref>see derivations at https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses</ref><br />
<br />
<math>\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}</math><br />
<br />
According to the thin lens sign convention,<br />
* di is positive if it is a real image on the opposite side of the lens as the object, and it is negative if it is a virtual image on the same side of the lens as the object.<br />
* f is positive for converging lens and negative for diverging.<br />
<br />
This is also sometimes presented in the Newtonian form:<br />
<br />
<math>\left(d_o-f\right)\left(d_i-f\right)=f^2</math><br />
<br />
====Examples====<br />
"Full correction" takes an object at infinity and produces a virtual image at your far point distance d:<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{-d}=-\frac{1}{d}</math><br />
<br />
<br />
This is the resulting equation at the beginning of the article. It also explains why the focal power is increased for objects at closer distances: mainstream optometry calls this the "add" for presbyopia, although they typically use the minimum amount required for you to see at 40 cm with full distance correction using accommodation. For example, if you choose 80 cm as the working distance for your [[differentials]] (resulting in a +1.25 dpt "add"), and your blur horizon is 50 cm (resulting in -2 dpt), the formula is<br />
<br />
<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{80\ cm}+\frac{1}{-50\ cm}=1.25\ dpt + \left(-2\ dpt\right) = -0.75\ dpt</math><br />
<br />
=== Cylinder ===<br />
A cylindrical lens of power F<sub>c</sub> has focal power F at angle θ from its axis:<br />
<br />
<math>F = F_{cyl} (\sin\theta)^2</math><br />
<br />
==== Transposition ====<br />
We can understand why there are two different ways to write a spherical and cylindrical lens combination, using the Pythagorean trigonometric identity and the complementary angle identity:<br />
<br />
<math>(\sin\theta)^2 + (\cos\theta)^2 = 1</math><br />
<br />
<math>\cos\theta = \sin{\left(90^{\circ} - \theta\right)} = -\sin{\left(\theta - 90^{\circ}\right)}</math><br />
<br />
<br />
<math>F = F_{cyl} \left( 1 - (\cos\theta)^2 \right) = F_{cyl} + \left(-F_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math><br />
<br />
We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (same as subtracting 90 degrees, since the axis is in modulo 180 degrees) to the axis, we get an equivalent combination.<br />
<br />
For example, -1 sph -1 cyl 1 axis is the same as -2 sph +1 cyl 91 axis.<br />
<br />
In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two forms are equivalent.<br />
<br />
==== Spherical Equivalent ====<br />
By calculating the average value over all angles using an integral, the result<ref>it is only necessary to integrate one or two periods: https://www.wolframalpha.com/input/?i=average+of+%28sin+x%29%5E2+from+0+to+2+pi</ref> is<br />
<br />
<math>F_{avg} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} F_{cyl} (\sin{t})^2 \,dt = \frac{1}{2} F_{cyl}</math><br />
<br />
This is why the spherical equivalent has power equal to half of the cylinder's power.<br />
<br />
==== Adding/Combining Lenses ====<br />
Multiple lens, each with spherical and cylindrical components (not necessarily at the same axis) can be added to form one lens with a spherical and cylindrical component.<br />
<br />
We can use the double angle formula to convert each cylindrical lens into a constant plus a cosine:<br />
<br />
<math>\cos{2\theta}=1-2(\sin\theta)^2</math><br />
<br />
<br />
<math>F = F_{cyl} (\sin{\left(\theta + \phi\right)})^2 = F_{cyl} \left( \frac{1-\cos{\left(2\theta + 2\phi\right)}}{2} \right) = \frac{1}{2} F_{cyl} + \frac{-F_{cyl}}{2} \cos{\left(2\theta + 2\phi\right)}</math><br />
<br />
The constant parts are added with the spherical components. The cosines can be added by converting them to [https://en.wikipedia.org/wiki/Phasor phasors] and adding the phasors together. The resulting phasor corresponds to one of two cylindrical lenses (see the section on Transposition), and its corresponding spherical component must be subtracted from the total spherical component.<br />
<br />
There are implementations of this at<br />
* http://opticampus.opti.vision/tools/cylinders.php<br />
* http://billauer.co.il/simulator.html<br />
<br />
=== Decentration ===<br />
Induced prism can be calculated using Prentice's rule. Similar to Vertex Distance, decentration is less of an issue for smaller power lenses.<br />
<br />
The amount of prism P induced by decentration c of a lens of power f is<br />
<br />
<math>P=cf</math><br />
<br />
1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm, and f is in diopters, then P is in prism diopters.<br />
<br />
A prism with apex angle a and refractive index n results in angle of deviation of the light d, which is equal to P prism diopters:<br />
<br />
<math>d=(n-1)a</math><br />
<br />
<br />
<math>P=100\tan{d}=100\tan((n-1)a)</math><br />
<br />
=== Vertex Distance ===<br />
See [[Vertex distance#Calculation]]<br />
<br />
==References==<br />
{{reflist}}<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Guide:High_diopter_gap&diff=16529Guide:High diopter gap2022-03-28T15:32:48Z<p>User: </p>
<hr />
<div>If you are here, chances are that you have a large left-right [[diopter gap]] ([[diopter ratio]] exceeding 20%), such as -1 diopter or less of correction in one eye while having -4 diopters or more in the other. This goes beyond the typical case of over compensated [[ocular dominance]], though it may have begun that way. This may well be what is known as amblyopia, or "lazy eye". If this condition has been present since birth and/or is a medical condition it is probable that there are limits to how much the EndMyopia method can help you; but you won’t know what they are unless you try. Most often amblyopia is treated with [[vision training]]. If you seek out a behavioral optometrist they may be able to aid you with therapies you can use in conjunction with EndMyopia, though in theory a determined person would be able to improve either way. If the condition is accompanied by a [[convergence]] issue keep in mind this method only deals with [[refractive state]] not medical conditions. You should have a full eye health screening by an ophthalmologist on a regular basis. <br />
<br />
If this diopter gap happened more recently, take inventory of how you are using your eyes to create this one sided stimulus, since this will be important to address as you proceed.<br />
<br />
==How to proceed==<br />
You will need to learn the method, and just like anyone else you will need to tailor it to your own specific correction needs. If you have not already start with the [https://endmyopia.org/7-day-e-mail-guide-sign-up-page/ 7 Day free email series]. Once you have done that you can get very serious about exploring the additional resources available to you. Your process will proceed much the same as anyone else using the EndMyopia method, except that you will be focusing on that one weaker eye. Your [[differentials]] will probably be plano (zero correction) or very low on one side and properly set for the weaker eye so that it can engage in the stimulus. It is important to engage that weaker eye and not continue to rely on the stronger one alone. <br />
<br />
You will need to incorporate [[patching]], probably more frequently than is typically recommended. However, make sure you are being mindful to “listen” to your eyes. The visual cortex doesn’t typically like over zealous patching; so in between sessions you might try this student’s tag-in method [https://www.youtube.com/watch?v=GSLpywu8goI&t=7s "Tag-In Method"] to re-engage that weaker eye.<br />
After the standard 4-6 weeks with differentials you will want to get [[normalized]] but in your case you will have to make exceptions to the typical [[equalizing]] approach in that you will have multiple monocular (single eye) reductions in a row throughout the process. It is even more important as you proceed to be patient and <u>not reduce too soon or too much</u>. Severe under correction will be counter productive to progress. You will likely find that your improvements will come slower than the typical student of EndMyopia since it is not uncommon for monocular reductions to take longer than binocular reductions. It is also not uncommon in monocular reductions to need to step back to the previous correction for a few weeks from time to time to help reset the clarity reference and avoid blur adaptation.<br />
<br />
==See Also==<br />
<br />
[[Blur adaptation]]<br />
<br />
==References==<br />
https://www.optometrists.org/vision-therapy-for-lazy-eye/amblyopia-lazy-eye/</div>Userhttps://wiki.endmyopia.org/index.php?title=Guide:High_diopter_gap&diff=16528Guide:High diopter gap2022-03-28T15:32:17Z<p>User: </p>
<hr />
<div>If you are here, chances are that you have a large left-right diopter gap ([[diopter ratio]] exceeding 20%), such as -1 diopter or less of correction in one eye while having -4 diopters or more in the other. This goes beyond the typical case of over compensated [[ocular dominance]], though it may have begun that way. This may well be what is known as amblyopia, or "lazy eye". If this condition has been present since birth and/or is a medical condition it is probable that there are limits to how much the EndMyopia method can help you; but you won’t know what they are unless you try. Most often amblyopia is treated with [[vision training]]. If you seek out a behavioral optometrist they may be able to aid you with therapies you can use in conjunction with EndMyopia, though in theory a determined person would be able to improve either way. If the condition is accompanied by a [[convergence]] issue keep in mind this method only deals with [[refractive state]] not medical conditions. You should have a full eye health screening by an ophthalmologist on a regular basis. <br />
<br />
If this [[diopter ratio]] gap happened more recently take inventory of how you are using your eyes to create this one sided stimulus, this will be important to address as you proceed.<br />
<br />
==How to proceed==<br />
You will need to learn the method, and just like anyone else you will need to tailor it to your own specific correction needs. If you have not already start with the [https://endmyopia.org/7-day-e-mail-guide-sign-up-page/ 7 Day free email series]. Once you have done that you can get very serious about exploring the additional resources available to you. Your process will proceed much the same as anyone else using the EndMyopia method, except that you will be focusing on that one weaker eye. Your [[differentials]] will probably be plano (zero correction) or very low on one side and properly set for the weaker eye so that it can engage in the stimulus. It is important to engage that weaker eye and not continue to rely on the stronger one alone. <br />
<br />
You will need to incorporate [[patching]], probably more frequently than is typically recommended. However, make sure you are being mindful to “listen” to your eyes. The visual cortex doesn’t typically like over zealous patching; so in between sessions you might try this student’s tag-in method [https://www.youtube.com/watch?v=GSLpywu8goI&t=7s "Tag-In Method"] to re-engage that weaker eye.<br />
After the standard 4-6 weeks with differentials you will want to get [[normalized]] but in your case you will have to make exceptions to the typical [[equalizing]] approach in that you will have multiple monocular (single eye) reductions in a row throughout the process. It is even more important as you proceed to be patient and <u>not reduce too soon or too much</u>. Severe under correction will be counter productive to progress. You will likely find that your improvements will come slower than the typical student of EndMyopia since it is not uncommon for monocular reductions to take longer than binocular reductions. It is also not uncommon in monocular reductions to need to step back to the previous correction for a few weeks from time to time to help reset the clarity reference and avoid blur adaptation.<br />
<br />
==See Also==<br />
<br />
[[Blur adaptation]]<br />
<br />
==References==<br />
https://www.optometrists.org/vision-therapy-for-lazy-eye/amblyopia-lazy-eye/</div>Userhttps://wiki.endmyopia.org/index.php?title=Guide:Reducing_lens_complexity&diff=16527Guide:Reducing lens complexity2022-03-28T15:29:55Z<p>User: /* How to reduce lens complexity */</p>
<hr />
<div><br />
<br />
TODO: this article needs to be expanded for edge cases like already low diopters.<br />
<br />
==When to reduce lens complexity==<br />
<br />
[[Lens complexity]] is best reduced before getting into the [[low diopters]] range. Ideally, both eyes would be equal before the normalized correction reaches -1.5 [[diopters]].{{citation needed}}<br />
<br />
==How to reduce lens complexity==<br />
<br />
'''Make your first reduction a simple [[spherical]] reduction. This will teach you the basics of the [[EndMyopia]] methods.'''<br />
<br />
There are two types of reductions:<br />
<br />
* <div>A simple reduction is a 0.25 [[diopter]] drop in lense power for both eyes, simultaneously</div><br />
* <div>An equalizing reduction is a 0.25 [[diopter]] drop in lense power for one eye, the eye with greater correction (more negative)</div><br />
<br />
An [[equalizing]] reduction is done to bring the eyes closer to having the same level of correction. Jake said that "...if you do reduce the ratio, you should have at least 2 regular spherical reductions in between."<ref>https://community.endmyopia.org/t/key-to-patching-successfully-reducing-diopter-ratio/333/6</ref> This is not always possible, especially when [[Guide:High diopter gap|high anisometropia]] is involved.<br />
<br />
Either type of reduction can be applied to [[spherical]] power or [[cylindrical]] power.<br />
<br />
'''There are four rules for reducing complexity:'''<br />
# <div>Alternate types of reductions. Simple > Equalizing > Simple > Equalizing...</div><br />
# <div>Change only spherical or only cylindrical and never both simultaneously.</div><br />
# <div>For an equalizing reduction, change both differential lenses and normalized lenses simultaneously to keep the [[focal planes]] in sync.</div><br />
# <div>For a simple reduction, change differential lenses a few weeks after normalized lenses to keep changes to [[focal planes]] to a minimum.</div><br />
<br />
<br />
'''A note on rule 3 and rule 4:''' Keeping focal planes in sync is a higher priority than keeping changes to focal planes to a minimum, thus rule 3 exists.<br />
<br />
{| class="wikitable" style="text-align:center;"<br />
|+ Example Spherical Reduction Schedule<br />
|-<br />
! style="text-align:left;" | Reduction Type<br />
! colspan="2" | Normalized<br />
! colspan="2" | Differentials<br />
! style="text-align:left;" | Explanation<br />
|-<br />
| style="text-align:left;" |<br />
| Left<br />
| Right<br />
| Left<br />
| Right<br />
| style="text-align:left;" |<br />
|-<br />
| rowspan="2" style="text-align:left;" |<br />
| -3.50<br />
| -4.00<br />
| -2.25<br />
| -2.75<br />
| style="text-align:left;" | This is the '''starting point'''.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 8 - 16 weeks<br />
|<br />
|-<br />
| rowspan="4" | Simple<br />
| -3.25<br />
| -3.75<br />
|<br />
|<br />
| style="text-align:left;" | Perform normalized reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
| (rule 4)<br />
|-<br />
|<br />
|<br />
| -2.00<br />
| -2.50<br />
| style="text-align:left;" | Perform differential reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
|<br />
|- style="font-weight:bold;"<br />
| rowspan="2" | Equalizing<br />
| -3.25<br />
| -3.50<br />
| -2.00<br />
| -2.25<br />
| style="text-align:left;" | Both norms and diffs are reduced simultaneously. (rule 3)<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center; font-weight:bold;" | wait 8 - 16 weeks<br />
|<br />
|-<br />
| rowspan="4" | Simple<br />
| -3.00<br />
| -3.25<br />
|<br />
|<br />
| style="text-align:left;" | Perform normalized reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
| (rule 4)<br />
|-<br />
|<br />
|<br />
| -1.75<br />
| -2.00<br />
| style="text-align:left;" | Perform differential reduction.<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center;" | wait 4 - 8 weeks<br />
|<br />
|- style="font-weight:bold;"<br />
| rowspan="2" | Equalizing<br />
| -3.00<br />
| -3.00<br />
| -1.75<br />
| -1.75<br />
| style="text-align:left;" | Both norms and diffs are reduced simultaneously. (rule 3)<br />
|- style="text-align:left;"<br />
| colspan="4" style="text-align:center; font-weight:bold;" | wait 8 - 16 weeks<br />
|<br />
|}<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
==See also==<br />
* [[Equalizing]]<br />
<br />
* [[Guide:Resolving double vision | Resolving double vision]]<br />
<br />
* [[reduction | Reduction]]<br />
<br />
[[Category:Guides]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Accommodation&diff=16513Accommodation2022-03-20T22:13:10Z<p>User: </p>
<hr />
<div>'''Accommodation''' is the ability of the healthy eye to focus on both near and far objects. The relaxed state of the [[ciliary muscle]] is distance vision, and the flexed state is near vision. <br />
<br />
Kids start with a lot of power of accommodation (about 25 D). As you age, the lens in your eye becomes less flexible, resulting in less power of accommodation, which is called [[presbyopia]], especially when it is less than 2.5 D (40 cm through distance correction).<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Presbyopia&diff=16512Presbyopia2022-03-20T22:11:40Z<p>User: /* Correction */</p>
<hr />
<div>Presbyopia is the hardening of the [[lens]] in the [[eyeballs]] such that it becomes difficult to see [[near work]]. This is common in older adults and is commonly treated with [[reading glasses]] (reduced minus for myopes), progressive lenses, or [[bifocals]].<br />
<br />
==Correction==<br />
As you age, the lens in your eye becomes less flexible. This makes [[accommodation]] more difficult and brings on "arms are not long enough to read" symptoms. Someone may be both [[myopic]] and presbyopic, and have deficits in both near and far vision. Your [[Prescription]] will have an "Add" section specifying bifocals or multifocals if you have diagnosed presbyopia, or if your doctor thinks it best to reduce eye strain.<br />
<br />
===Two glasses===<br />
It is an option to have two pairs of glasses, one for close-up, and one for distance, instead of trying to combine both near and far corrections in one pair of glasses.<br />
<br />
===Bifocals===<br />
Glasses with a lower section that is specifically for close work.<br />
<br />
===Progressive lenses===<br />
Glasses with a gradient from zero to near plus addition spherical power from top to bottom.<br />
<br />
===Multifocals===<br />
Contacts that have sections for near and far work, which the [[visual cortex]] will selectively use when looking at different distances.<br />
<br />
== Measuring ==<br />
To determine '''power of accommodation''', also sometimes called '''amplitude of accommodation''', measure '''far power''' and '''near power'''.<br />
<br />
'''Far power''' is straightforward, and it’s the typical [[cm measurement]]: just measure the furthest distance you can see clearly without blur, with a lens to adjust as needed. The far power is ''1/(distance to blur) - (lens power)''.<br />
<br />
* For example, 80 cm with a -0.25 lens is calculated as 1/(80 cm) - (-0.25 D) = 1.25 D + 0.25 D = 1.5 D.<br />
* It might be useful to use a plus lens to measure low myopia. For example, 80 cm with a +0.75 lens is calculated as 1/(80 cm) - (+0.75 D) = 0.5 D.<br />
<br />
'''Near power''' is the same, but measure the '''closest''' distance you can see clearly without blur.<br />
<br />
* For example, if the closest you can see is 10 cm without lenses, it’s calculated as 1/(10 cm) - 0 = 10 D.<br />
* It might be useful to use a big minus lens to measure young people (don’t look through it for too long!). In the example above, you expect to see as close as 50 cm with a -8 lens, which is 1/(50 cm) - (-8 D) = 2 D + 8 D = 10 D.<br />
<br />
The '''power of accommodation''' is (near power) - (far power). With the first example in each of the above, it would be 10 D - 1.5 D = 8.5 D.<br />
<br />
A person is generally considered to have presbyopia [[wikipedia:if and only if | iff]] his power of accommodation is less than 2.5 D.<br />
<br />
===Caveats===<br />
<br />
This technique might need to be refined for cylinder, if spherical equivalent is not used.<br />
<br />
The cornea and lens actually have more power because the total power has to focus the image on your retina, but they cancel out in the subtraction step, so it’s easier to ignore them.<br />
<br />
== Videos ==<br />
<br />
{{#ev:vimeo|284921410||inline}}<br/><br />
{{#ev:youtube|UMAjh11RL5A||inline}}<br/><br />
{{#ev:youtube|QvmOkVjwPyI||inline}}<br />
<br />
== Resources ==<br />
<br />
* Here is a resource that may be of interest to people with presbyopia that was found in the Discord chat. The resource is used for training convergence. http://www.i-see.org/rizzi_charts_readvertical.pdf<br />
<br />
[[Category:Articles]]<br />
[[Category:Eye conditions]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Pseudomyopia&diff=16498Pseudomyopia2022-03-13T04:45:29Z<p>User: </p>
<hr />
<div><br />
'''Pseudomyopia''' is a temporary shift towards near-sightness and occurs when the [[ciliary muscle]] inside of your eye temporarily locks up due to extended periods of closeup focus, resulting in [[blur]]red distance vision. This is usually the condition people get before they go to the optometrist, and then go onto to develop [[lens-induced myopia]]. If the ciliary muscle spasm is not relieved, then that muscle spasm's degree can worsen over time. Now, it will take longer to fully relax that muscle. Proper [[eye strain]] management and [[active focus]] habits will help to tackle this.<br />
<br />
The [[3 hour rule]] is useful to avoid a lock up of the [[ciliary muscle]], but the [[20-20-20 rule]] is questionable.<br />
==Videos==<br />
{{#ev:youtube|eW4GlNrzZmw}}<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
== See also ==<br />
* [[3 hour rule]]<br />
* [[20-20-20 rule]]<br />
* [[Low myopia]]<br />
* [[Strain Awareness]]<br />
<br />
[[Category:Articles]]<br />
[[Category:Eye conditions]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Accommodation&diff=16478Accommodation2022-03-09T18:01:40Z<p>User: </p>
<hr />
<div>'''Accommodation''' is the ability of the healthy eye to focus on both near and far objects. The relaxed state of the [[ciliary muscle]] is distance vision, and the flexed state is near vision. <br />
<br />
As you age, the lens in your eye becomes less flexible, resulting in [[presbyopia]].<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Presbyopia&diff=16477Presbyopia2022-03-09T18:00:32Z<p>User: </p>
<hr />
<div>Presbyopia is the hardening of the [[lens]] in the [[eyeballs]] such that it becomes difficult to see [[near work]]. This is common in older adults and is commonly treated with [[reading glasses]] (reduced minus for myopes), progressive lenses, or [[bifocals]].<br />
<br />
==Correction==<br />
As you age, the lens in your eye becomes less flexible. This makes [[accommodation]] more difficult and brings on "arms are not long enough to read" symptoms. Someone may be both [[myopic]] and presbyopic, and have deficits in both near and far vision. Your [[Prescription]] will have an "Add" section specifying bifocals or multifocals if you have diagnosed presbyopia, or if your doctor thinks it best to reduce eye strain.<br />
<br />
===Two glasses===<br />
Having two pairs of glasses, one for close-up, and one for distance, instead of trying to combine both near and far corrections in one pair of glasses, is an option.<br />
<br />
===Bifocals===<br />
Glasses with a lower section that is specifically for close work.<br />
<br />
===Multifocals===<br />
Contacts that have sections for near and far work, which the [[visual cortex]] will selectively use when looking at different distances.<br />
<br />
== Measuring ==<br />
To determine '''power of accommodation''', also sometimes called '''amplitude of accommodation''', measure '''far power''' and '''near power'''.<br />
<br />
'''Far power''' is straightforward, and it’s the typical [[cm measurement]]: just measure the furthest distance you can see clearly without blur, with a lens to adjust as needed. The far power is ''1/(distance to blur) - (lens power)''.<br />
<br />
* For example, 80 cm with a -0.25 lens is calculated as 1/(80 cm) - (-0.25 D) = 1.25 D + 0.25 D = 1.5 D.<br />
* It might be useful to use a plus lens to measure low myopia. For example, 80 cm with a +0.75 lens is calculated as 1/(80 cm) - (+0.75 D) = 0.5 D.<br />
<br />
'''Near power''' is the same, but measure the '''closest''' distance you can see clearly without blur.<br />
<br />
* For example, if the closest you can see is 10 cm without lenses, it’s calculated as 1/(10 cm) - 0 = 10 D.<br />
* It might be useful to use a big minus lens to measure young people (don’t look through it for too long!). In the example above, you expect to see as close as 50 cm with a -8 lens, which is 1/(50 cm) - (-8 D) = 2 D + 8 D = 10 D.<br />
<br />
The '''power of accommodation''' is (near power) - (far power). With the first example in each of the above, it would be 10 D - 1.5 D = 8.5 D.<br />
<br />
A person is generally considered to have presbyopia [[wikipedia:if and only if | iff]] his power of accommodation is less than 2.5 D.<br />
<br />
===Caveats===<br />
<br />
This technique might need to be refined for cylinder, if spherical equivalent is not used.<br />
<br />
The cornea and lens actually have more power because the total power has to focus the image on your retina, but they cancel out in the subtraction step, so it’s easier to ignore them.<br />
<br />
== Videos ==<br />
<br />
{{#ev:vimeo|284921410||inline}}<br/><br />
{{#ev:youtube|UMAjh11RL5A||inline}}<br/><br />
{{#ev:youtube|QvmOkVjwPyI||inline}}<br />
<br />
== Resources ==<br />
<br />
* Here is a resource that may be of interest to people with presbyopia that was found in the Discord chat. The resource is used for training convergence. http://www.i-see.org/rizzi_charts_readvertical.pdf<br />
<br />
[[Category:Articles]]<br />
[[Category:Eye conditions]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Correction&diff=16476Correction2022-03-09T17:58:37Z<p>User: </p>
<hr />
<div>An [[optometrist]] will test your vision and determine the amount of refractive error in your eyes, and write a "prescription" as close as possible to that. A standard "prescription" should correct your vision so that there is no [[blur]] at 20 feet. If you can not see clearly on your corrective lenses at 20 feet, see your optometrist and make sure you know about and understand any underlying conditions you have that affect your eyesight. Remember that having refractive error does not indicate a medical condition, despite the implication in the word "prescription".<br />
<br />
A "prescription" may look like this:<br />
{| class="wikitable"<br />
|-<br />
!Rx <br />
![[Sphere|SPH]]<br />
![[Cylinder|CYL]]<br />
![[Axis|AXIS]]<br />
![[Prism|PRISM]]<br />
![[Prism|BASE]]<br />
![[Presbyopia|Add]]<br />
|-<br />
| O.D.<br />
| -2.0<br />
| -0.5<br />
| 130<br />
| 1Δ<br />
| BO<br />
| +1.5<br />
|-<br />
| O.S.<br />
| -2.25<br />
| -0.75<br />
| 42<br />
| 2Δ<br />
| BI<br />
| +1.25<br />
|}<br />
<br />
* OD is oculus dextrus, or Latin for right eye.<br />
* OS is oculus sinister, or Latin for left eye.<br />
* BO is Base out, BI is Base in, BU is Base up and BD is Base down for [[prism]]<br />
<br />
[[Pupillary Distance]] or PD, is the final set of numbers you need to be aware of. Most likely this is not listed on your "prescription" you will need to ask for it or [https://endmyopia.org/how-to-measure-pd-pupillary-distance/ measure it yourself]. Some optometrists will charge you e.g. $30 to tell you your PD, but many others will tell you for free. <br />
<br />
==Rounding==<br />
You will note that most "prescriptions" will round to the nearest quarter [[diopter]]. This is the level of precision available in standard pre-ground lenses, which make glasses cheaper and faster to make than custom ground lenses. You may have a more precise prescription if it is written for specific lens grinding systems, or a less precise prescription if it is written for contacts.<br />
<br />
==Contacts Vs Glasses==<br />
''See also [[Lens#Glasses or Contacts]]''<br />
<br />
Your "prescription" is specifically written for either contacts or glasses. [[Vertex Distance]] plays a role in effective lens strength, so the contacts which sit closer to your eye may be written with less correction than glasses. Vertex Distance is hard to measure, and contacts may act differently as the eye adapts to them, so if you have a strong lens your optometrist may need to do additional refraction tests with the contacts in and adjust your prescription slightly.<br />
<br />
==See also==<br />
* [[Normalized]]<br />
* [[Differentials]]<br />
* [[20/20 correction]]<br />
* [[Overcorrection]]<br />
* [[Guide:Reading glasses prescriptions]]<br />
* [[:Category:Lens selections]]<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Correction&diff=16475Correction2022-03-09T17:57:36Z<p>User: </p>
<hr />
<div>An [[optometrist]] will test your vision and determine the amount of refractive error in your eyes, and write a "prescription" as close as possible to that. A standard "prescription" should correct your vision so that there is no [[blur]] at 20 feet. If you can not see clearly on your corrective lenses at 20 feet, see your optometrist and make sure you know about and understand any underlying conditions you have that affect your eyesight. Remember that having refractive error does not indicate a medical condition, despite the implication in the word "prescription".<br />
<br />
A "prescription" may look like this:<br />
{| class="wikitable"<br />
|-<br />
!Rx <br />
![[Sphere|SPH]]<br />
![[Cylinder|CYL]]<br />
![[Axis|AXIS]]<br />
![[Prism|PRISM]]<br />
![[Prism|BASE]]<br />
![[Accommodation#Presbyopia|Add]]<br />
|-<br />
| O.D.<br />
| -2.0<br />
| -0.5<br />
| 130<br />
| 1Δ<br />
| BO<br />
| +1.5<br />
|-<br />
| O.S.<br />
| -2.25<br />
| -0.75<br />
| 42<br />
| 2Δ<br />
| BI<br />
| +1.25<br />
|}<br />
<br />
* OD is oculus dextrus, or Latin for right eye.<br />
* OS is oculus sinister, or Latin for left eye.<br />
* BO is Base out, BI is Base in, BU is Base up and BD is Base down for [[prism]]<br />
<br />
[[Pupillary Distance]] or PD, is the final set of numbers you need to be aware of. Most likely this is not listed on your "prescription" you will need to ask for it or [https://endmyopia.org/how-to-measure-pd-pupillary-distance/ measure it yourself]. Some optometrists will charge you e.g. $30 to tell you your PD, but many others will tell you for free. <br />
<br />
==Rounding==<br />
You will note that most "prescriptions" will round to the nearest quarter [[diopter]]. This is the level of precision available in standard pre-ground lenses, which make glasses cheaper and faster to make than custom ground lenses. You may have a more precise prescription if it is written for specific lens grinding systems, or a less precise prescription if it is written for contacts.<br />
<br />
==Contacts Vs Glasses==<br />
''See also [[Lens#Glasses or Contacts]]''<br />
<br />
Your "prescription" is specifically written for either contacts or glasses. [[Vertex Distance]] plays a role in effective lens strength, so the contacts which sit closer to your eye may be written with less correction than glasses. Vertex Distance is hard to measure, and contacts may act differently as the eye adapts to them, so if you have a strong lens your optometrist may need to do additional refraction tests with the contacts in and adjust your prescription slightly.<br />
<br />
==See also==<br />
* [[Normalized]]<br />
* [[Differentials]]<br />
* [[20/20 correction]]<br />
* [[Overcorrection]]<br />
* [[Guide:Reading glasses prescriptions]]<br />
* [[:Category:Lens selections]]<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Correction&diff=16474Correction2022-03-09T17:57:16Z<p>User: </p>
<hr />
<div>An [[optometrist]] will test your vision and determine the amount of refractive error in your eyes, and write a "prescription" as close as possible to that. A standard "prescription" should correct your vision so that there is no [[blur]] at 20 feet. If you can not see clearly on your corrective lenses at 20 feet, see your optometrist and make sure you know about and understand any underlying conditions you have that affect your eyesight. Remember that having refractive error does not indicate a medical condition, despite the implication in the word "prescription".<br />
<br />
A "prescription" may look like this:<br />
{| class="wikitable"<br />
|-<br />
!Rx <br />
![[Sphere|SPH]]<br />
![[Cylinder|CYL]]<br />
![[Axis|AXIS]]<br />
![[PRISM]]<br />
![[PRISM|BASE]]<br />
![[Accommodation#Presbyopia|Add]]<br />
|-<br />
| O.D.<br />
| -2.0<br />
| -0.5<br />
| 130<br />
| 1Δ<br />
| BO<br />
| +1.5<br />
|-<br />
| O.S.<br />
| -2.25<br />
| -0.75<br />
| 42<br />
| 2Δ<br />
| BI<br />
| +1.25<br />
|}<br />
<br />
* OD is oculus dextrus, or Latin for right eye.<br />
* OS is oculus sinister, or Latin for left eye.<br />
* BO is Base out, BI is Base in, BU is Base up and BD is Base down for [[prism]]<br />
<br />
[[Pupillary Distance]] or PD, is the final set of numbers you need to be aware of. Most likely this is not listed on your "prescription" you will need to ask for it or [https://endmyopia.org/how-to-measure-pd-pupillary-distance/ measure it yourself]. Some optometrists will charge you e.g. $30 to tell you your PD, but many others will tell you for free. <br />
<br />
==Rounding==<br />
You will note that most "prescriptions" will round to the nearest quarter [[diopter]]. This is the level of precision available in standard pre-ground lenses, which make glasses cheaper and faster to make than custom ground lenses. You may have a more precise prescription if it is written for specific lens grinding systems, or a less precise prescription if it is written for contacts.<br />
<br />
==Contacts Vs Glasses==<br />
''See also [[Lens#Glasses or Contacts]]''<br />
<br />
Your "prescription" is specifically written for either contacts or glasses. [[Vertex Distance]] plays a role in effective lens strength, so the contacts which sit closer to your eye may be written with less correction than glasses. Vertex Distance is hard to measure, and contacts may act differently as the eye adapts to them, so if you have a strong lens your optometrist may need to do additional refraction tests with the contacts in and adjust your prescription slightly.<br />
<br />
==See also==<br />
* [[Normalized]]<br />
* [[Differentials]]<br />
* [[20/20 correction]]<br />
* [[Overcorrection]]<br />
* [[Guide:Reading glasses prescriptions]]<br />
* [[:Category:Lens selections]]<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Overcorrection&diff=16473Overcorrection2022-03-09T17:55:55Z<p>User: </p>
<hr />
<div>'''''Overcorrection''''' ('''''full correction''''' rounded to stronger 0.25 D step or more) is a [[correction]] you might sometimes get from a licensed optician.<br />
<br />
One characteristic is that it usually gives you much better visual acuity than 20/20. It is not clearly defined at which ambient light level this is to be considered over-correction. However, it should be considered that opticians often prescribe lenses that correct you to at least 20/20 night vision on a 6m Snellen chart, therefore you may see better than 20/20 in bright sunlight without it being considered over-correction. If you can see better than 20/20 on a 6m Snellen chart at night with low levels of ambient light, it is probable that you are over-corrected, but it is possible that [[20/20 correction]] gives you better than 20/20 vision while still being rounded towards the weak side of the 0.25 D step.<br />
<br />
== Overprescription ==<br />
Overprescription is when an [[optometrist]] prescribes more [[diopter]]s of [[correction]] than you need to see clearly. <br />
<br />
This is easily done, as any perceived benefit from the additional lenses given is often on the fringes of making any real difference in your eyesight. It might be very minor, but once the optometrist is aware there is ''some improvement'' in eyesight, no matter how small, often the additional diopters remain. It is not uncommon for optometrists to correct to more than 20/20, such as 20/15. This may be done to give you the best possible vision at all times, including low light conditions such as night driving. The problem with this is that the majority of myopes spend a lot of time wearing these powerful glasses up close, which contributes to [[hyperopic defocus]].<br />
<br />
Standard lens are only available in 0.25D increments, so the optometrist cannot give you the exact strength you need. Rounding towards the weaker strength would introduce (a very slight) [[blur]], so it's not unreasonable (from their perspective) that they might choose to round towards the stronger end.<br />
<br />
Overprescription is very easy to correct by wearing less diopters. The wearer never needed those diopters in the first place.</div>Userhttps://wiki.endmyopia.org/index.php?title=20/20_correction&diff=1647220/20 correction2022-03-09T17:55:47Z<p>User: </p>
<hr />
<div>{{For|the the condition of eyes having perfect vision|emmetropia}}<br />
'''''20/20 correction''''' ('''''full correction''''' rounded to weaker 0.25 D step) is a [[correction]] you normally get from a licensed optician, which corrects your eyesight up to a degree of [[visual acuity]] that an [[emmetropic]] (or "normal-seeing") person achieves on a [[Snellen Chart]], putting your [[blur horizon]] within 0.25 D of the chart.<br />
<br />
If you can see 20/15 or even better, this might mean that you are [[overcorrected]] ('''''full correction''''' rounded towards stronger 0.25 D step). (It is not necessarily considered super-human acuity, but it is unnecessary to correct to this level. Also, 20/15 isn't always a good measurement, as some people can sometimes see 20/20 with blur horizon 0.5 D away or even 20/10 with overcorrection on a bright Snellen)<br />
<br />
It is very difficult or impossible to perform [[Active Focus]] at this level of correction, as there is not enough of a [[blur horizon]] to produce [[stimulus]] - see [[Distance vision]], unless there is some sort of [[Guide:Reducing lens complexity|cylinder reduction]] or [[transient astigmatism]] involved.<br />
<br />
A good [[normalized]] might be a further 0.25 D reduction from 20/20 correction, resulting in a 0.25 to 0.5 D undercorrection, or even a 0.5 D reduction, resulting in 0.5 D to 0.75 D of undercorrection.<br />
<br />
==See also==<br />
[[20/x vision]]<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Full_correction&diff=16471Full correction2022-03-09T17:55:24Z<p>User: Changed redirect target from Correction to 20/20 correction</p>
<hr />
<div>#REDIRECT [[20/20 correction]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Natural_focal_plane&diff=16470Natural focal plane2022-03-09T17:55:10Z<p>User: </p>
<hr />
<div>The '''natural focal plane''' refers to zero (plano) correction. Note that plano lenses might have quality issues, so it is recommended not to wear plano glasses or contacts, except plano sunglasses.<br />
<br />
== Differentials ==<br />
Natural focal plane is used as differentials in some cases of [[low myopia]].<br />
<br />
== Normalized ==<br />
Natural focal plane is used along with normalized by alternating between zero and normalized/full correction in some cases of [[low myopia]].<br />
<br />
At [[emmetropia]], the natural focal plane is [[full correction]].<br />
<br />
== Zero Diopter Reset ==<br />
Natural focal plane is used for [[zero diopter reset]]s, except in cases of high myopia, for which [[differentials]] are used.</div>Userhttps://wiki.endmyopia.org/index.php?title=Emmetropia&diff=16469Emmetropia2022-03-09T17:53:42Z<p>User: </p>
<hr />
<div>{{For|corrective lenses used to get someone to 20/20 vision|20/20 correction}}<br />
'''Emmetropia''' is the zero [[refractive state]] in which an eye is neither [[nearsighted]], [[farsighted]], nor [[astigmatism|astigmatic]]. This causes the [[natural focal plane]] to be [[full correction]]. An eye is said to be emmetropic when the image of an object at infinity (parallel light rays) forms on the [[retina]], rather than in front of or behind it, implying it is also free of [[astigmatism]].<br />
<br />
Babies are born [[farsighted]], and become emmetropic over time after birth through [[axial elongation]] during emmetropization.<br />
<br />
==Thresholds==<br />
Eyes are generally regarded as emmetropic if their spherical equivalent is between -0.5 and +0.5 D and can achieve 20/20 distance [[visual acuity]] without lenses.<br />
<br />
This permits some [[myopia]], [[hyperopia]], and [[astigmatism]]. However, a truly emmetropic eye would typically achieve 20/8 acuity (no myopia or astigmatism) and be blurred to 20/20 through a +0.25 lens (no hyperopia).<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
[[Category:Articles]]<br />
[[Category:Eye conditions]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Emmetropia&diff=16468Emmetropia2022-03-09T17:53:31Z<p>User: </p>
<hr />
<div>{{For|corrective lenses used to get someone to 20/20 vision|20/20 correction}}<br />
'''Emmetropia''' is the zero [[refractive state]] in which an eye is neither [[nearsighted]] nor [[farsighted]] nor [[astigmatism|astigmatic]]. This causes the [[natural focal plane]] to be [[full correction]]. An eye is said to be emmetropic when the image of an object at infinity (parallel light rays) forms on the [[retina]], rather than in front of or behind it, implying it is also free of [[astigmatism]].<br />
<br />
Babies are born [[farsighted]], and become emmetropic over time after birth through [[axial elongation]] during emmetropization.<br />
<br />
==Thresholds==<br />
Eyes are generally regarded as emmetropic if their spherical equivalent is between -0.5 and +0.5 D and can achieve 20/20 distance [[visual acuity]] without lenses.<br />
<br />
This permits some [[myopia]], [[hyperopia]], and [[astigmatism]]. However, a truly emmetropic eye would typically achieve 20/8 acuity (no myopia or astigmatism) and be blurred to 20/20 through a +0.25 lens (no hyperopia).<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
[[Category:Articles]]<br />
[[Category:Eye conditions]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Emmetropia&diff=16467Emmetropia2022-03-09T17:52:49Z<p>User: </p>
<hr />
<div>{{For|corrective lenses used to get someone to 20/20 vision|20/20 correction}}<br />
'''Emmetropia''' is the state in which an eye is neither [[nearsighted]] nor [[farsighted]] nor [[astigmatism|astigmatic]]. An eye is said to be emmetropic when the image of an object at infinity (parallel light rays) forms on the [[retina]], rather than in front of or behind it, resulting in zero [[refractive state]] and implying it is also free of [[astigmatism]]. This causes the [[natural focal plane]] to be [[full correction]].<br />
<br />
Babies are born [[farsighted]], and become emmetropic over time after birth through [[axial elongation]] during emmetropization.<br />
<br />
==Thresholds==<br />
Eyes are generally regarded as emmetropic if their spherical equivalent is between -0.5 and +0.5 D and can achieve 20/20 distance [[visual acuity]] without lenses.<br />
<br />
This permits some [[myopia]], [[hyperopia]], and [[astigmatism]]. However, a truly emmetropic eye would typically achieve 20/8 acuity (no myopia or astigmatism) and be blurred to 20/20 through a +0.25 lens (no hyperopia).<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
[[Category:Articles]]<br />
[[Category:Eye conditions]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Refractive_state&diff=16466Refractive state2022-03-09T17:51:41Z<p>User: </p>
<hr />
<div><br />
'''Refractive state''' (also called '''refractive error''') is the lens that causes parallel light rays (distant light) to be focused on the retina when [[accommodation]] is relaxed.<br />
<br />
Your [[eye]] is a complex system of multiple layers of material with different [[refraction|refractive indexes]], all trying to project the great big wide world onto your tiny retina. Sometimes there is a mismatch between the refraction of light into the eye and its length, and the focusing system at the front of the eye misses its target in the back. This causes [[near-sightedness]] or [[far-sightedness]], which is not a medical disease in and of itself, but just a result of your refractive state not being [[emmetropia|zero]].<br />
<br />
==[[LEGAL:NMA|EndMyopia:No medical advice]]==<br />
There are medical conditions that can accelerate near-sightedness or far-sightedness progression, so please see an [[optometrist]] or other medical doctor for an exam to be sure you don't have any medical issues. Just like you'd get your kid checked out if he was a little short for his age, but just focus on healthy lifestyle choices if his health was otherwise good.<br />
<br />
If your vision problems are entirely due to refractive state, your doctor will probably prescribe glasses that give a [[20/20 correction]]. At the point that you've been medically cleared and have a [[prescription]] you are ready to start the EM method.<br />
<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Refractive_state&diff=16465Refractive state2022-03-09T17:51:26Z<p>User: </p>
<hr />
<div><br />
'''Refractive state''' (also called '''refractive error''') is the lens that causes parallel light rays (distant light) to be focused on the retina when [[accommodation]] is relaxed.<br />
<br />
Your [[eye]] is a complex system of multiple layers of material with different [[refraction|refractive indexes]], all trying to project the great big wide world onto your tiny retina. Sometimes there is a mismatch between the refraction of light into the eye and its length, and the focusing system at the front of the eye misses its target in the back. This causes [[near-sightedness]] or [[far-sightedness]], which is not a medical disease in and of itself, but just a result of your refractive state not being [[natural focal plane|zero]].<br />
<br />
==[[LEGAL:NMA|EndMyopia:No medical advice]]==<br />
There are medical conditions that can accelerate near-sightedness or far-sightedness progression, so please see an [[optometrist]] or other medical doctor for an exam to be sure you don't have any medical issues. Just like you'd get your kid checked out if he was a little short for his age, but just focus on healthy lifestyle choices if his health was otherwise good.<br />
<br />
If your vision problems are entirely due to refractive state, your doctor will probably prescribe glasses that give a [[20/20 correction]]. At the point that you've been medically cleared and have a [[prescription]] you are ready to start the EM method.<br />
<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Refractive_error&diff=16464Refractive error2022-03-09T17:49:10Z<p>User: Redirected page to Refractive state</p>
<hr />
<div>#REDIRECT [[Refractive state]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Visual_acuity&diff=16463Visual acuity2022-03-09T17:48:53Z<p>User: /* Reasons for differing visual acuity */</p>
<hr />
<div>Visual acuity (VA) is the measurement of how well the entire vision system can recognize what it sees. Formally, it is defined as the reciprocal of the smallest angle that the visual system can resolve.<br />
<br />
It will depend on the amount of defocus that [[accommodation]] cannot overcome because it is outside of the focus range or due to other defects such as [[astigmatism]]. Defocus causes [[blur]] and [[double vision]].<br />
<br />
For distance, this is typically measured with a [[Snellen chart]] and expressed as the distance you need to be from the chart to recognize the characters over the distance that someone with normal vision can recognize the characters. Lens or mirrors may be used to change the effective test distance in a smaller room.<br />
<br />
For near, this is typically measured with a near vision test chart at 40 cm.<br />
<br />
20/20 (VA of 1) corresponds to an angle of 1 minute of arc. The 20/20 line is 5 minutes of arc in height and width, but the smallest detail subtends 1 arcmin. 20/200 (VA of 0.1) corresponds to 10 arcmin. 20/10 (VA of 2) corresponds to 0.5 arcmin.<br />
<br />
==Reading a Snellen chart==<br />
{{main|Snellen chart}}<br />
* 20/200 would be very bad (possibly just [[myopic]]),<br />
* 20/70 is a typical threshold of low vision (being unable to read 20/70 with best possible correction),<br />
* 20/20 is good enough,<br />
* 20/15 is average, and<br />
* 20/10 is excellent.<br />
<br />
The [[prescription]] for [[myopes]] and [[hyperopes]] is typically the weakest lens power required to achieve 20/20 or better vision measured at [[distance vision|20 feet or 6 meters]]. The prescription for a [[presbyope]] is the smallest plus power added to the distance prescription to see 20/20 at 40 cm. Emmetropic presbyopes have zero distance prescription, so their near prescription is simple spherical [[plus lenses]].<br />
<br />
===Caveats===<br />
With text that we are familiar with, the brain may clear up that text more than our vision would actually allow.<br />
<br />
20/20 is "good enough" for most purposes, but not "perfect" in any way. Rather, 20/20 vision is slightly defective. It is possible to have 20/20 vision with 0.25 to 0.5 D of defocus, and 20/20 does not imply clear or sharp vision. As [[normalized]] correction typically imposes 0.25 D of extra myopic defocus on [[20/20 correction]], it can be considered to be 0.25 to 0.75 D of undercorrection.<br />
<br />
Tscherning writes in ''Physiologic Optics: Dioptrics of the Eye, Functions of the Retina, Ocular Movements and Binocular Vision'':<br />
<blockquote>We have found also that the best eyes have a visual acuity <br />
which approaches 2, and we can be almost certain that if, with a good illumination, the acuity is only equal to 1, the eye presents defects sufficiently pronounced to be easily established.</blockquote><br />
<br />
==Reasons for differing visual acuity==<br />
Non-zero [[refractive state]], which causes [[blur]] and [[double vision]], is only one factor of visual acuity. Various medical conditions can cause physical blockage/dispersion of light in the eye, problems detecting light in the eye, or problems with the visual processing that turns a series of electrochemical signals into a picture in our mind's eye. See an [[optometrist]] if your vision can't be corrected with [[refraction]].<br />
<br />
==20/x==<br />
Shorthand for 20 over a single digit (such as 20/9), or considerably better than 20/20 vision (VA > 2).<br />
<br />
==See Also==<br />
* [[Emmetropia]]<br />
* [[Optics_related_math#Visual_acuity]]<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
==External links==<br />
* [http://billauer.co.il/simulator.html Visual acuity simulator]<br />
<br />
[[Category:Articles]]</div>Userhttps://wiki.endmyopia.org/index.php?title=Visual_acuity&diff=16462Visual acuity2022-03-09T17:47:13Z<p>User: /* Reasons differing visual acuity */</p>
<hr />
<div>Visual acuity (VA) is the measurement of how well the entire vision system can recognize what it sees. Formally, it is defined as the reciprocal of the smallest angle that the visual system can resolve.<br />
<br />
It will depend on the amount of defocus that [[accommodation]] cannot overcome because it is outside of the focus range or due to other defects such as [[astigmatism]]. Defocus causes [[blur]] and [[double vision]].<br />
<br />
For distance, this is typically measured with a [[Snellen chart]] and expressed as the distance you need to be from the chart to recognize the characters over the distance that someone with normal vision can recognize the characters. Lens or mirrors may be used to change the effective test distance in a smaller room.<br />
<br />
For near, this is typically measured with a near vision test chart at 40 cm.<br />
<br />
20/20 (VA of 1) corresponds to an angle of 1 minute of arc. The 20/20 line is 5 minutes of arc in height and width, but the smallest detail subtends 1 arcmin. 20/200 (VA of 0.1) corresponds to 10 arcmin. 20/10 (VA of 2) corresponds to 0.5 arcmin.<br />
<br />
==Reading a Snellen chart==<br />
{{main|Snellen chart}}<br />
* 20/200 would be very bad (possibly just [[myopic]]),<br />
* 20/70 is a typical threshold of low vision (being unable to read 20/70 with best possible correction),<br />
* 20/20 is good enough,<br />
* 20/15 is average, and<br />
* 20/10 is excellent.<br />
<br />
The [[prescription]] for [[myopes]] and [[hyperopes]] is typically the weakest lens power required to achieve 20/20 or better vision measured at [[distance vision|20 feet or 6 meters]]. The prescription for a [[presbyope]] is the smallest plus power added to the distance prescription to see 20/20 at 40 cm. Emmetropic presbyopes have zero distance prescription, so their near prescription is simple spherical [[plus lenses]].<br />
<br />
===Caveats===<br />
With text that we are familiar with, the brain may clear up that text more than our vision would actually allow.<br />
<br />
20/20 is "good enough" for most purposes, but not "perfect" in any way. Rather, 20/20 vision is slightly defective. It is possible to have 20/20 vision with 0.25 to 0.5 D of defocus, and 20/20 does not imply clear or sharp vision. As [[normalized]] correction typically imposes 0.25 D of extra myopic defocus on [[20/20 correction]], it can be considered to be 0.25 to 0.75 D of undercorrection.<br />
<br />
Tscherning writes in ''Physiologic Optics: Dioptrics of the Eye, Functions of the Retina, Ocular Movements and Binocular Vision'':<br />
<blockquote>We have found also that the best eyes have a visual acuity <br />
which approaches 2, and we can be almost certain that if, with a good illumination, the acuity is only equal to 1, the eye presents defects sufficiently pronounced to be easily established.</blockquote><br />
<br />
==Reasons for differing visual acuity==<br />
[[Refraction]], which causes [[blur]] and [[double vision]], is only one factor of visual acuity. Various medical conditions can cause physical blockage/dispersion of light in the eye, problems detecting light in the eye, or problems with the visual processing that turns a series of electrochemical signals into a picture in our mind's eye. See an [[optometrist]] if your vision can't be corrected with [[refraction]].<br />
<br />
==20/x==<br />
Shorthand for 20 over a single digit (such as 20/9), or considerably better than 20/20 vision (VA > 2).<br />
<br />
==See Also==<br />
* [[Emmetropia]]<br />
* [[Optics_related_math#Visual_acuity]]<br />
<br />
==References==<br />
{{reflist}}<br />
<br />
==External links==<br />
* [http://billauer.co.il/simulator.html Visual acuity simulator]<br />
<br />
[[Category:Articles]]</div>User