Endmyopia Wiki - User contributions [en]

Diopters

2023-03-26T09:37:28Z

Endmpiauser: /* Gap and ratio: fixed refs */

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 the [[ focal length ]] in meters . The most common unit symbol for diopters is dpt, D, or m - 1 .

<math>P = \frac{1}{f} = - \frac{1}{d}</math>

* In [[ EM ]] , we use the [[ cm measurement ]] to calculate the diopters needed to correct [[ refraction]] of the eye. If you can see clearly at 50cm, your diopters will be <math> - \frac{1}{0.50}= - 2 dpt</math> OR <math> - \frac{100}{50}= - 2 dpt</math>.

* Serial lenses add their powers: if you wear - 2 diopter contact lenses ( [[ vertex distance | adjusted for glasses strength ]] ) and put on reading glasses +1 diopter on the lenses you actually wear - 1 diopter.
**There are a few caveats such as vertex distance because moving the lens further away effectively gives you a weaker negative lens or a stronger positive lens. There's also shift, which induces a prism when the lens is moved sideways. These effects become negligible for weaker lenses.
* According to the thin lens sign convention, the negative focal power is divergent and the positive focal power is convergent.
** A lens with a negative diopter sign compensates for [[ myopia ]] while a lens with a positive diopter sign compensates for [[ hyperopia ]] .

{| class="wikitable"
|+ Approximate categorizations of myopia by [[ spherical ]] lens power :
| -
| 0.00 to - 0.50 dpt || Not really considered myopic, probably doesn't need glasses
| -
| - 0.50 to - 1.00 dpt || Mild myopia, [[ normalized ]] sometimes unnecessary
| -
| - 1.00 to - 2.50 dpt || Low myopia, possibly unnecessary [[ differentials ]]
| -
| -2.50 to - 3.00 dpt|| Low myopia, differentials probably needed
| - | - 3.00 to - 6.00 dpt || Moderate myopia, glasses still needed

| - | - 6.00 to - 10.00 dpt || High myopia

| - | - 10.00+ deposit || Very high myopia. Significantly reduced field of vision.

|}

== Gap and ratio ==

Comparisons between two diopters are usually expressed using one of these terms:

* '' diopter gap'' (or '' diopter difference '' ): absolute difference in diopters between two values
* '' diopter ratio '' : ratio of one diopter value to another (like right eye / left eye)

For example, consider the following correction:

OD: - 1.5 SPH / - 1.5 CYL
OS: - 1.0 SPH / - 2.0 CYL

It can be expressed as a difference of 0.5 dpt in SPH and CYL, a ratio of 1.5 in SPH and a ratio of 0.75 in CYL:

|( - 1.5 dpt) - ( - 1.0 dpt)| = 0,
- 1.5 dpt) - ( - 2.0 dpt)| = 0.5 dpt
( - 1.5 dpt) / ( - 1.0 dpt) = 1.5 ( - 1.5 dpt ) / ( - 2.0 dpt ) = 0.75 <ref> {{ quote jake | https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/ | _ _ _ _ _ _ _ _ _ _ _ _ _ _ The diopter trap: don't favor one eye }} </ref>

, for example when talking about reducing a correction while keeping the same '' gap '' . This can also be expressed as a [[ wikipedia: Percent Difference | percentage difference ]] between the two diopter values <ref> {{ quote jake | https://endmyopia.org/reducing - diopter - ratio - diy - patching - solution - pro - topic/ | Diopter Ratio Reduction: DIY Solution (PRO TOPIC) }} </ref> (for example, the <tt> 0.5 dpt </tt> difference between the right eye and the left eye is here equivalent to <tt> 0.5 dpt / | - 1.5 dpt | = 0.33 </tt> or 33%). The general recommendation is that the left -

diopter differenceshould be constant on all lenses used. However, some old EM papers show successful cases where the differentials are equalized but normalized with a deviation of 0.25 D.<ref>[https://endmyopia.org/progress-improving-centimeter-62-90/ Sara: Improving Centimeter from 62 to 90]</ref><ref>[https://endmyopia.org/saras-journey-truth-long-term-vision-improvement-potential/ Sara’s Journey: The Truth About Long Term Vision Improvement Potential]</ref>

Confusingly, diopter deviation is also sometimes used to refer to diff - norm deviation, the difference between [[ differentials ]] and [[ normalized ]] or the [[ spherical equivalent ]] of this difference. <ref>[https://endmyopia.org/pro-qa-equalize-differentials-first/ Pro Q&A: Should You Equalize Your Differentials First?]</ref>

It is often useful to disambiguate what is being compared:
* '' left - right deviation '' : diopters left eye minus diopters right eye, without taking into account the axis
** In the example above , the left - right deviation is +0.5 SPH - 0.5 CYL.
** Axis is ignored and cylinder powers are subtracted without using [[ Diopters#Adding/Combining Lenses | goal combination calculations ]] .
* '' diff - norm deviation '' : differential diopter minus normalized diopter, without taking into account the axis
** For example, if the norm is - 2 SPH - 0.5 CYL and the differentials are - 0.75 SPH, the diff - standard deviation is 1.25 SPH 0.5 CYL or 1.5 SPH equivalent.
** The axis is ignored.
** This quantity is usually positive, because more positive sphere is needed for [[ close-up ]] than for [[ distance vision ]] .

==Technical Details==
This section is for the math - savvy people. He explains the concepts in more detail, but his knowledge is not strictly necessary to use the EM method.

=== Thin lens equation ===
The focal length of a lens is given by the lens manufacturer's equation. Assuming the lens is much thinner than the radius of curvature, so assuming the lens thickness is zero, we get a simplified version of the lens maker's equation. We can do a few more derivations, we arrive at the thin - lens equation: <ref> see derivations athttps://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> <math>{1}\frac{1} d_o}+\frac{1}{d_i}=\frac{1}{f}</math> According to the fineness lens sign convention, * di is positive if it is a real image from the side opposite of the lens to the object, and it is negative if it is a virtual image on the same side of the lens as the object. * f is positive for a converging lens and negative for a diverging lens. This is also sometimes presented in the Newtonian form: <math>

f\right)\left(d_i - f\right)=f^2</math>

==== Examples ====
"Full correction" takes an object at infinity and produces a virtual image at your distance d :

<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{ - d} = - \frac{1}{d}</math>

This is the resulting equation at the beginning of the article. This also explains why focal power is increased for objects at closer distances: traditional optometry calls this "addition" for [[ presbyopia ]], although they generally use the minimum amount required for you to be able to see at 40cm with full distance correction using housing. For example, if you choose 80 cm as the working distance for your [[ differentials ]] (resulting in an "addition" of +1.25 dpt), and your blur horizon is 50 cm (resulting in -2 dpt ), the formula is

< 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>

=== Cylinder ===
A cylindrical lens of focal power P cyl has a power P at the angle θ of its axis: <math>P = P_{cyl} ( \sin\theta)^2</math> ==== Axis ==== L' axis is usually in degrees modulo 180. It is common for 0 to be written as 180 in some regions. ==== Transposition ==== We can understand why there are two different ways to write a combination of spherical and cylindrical lens, using the Pythagorean trigonometric identity and the complementary angle identity: <math>( \sin\theta)^2 + (\cos\theta)^2 = 1</math> <math> - 90^{\circ}\right)}</math> <math>

P_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math>

We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (like subtracting 90 degrees, since the axis is modulo 180 degrees) to the axis, we get an equivalent combination.

For example, - 1 sph - 1 cyl 1 axis is the same as - 2 sph +1 cyl 91 axis.

In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two shapes are equivalent.

==== Spherical equivalent ====
{{ See also |Astigmatism#Spherical equivalent }}

Calculating the average value over all angles using an integral, the result <ref> just integrate one or two periods: https://www.wolframalpha.com/input /?i=average +de+%28sin+x%29%5E2+de+0+à+2+pi </ref> is

<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>

C' is why the spherical equivalent has power equal to half the power of the cylinder.

==== Adding/Combining Lenses ====
Multiple lenses, each with spherical and cylindrical components (not necessarily on the same axis) can be added to form a lens with a spherical and cylindrical component.

We can use the double angle formula to convert each cylindrical lens to a constant plus a cosine:

<math>\cos{2\theta}=1 - 2(\sin\theta)^2</math>

<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>

The constant parts are added to the spherical components. 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 the two cylindrical lenses (see the section on transposition), and its corresponding spherical component must be subtracted from the total spherical component.

There are implementations of this at
* http://opticampus.opti.vision/tools/cylinders.php
* http://billauer.co.il/simulator.html

=== Decentration ===
The Induced prism can be calculated using Prentice reign. Similar to Vertex Distance, shift is less of an issue for lower power lenses.

The amount of prism power P induced by the decentration c of a lens of power f is <math>P=cf</math> 1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm and f in diopters, then P is in prismatic diopters. A prism with vertex angle a and refractive index n gives an angle of light deflection d, which is equal to P diopters of the prism: <math>d=(n - 1)a</math> <math >P=100\tan{d}=100\tan((n - 1)a)</math>

See [[Vertex distance#Calculation|Vertex distance -> Calculation]]

== References ==

{{ reflist }}
[[ Category: Article ]]

Diopters

2023-03-26T09:24:58Z

Endmpiauser: added alternative notation for calculating diopter from the newsletter

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 the [[ focal length ]] in meters . The most common unit symbol for diopters is dpt, D, or m - 1 .

<math>P = \frac{1}{f} = - \frac{1}{d}</math>

* In [[ EM ]] , we use the [[ cm measurement ]] to calculate the diopters needed to correct [[ refraction]] of the eye. If you can see clearly at 50cm, your diopters will be <math> - \frac{1}{0.50}= - 2 dpt</math> OR <math> - \frac{100}{50}= - 2 dpt</math>.

* Serial lenses add their powers: if you wear - 2 diopter contact lenses ( [[ vertex distance | adjusted for glasses strength ]] ) and put on reading glasses +1 diopter on the lenses you actually wear - 1 diopter.
**There are a few caveats such as vertex distance because moving the lens further away effectively gives you a weaker negative lens or a stronger positive lens. There's also shift, which induces a prism when the lens is moved sideways. These effects become negligible for weaker lenses.
* According to the thin lens sign convention, the negative focal power is divergent and the positive focal power is convergent.
** A lens with a negative diopter sign compensates for [[ myopia ]] while a lens with a positive diopter sign compensates for [[ hyperopia ]] .

{| class="wikitable"
|+ Approximate categorizations of myopia by [[ spherical ]] lens power :
| -
| 0.00 to - 0.50 dpt || Not really considered myopic, probably doesn't need glasses
| -
| - 0.50 to - 1.00 dpt || Mild myopia, [[ normalized ]] sometimes unnecessary
| -
| - 1.00 to - 2.50 dpt || Low myopia, possibly unnecessary [[ differentials ]]
| -
| -2.50 to - 3.00 dpt|| Low myopia, differentials probably needed
| - | - 3.00 to - 6.00 dpt || Moderate myopia, glasses still needed

| - | - 6.00 to - 10.00 dpt || High myopia

| - | - 10.00+ deposit || Very high myopia. Significantly reduced field of vision.

|}

== Gap and ratio ==

Comparisons between two diopters are usually expressed using one of these terms:

* '' diopter gap'' (or '' diopter difference '' ): absolute difference in diopters between two values
* '' diopter ratio '' : ratio of one diopter value to another (like right eye / left eye)

For example, consider the following correction:

OD: - 1.5 SPH / - 1.5 CYL
OS: - 1.0 SPH / - 2.0 CYL

It can be expressed as a difference of 0.5 dpt in SPH and CYL, a ratio of 1.5 in SPH and a ratio of 0.75 in CYL:

|( - 1.5 dpt) - ( - 1.0 dpt)| = 0,
- 1.5 dpt) - ( - 2.0 dpt)| = 0.5 dpt
( - 1.5 dpt) / ( - 1.0 dpt) = 1.5 ( - 1.5 dpt ) / ( - 2.0 dpt ) = 0.75 <ref> {{ quote jake | https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/ | _ _ _ _ _ _ _ _ _ _ _ _ _ _ The diopter trap: don't favor one eye }} </ref>

, for example when talking about reducing a correction while keeping the same '' gap '' . This can also be expressed as a [[ wikipedia: Percent Difference | percentage difference ]] between the two diopter values <ref> {{ quote jake | https://endmyopia.org/reducing - diopter - ratio - diy - patching - solution - pro - topic/ | Diopter Ratio Reduction: DIY Solution (PRO TOPIC) }} </ref> (for example, the <tt> 0.5 dpt </tt> difference between the right eye and the left eye is here equivalent to <tt> 0.5 dpt / | - 1.5 dpt | = 0.33 </tt> or 33%). The general recommendation is that the left -

diopter differenceshould be constant on all lenses used. However, some old EM papers show successful cases where the differentials are equalized but normalized with a deviation of 0.25 D.<ref>https://endmyopia.org/progress-improvement-centimeter-62-90/ and https://endmyopia.org/saras - journey - truth - long term - vision - improvement - potential/ < /ref>

Confusingly, diopter deviation is also sometimes used to refer to diff - norm deviation, the difference between [[ differentials ]] and [[ normalized ]] or the [[ spherical equivalent ]] of this difference. <ref> https://endmyopia.org/pro - topic - manage - your -maximum - diopter - deviation/ </ref>

It is often useful to disambiguate what is being compared:
* '' left - right deviation '' : diopters left eye minus diopters right eye, without taking into account the axis
** In the example above , the left - right deviation is +0.5 SPH - 0.5 CYL.
** Axis is ignored and cylinder powers are subtracted without using [[ Diopters#Adding/Combining Lenses | goal combination calculations ]] .
* '' diff - norm deviation '' : differential diopter minus normalized diopter, without taking into account the axis
** For example, if the norm is - 2 SPH - 0.5 CYL and the differentials are - 0.75 SPH, the diff - standard deviation is 1.25 SPH 0.5 CYL or 1.5 SPH equivalent.
** The axis is ignored.
** This quantity is usually positive, because more positive sphere is needed for [[ close-up ]] than for [[ distance vision ]] .

==Technical Details==
This section is for the math - savvy people. He explains the concepts in more detail, but his knowledge is not strictly necessary to use the EM method.

=== Thin lens equation ===
The focal length of a lens is given by the lens manufacturer's equation. Assuming the lens is much thinner than the radius of curvature, so assuming the lens thickness is zero, we get a simplified version of the lens maker's equation. We can do a few more derivations, we arrive at the thin - lens equation: <ref> see derivations athttps://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> <math>{1}\frac{1} d_o}+\frac{1}{d_i}=\frac{1}{f}</math> According to the fineness lens sign convention, * di is positive if it is a real image from the side opposite of the lens to the object, and it is negative if it is a virtual image on the same side of the lens as the object. * f is positive for a converging lens and negative for a diverging lens. This is also sometimes presented in the Newtonian form: <math>

f\right)\left(d_i - f\right)=f^2</math>

==== Examples ====
"Full correction" takes an object at infinity and produces a virtual image at your distance d :

<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{ - d} = - \frac{1}{d}</math>

This is the resulting equation at the beginning of the article. This also explains why focal power is increased for objects at closer distances: traditional optometry calls this "addition" for [[ presbyopia ]], although they generally use the minimum amount required for you to be able to see at 40cm with full distance correction using housing. For example, if you choose 80 cm as the working distance for your [[ differentials ]] (resulting in an "addition" of +1.25 dpt), and your blur horizon is 50 cm (resulting in -2 dpt ), the formula is

< 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>

=== Cylinder ===
A cylindrical lens of focal power P cyl has a power P at the angle θ of its axis: <math>P = P_{cyl} ( \sin\theta)^2</math> ==== Axis ==== L' axis is usually in degrees modulo 180. It is common for 0 to be written as 180 in some regions. ==== Transposition ==== We can understand why there are two different ways to write a combination of spherical and cylindrical lens, using the Pythagorean trigonometric identity and the complementary angle identity: <math>( \sin\theta)^2 + (\cos\theta)^2 = 1</math> <math> - 90^{\circ}\right)}</math> <math>

P_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math>

We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (like subtracting 90 degrees, since the axis is modulo 180 degrees) to the axis, we get an equivalent combination.

For example, - 1 sph - 1 cyl 1 axis is the same as - 2 sph +1 cyl 91 axis.

In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two shapes are equivalent.

==== Spherical equivalent ====
{{ See also |Astigmatism#Spherical equivalent }}

Calculating the average value over all angles using an integral, the result <ref> just integrate one or two periods: https://www.wolframalpha.com/input /?i=average +de+%28sin+x%29%5E2+de+0+à+2+pi </ref> is

<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>

C' is why the spherical equivalent has power equal to half the power of the cylinder.

==== Adding/Combining Lenses ====
Multiple lenses, each with spherical and cylindrical components (not necessarily on the same axis) can be added to form a lens with a spherical and cylindrical component.

We can use the double angle formula to convert each cylindrical lens to a constant plus a cosine:

<math>\cos{2\theta}=1 - 2(\sin\theta)^2</math>

<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>

The constant parts are added to the spherical components. 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 the two cylindrical lenses (see the section on transposition), and its corresponding spherical component must be subtracted from the total spherical component.

There are implementations of this at
* http://opticampus.opti.vision/tools/cylinders.php
* http://billauer.co.il/simulator.html

=== Decentration ===
The Induced prism can be calculated using Prentice reign. Similar to Vertex Distance, shift is less of an issue for lower power lenses.

The amount of prism power P induced by the decentration c of a lens of power f is <math>P=cf</math> 1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm and f in diopters, then P is in prismatic diopters. A prism with vertex angle a and refractive index n gives an angle of light deflection d, which is equal to P diopters of the prism: <math>d=(n - 1)a</math> <math >P=100\tan{d}=100\tan((n - 1)a)</math>

See [[Vertex distance#Calculation|Vertex distance -> Calculation]]

== References ==

{{ reflist }}
[[ Category: Article ]]

Diopters

2023-03-26T09:21:09Z

Endmpiauser: fix section formatting again

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 the [[ focal length ]] in meters . The most common unit symbol for diopters is dpt, D, or m - 1 .

<math>P = \frac{1}{f} = - \frac{1}{d}</math>

* In [[ EM ]] , we use the [[ cm measurement ]] to calculate the diopters needed to correct [[ refraction]] of the eye. If you can see clearly at 50cm, your diopters will be <math> - \frac{1}{0.50}= - 2 dpt</math>.

* Serial lenses add their powers: if you wear - 2 diopter contact lenses ( [[ vertex distance | adjusted for glasses strength ]] ) and put on reading glasses +1 diopter on the lenses you actually wear - 1 diopter.
**There are a few caveats such as vertex distance because moving the lens further away effectively gives you a weaker negative lens or a stronger positive lens. There's also shift, which induces a prism when the lens is moved sideways. These effects become negligible for weaker lenses.
* According to the thin lens sign convention, the negative focal power is divergent and the positive focal power is convergent.
** A lens with a negative diopter sign compensates for [[ myopia ]] while a lens with a positive diopter sign compensates for [[ hyperopia ]] .

{| class="wikitable"
|+ Approximate categorizations of myopia by [[ spherical ]] lens power :
| -
| 0.00 to - 0.50 dpt || Not really considered myopic, probably doesn't need glasses
| -
| - 0.50 to - 1.00 dpt || Mild myopia, [[ normalized ]] sometimes unnecessary
| -
| - 1.00 to - 2.50 dpt || Low myopia, possibly unnecessary [[ differentials ]]
| -
| -2.50 to - 3.00 dpt|| Low myopia, differentials probably needed
| - | - 3.00 to - 6.00 dpt || Moderate myopia, glasses still needed

| - | - 6.00 to - 10.00 dpt || High myopia

| - | - 10.00+ deposit || Very high myopia. Significantly reduced field of vision.

|}

== Gap and ratio ==

Comparisons between two diopters are usually expressed using one of these terms:

* '' diopter gap'' (or '' diopter difference '' ): absolute difference in diopters between two values
* '' diopter ratio '' : ratio of one diopter value to another (like right eye / left eye)

For example, consider the following correction:

OD: - 1.5 SPH / - 1.5 CYL
OS: - 1.0 SPH / - 2.0 CYL

It can be expressed as a difference of 0.5 dpt in SPH and CYL, a ratio of 1.5 in SPH and a ratio of 0.75 in CYL:

|( - 1.5 dpt) - ( - 1.0 dpt)| = 0,
- 1.5 dpt) - ( - 2.0 dpt)| = 0.5 dpt
( - 1.5 dpt) / ( - 1.0 dpt) = 1.5 ( - 1.5 dpt ) / ( - 2.0 dpt ) = 0.75 <ref> {{ quote jake | https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/ | _ _ _ _ _ _ _ _ _ _ _ _ _ _ The diopter trap: don't favor one eye }} </ref>

, for example when talking about reducing a correction while keeping the same '' gap '' . This can also be expressed as a [[ wikipedia: Percent Difference | percentage difference ]] between the two diopter values <ref> {{ quote jake | https://endmyopia.org/reducing - diopter - ratio - diy - patching - solution - pro - topic/ | Diopter Ratio Reduction: DIY Solution (PRO TOPIC) }} </ref> (for example, the <tt> 0.5 dpt </tt> difference between the right eye and the left eye is here equivalent to <tt> 0.5 dpt / | - 1.5 dpt | = 0.33 </tt> or 33%). The general recommendation is that the left -

diopter differenceshould be constant on all lenses used. However, some old EM papers show successful cases where the differentials are equalized but normalized with a deviation of 0.25 D.<ref>https://endmyopia.org/progress-improvement-centimeter-62-90/ and https://endmyopia.org/saras - journey - truth - long term - vision - improvement - potential/ < /ref>

Confusingly, diopter deviation is also sometimes used to refer to diff - norm deviation, the difference between [[ differentials ]] and [[ normalized ]] or the [[ spherical equivalent ]] of this difference. <ref> https://endmyopia.org/pro - topic - manage - your -maximum - diopter - deviation/ </ref>

It is often useful to disambiguate what is being compared:
* '' left - right deviation '' : diopters left eye minus diopters right eye, without taking into account the axis
** In the example above , the left - right deviation is +0.5 SPH - 0.5 CYL.
** Axis is ignored and cylinder powers are subtracted without using [[ Diopters#Adding/Combining Lenses | goal combination calculations ]] .
* '' diff - norm deviation '' : differential diopter minus normalized diopter, without taking into account the axis
** For example, if the norm is - 2 SPH - 0.5 CYL and the differentials are - 0.75 SPH, the diff - standard deviation is 1.25 SPH 0.5 CYL or 1.5 SPH equivalent.
** The axis is ignored.
** This quantity is usually positive, because more positive sphere is needed for [[ close-up ]] than for [[ distance vision ]] .

==Technical Details==
This section is for the math - savvy people. He explains the concepts in more detail, but his knowledge is not strictly necessary to use the EM method.

=== Thin lens equation ===
The focal length of a lens is given by the lens manufacturer's equation. Assuming the lens is much thinner than the radius of curvature, so assuming the lens thickness is zero, we get a simplified version of the lens maker's equation. We can do a few more derivations, we arrive at the thin - lens equation: <ref> see derivations athttps://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> <math>{1}\frac{1} d_o}+\frac{1}{d_i}=\frac{1}{f}</math> According to the fineness lens sign convention, * di is positive if it is a real image from the side opposite of the lens to the object, and it is negative if it is a virtual image on the same side of the lens as the object. * f is positive for a converging lens and negative for a diverging lens. This is also sometimes presented in the Newtonian form: <math>

f\right)\left(d_i - f\right)=f^2</math>

==== Examples ====
"Full correction" takes an object at infinity and produces a virtual image at your distance d :

<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{ - d} = - \frac{1}{d}</math>

This is the resulting equation at the beginning of the article. This also explains why focal power is increased for objects at closer distances: traditional optometry calls this "addition" for [[ presbyopia ]], although they generally use the minimum amount required for you to be able to see at 40cm with full distance correction using housing. For example, if you choose 80 cm as the working distance for your [[ differentials ]] (resulting in an "addition" of +1.25 dpt), and your blur horizon is 50 cm (resulting in -2 dpt ), the formula is

< 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>

=== Cylinder ===
A cylindrical lens of focal power P cyl has a power P at the angle θ of its axis: <math>P = P_{cyl} ( \sin\theta)^2</math> ==== Axis ==== L' axis is usually in degrees modulo 180. It is common for 0 to be written as 180 in some regions. ==== Transposition ==== We can understand why there are two different ways to write a combination of spherical and cylindrical lens, using the Pythagorean trigonometric identity and the complementary angle identity: <math>( \sin\theta)^2 + (\cos\theta)^2 = 1</math> <math> - 90^{\circ}\right)}</math> <math>

P_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math>

We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (like subtracting 90 degrees, since the axis is modulo 180 degrees) to the axis, we get an equivalent combination.

For example, - 1 sph - 1 cyl 1 axis is the same as - 2 sph +1 cyl 91 axis.

In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two shapes are equivalent.

==== Spherical equivalent ====
{{ See also |Astigmatism#Spherical equivalent }}

Calculating the average value over all angles using an integral, the result <ref> just integrate one or two periods: https://www.wolframalpha.com/input /?i=average +de+%28sin+x%29%5E2+de+0+à+2+pi </ref> is

<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>

C' is why the spherical equivalent has power equal to half the power of the cylinder.

==== Adding/Combining Lenses ====
Multiple lenses, each with spherical and cylindrical components (not necessarily on the same axis) can be added to form a lens with a spherical and cylindrical component.

We can use the double angle formula to convert each cylindrical lens to a constant plus a cosine:

<math>\cos{2\theta}=1 - 2(\sin\theta)^2</math>

<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>

The constant parts are added to the spherical components. 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 the two cylindrical lenses (see the section on transposition), and its corresponding spherical component must be subtracted from the total spherical component.

There are implementations of this at
* http://opticampus.opti.vision/tools/cylinders.php
* http://billauer.co.il/simulator.html

=== Decentration ===
The Induced prism can be calculated using Prentice reign. Similar to Vertex Distance, shift is less of an issue for lower power lenses.

The amount of prism power P induced by the decentration c of a lens of power f is <math>P=cf</math> 1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm and f in diopters, then P is in prismatic diopters. A prism with vertex angle a and refractive index n gives an angle of light deflection d, which is equal to P diopters of the prism: <math>d=(n - 1)a</math> <math >P=100\tan{d}=100\tan((n - 1)a)</math>

See [[Vertex distance#Calculation|Vertex distance -> Calculation]]

== References ==

{{ reflist }}
[[ Category: Article ]]

Diopters

2023-03-26T09:13:36Z

Endmpiauser: fix formatting

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 the [[ focal length ]] in meters . The most common unit symbol for diopters is dpt, D, or m - 1 .

<math>P = \frac{1}{f} = - \frac{1}{d}</math>

* In [[ EM ]] , we use the [[ cm measurement ]] to calculate the diopters needed to correct [[ refraction]] of the eye. If you can see clearly at 50cm, your diopters will be <math> - \frac{1}{0.50}= - 2 dpt</math>.

* Serial lenses add their powers: if you wear - 2 diopter contact lenses ( [[ vertex distance | adjusted for glasses strength ]] ) and put on reading glasses +1 diopter on the lenses you actually wear - 1 diopter.
**There are a few caveats such as vertex distance because moving the lens further away effectively gives you a weaker negative lens or a stronger positive lens. There's also shift, which induces a prism when the lens is moved sideways. These effects become negligible for weaker lenses.
* According to the thin lens sign convention, the negative focal power is divergent and the positive focal power is convergent.
** A lens with a negative diopter sign compensates for [[ myopia ]] while a lens with a positive diopter sign compensates for [[ hyperopia ]] .

{| class="wikitable"
|+ Approximate categorizations of myopia by [[ spherical ]] lens power :
| -
| 0.00 to - 0.50 dpt || Not really considered myopic, probably doesn't need glasses
| -
| - 0.50 to - 1.00 dpt || Mild myopia, [[ normalized ]] sometimes unnecessary
| -
| - 1.00 to - 2.50 dpt || Low myopia, possibly unnecessary [[ differentials ]]
| -
| -2.50 to - 3.00 dpt|| Low myopia, differentials probably needed
| - | - 3.00 to - 6.00 dpt || Moderate myopia, glasses still needed

| - | - 6.00 to - 10.00 dpt || High myopia

| - | - 10.00+ deposit || Very high myopia. Significantly reduced field of vision.

|}

== Gap and ratio ==

Comparisons between two diopters are usually expressed using one of these terms:

* '' diopter gap'' (or '' diopter difference '' ): absolute difference in diopters between two values
* '' diopter ratio '' : ratio of one diopter value to another (like right eye / left eye)

For example, consider the following correction:

OD: - 1.5 SPH / - 1.5 CYL
OS: - 1.0 SPH / - 2.0 CYL

It can be expressed as a difference of 0.5 dpt in SPH and CYL, a ratio of 1.5 in SPH and a ratio of 0.75 in CYL:

|( - 1.5 dpt) - ( - 1.0 dpt)| = 0,
- 1.5 dpt) - ( - 2.0 dpt)| = 0.5 dpt
( - 1.5 dpt) / ( - 1.0 dpt) = 1.5 ( - 1.5 dpt ) / ( - 2.0 dpt ) = 0.75 <ref> {{ quote jake | https://endmyopia.org/the-diopter-ratio-trap-dont-favor-one-eye/ | _ _ _ _ _ _ _ _ _ _ _ _ _ _ The diopter trap: don't favor one eye }} </ref>

, for example when talking about reducing a correction while keeping the same '' gap '' . This can also be expressed as a [[ wikipedia: Percent Difference | percentage difference ]] between the two diopter values <ref> {{ quote jake | https://endmyopia.org/reducing - diopter - ratio - diy - patching - solution - pro - topic/ | Diopter Ratio Reduction: DIY Solution (PRO TOPIC) }} </ref> (for example, the <tt> 0.5 dpt </tt> difference between the right eye and the left eye is here equivalent to <tt> 0.5 dpt / | - 1.5 dpt | = 0.33 </tt> or 33%). The general recommendation is that the left -

diopter differenceshould be constant on all lenses used. However, some old EM papers show successful cases where the differentials are equalized but normalized with a deviation of 0.25 D.<ref>https://endmyopia.org/progress-improvement-centimeter-62-90/ and https://endmyopia.org/saras - journey - truth - long term - vision - improvement - potential/ < /ref>

Confusingly, diopter deviation is also sometimes used to refer to diff - norm deviation, the difference between [[ differentials ]] and [[ normalized ]] or the [[ spherical equivalent ]] of this difference. <ref> https://endmyopia.org/pro - topic - manage - your -maximum - diopter - deviation/ </ref>

It is often useful to disambiguate what is being compared:
* '' left - right deviation '' : diopters left eye minus diopters right eye, without taking into account the axis
** In the example above , the left - right deviation is +0.5 SPH - 0.5 CYL.
** Axis is ignored and cylinder powers are subtracted without using [[ Diopters#Adding/Combining Lenses | goal combination calculations ]] .
* '' diff - norm deviation '' : differential diopter minus normalized diopter, without taking into account the axis
** For example, if the norm is - 2 SPH - 0.5 CYL and the differentials are - 0.75 SPH, the diff - standard deviation is 1.25 SPH 0.5 CYL or 1.5 SPH equivalent.
** The axis is ignored.
** This quantity is usually positive, because more positive sphere is needed for [[ close-up ]] than for [[ distance vision ]] .

==Technical Details==
This section is for the math - savvy people. He explains the concepts in more detail, but his knowledge is not strictly necessary to use the EM method.

=== Thin lens equation ===
The focal length of a lens is given by the lens manufacturer's equation. Assuming the lens is much thinner than the radius of curvature, so assuming the lens thickness is zero, we get a simplified version of the lens maker's equation. We can do a few more derivations, we arrive at the thin - lens equation: <ref> see derivations athttps://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> <math>{1}\frac{1} d_o}+\frac{1}{d_i}=\frac{1}{f}</math> According to the fineness lens sign convention, * di is positive if it is a real image from the side opposite of the lens to the object, and it is negative if it is a virtual image on the same side of the lens as the object. * f is positive for a converging lens and negative for a diverging lens. This is also sometimes presented in the Newtonian form: <math>

f\right)\left(d_i - f\right)=f^2</math>

==== Examples ====
"Full correction" takes an object at infinity and produces a virtual image at your distance d :

<math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{ - d} = - \frac{1}{d}</math>

This is the resulting equation at the beginning of the article. This also explains why focal power is increased for objects at closer distances: traditional optometry calls this "addition" for [[ presbyopia ]], although they generally use the minimum amount required for you to be able to see at 40cm with full distance correction using housing. For example, if you choose 80 cm as the working distance for your [[ differentials ]] (resulting in an "addition" of +1.25 dpt), and your blur horizon is 50 cm (resulting in -2 dpt ), the formula is

< 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>

=== Cylinder ===
A cylindrical lens of focal power P cyl has a power P at the angle θ of its axis: <math>P = P_{cyl} ( \sin\theta)^2</math> ==== Axis ==== L' axis is usually in degrees modulo 180. It is common for 0 to be written as 180 in some regions. ==== Transposition ==== We can understand why there are two different ways to write a combination of spherical and cylindrical lens, using the Pythagorean trigonometric identity and the complementary angle identity: <math>( \sin\theta)^2 + (\cos\theta)^2 = 1</math> <math> - 90^{\circ}\right)}</math> <math>

P_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math>

We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (like subtracting 90 degrees, since the axis is modulo 180 degrees) to the axis, we get an equivalent combination.

For example, - 1 sph - 1 cyl 1 axis is the same as - 2 sph +1 cyl 91 axis.

In general, optometrists prefer to use a negative cylinder and ophthalmologists prefer to use a positive cylinder, but the two shapes are equivalent.

==== Spherical equivalent ====
{{ See also |Astigmatism#Spherical equivalent }}

Calculating the average value over all angles using an integral, the result <ref> just integrate one or two periods: https://www.wolframalpha.com/input /?i=average +de+%28sin+x%29%5E2+de+0+à+2+pi </ref> is

<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>

C' is why the spherical equivalent has power equal to half the power of the cylinder.

==== Adding/Combining Lenses ====
Multiple lenses, each with spherical and cylindrical components (not necessarily on the same axis) can be added to form a lens with a spherical and cylindrical component.

We can use the double angle formula to convert each cylindrical lens to a constant plus a cosine:

<math>\cos{2\theta}=1 - 2(\sin\theta)^2</math>

<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>

The constant parts are added to the spherical components. 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 the two cylindrical lenses (see the section on transposition), and its corresponding spherical component must be subtracted from the total spherical component.

There are implementations of this at
* http://opticampus.opti.vision/tools/cylinders.php
* http://billauer.co.il/simulator.html

=== Decentration === The
Induced prism can be calculated using Prentice reign. Similar to Vertex Distance, shift is less of an issue for lower power lenses.

The amount of prism power P induced by the decentration c of a lens of power f is <math>P=cf</math> 1 prism diopter displaces 1 cm for an object 1 m away. If c is in cm and f in diopters, then P is in prismatic diopters. A prism with vertex angle a and refractive index n gives an angle of light deflection d, which is equal to P diopters of the prism: <math>d=(n - 1)a</math> <math >P=100\tan{d}=100\tan((n - 1)a)</math>

See [[ Vertex distance#Calculation ]]

==References==
{{ reflist }}
[[ Category: Article ]]

Guide:Start your improvement here

2023-02-26T11:43:12Z

Endmpiauser: /* The Beginning Steps - Stop Myopia Progression: added more detail from the ref. */

[[File:EMBoxLogoTransparent.png|right|200px]]
'''Welcome to [[EndMyopia]]''', the prime place on the internet for regaining your own natural eyesight and reversing your [[Myopia]].

'''EndMyopia isn't a simple program of steps. This page is just the entrance to the rabbit hole.''' Nobody here can tell you how well your eyes will react to a specific change, or what glasses are right for your eyes and your vision habits and your work requirements, we can just give you the tools to understand your own eyesight, what causes myopia progression and how to stop and reverse it.

==The Beginning Steps - Stop Myopia Progression==
# Measure your eyes - you can start with a professional refraction, but you should also learn to measure your own vision at home.
#* If your refraction is better than -10, the [[Measurement#cm_Measurement|cm measurement]] is easy to do and compare values. The cm measurement measures your myopia.
#* The [[Snellen chart]] measures all the combined factors of [[Visual acuity]] and is necessary for checking if your vision meets the legal requirements in your jurisdiction for driving.
#* Measuring your myopia and visual acuity regularly will tell you when the steps you are taking are working.
# Take breaks from near work (Follow the [[3 hour rule]] or the [[20-20-20 rule]] for starters)
# Don't wear glasses for near work if you don't need them.
#* Avoid [[hyperopic defocus]]. The single worst thing, what you really don’t want to be doing at all, ever, is wearing your full-distance correcting prescription while looking at a screen 60 cm from your eyes.<ref>[https://endmyopia.org/day-57-myopia-progression-the-one-thing-you-have-to-stop-doing Myopia Progression: The One Thing You Have To Stop Doing]</ref>
# Get separate glasses for near work if you do need them. We call these [[Differentials]] if your doctor is willing to prescribe them, he may call them computer glasses or reading glasses.<ref>[https://endmyopia.org/day-67-differential-glasses-for-close-up-use Differential Glasses for CLOSE-UP Use]</ref>
# Give this a few weeks, you may be able to release [[Pseudomyopia]] with these steps alone, which will change your eye measurement that you will base your next pairs of glasses on.

==Time to Learn==
{{gif fixer|[[File:Cute cat with glasses and tie reading laptop.gif]]|right}}
Experience has shown many times that without adequate knowledge of the process, people are really unlikely to make any improvements in their eyesight. There is always more to learn about vision improvement, and you should not be afraid to spend significant amounts of time reading the resources already available to you. Arm yourself with knowledge to deal with any bumps in the road that come your way. The community won't answer your medical questions or diopter specific questions, take medical questions to your doctor, and do your own work to understand your specific diopter needs.
# Get the [[seven day free email guide]] - This is a must, if you ask a question in the community that's answered in this guide, your thread will quite possibly be closed by a moderator.
# Consult the [https://endmyopia.org/faqs/ Blog Frequently Asked Questions] and [[Frequently Asked Questions| Wiki Frequently Asked Questions]]
# Read the [{{em}} the blog]
## Hover over (with your mouse) “Blog and How-to’s” and check the “Eyesight How-To’s” and any other sections relevant to you.
## Search the blog. Do you know how to search the [https://endmyopia.org/ blog]? Hit the 🔍️ in the upper right corner and fill in the relevant search item there.
# Watch [[EndMyopia YouTube Channel]]
# Watch [[List:Community YouTubers]]
# Use the Wiki as a reference when you need an overview of a new topic.
# Read the [[Guide:How to ask for support]] then join the [[EndMyopia Forum]] and/or [[EndMyopia_Discord_Server | Discord]] Community.

==Future Steps - Reverse Your Myopia==

# Get slightly reduced glasses for other times when you don't need perfect vision. We call these [[normalized]]. They give a slight blur challenge at a distance. Because glasses are generally rounded off to the nearest quarter diopter, full strength lenses are likely to be slightly over prescribed even if your [[optometrist]] follows the best practices and procedures of his profession. A quarter diopter low would put your distance to blur at 4m, or about 13 feet, and allow your [[ciliary muscle]] to relax when viewing at that distance and beyond. <ref>[https://www.youtube.com/watch?v=LI9JphYXQ6A 20/50 Rule For Improving Eyesight]</ref>
# Find Active Focus, a way of getting your eyes to see slightly further than their normal distance to blur. [[Guide:How_to_find_Active_Focus|Guide: How to find Active Focus]] <ref>[https://endmyopia.org/active-focus-links/ There is a category of blog posts about Active Focus here.]</ref>
# When you're ready, do your first [[reduction]]<ref>[https://www.youtube.com/watch?v=zzrQb4pCFkQ Reduce Normalized Diopters]</ref>

== Putting it all together==

[https://endmyopia.org/wp-content/uploads/2021/12/one-page-cliff-notes-endmyopia.jpg The one page cliff notes]

==Keep Learning==
This page is just the entrance to the rabbit hole. Keep referring to the learning resources above even after you've made your first successful reductions.

You are likely to make mistakes along this journey: there is trial and error as you perfect the approach taken to improving vision. If at any time you have discomfort or disfunction in your new glasses, step back to the previous pair you were comfortable in. The basic ideas are really simple to understand, but there is a lot of nuance in how to apply them, and this can take time to understand fully.

==Beginner's Guide to Vision Improvement==
<youtube>XPIGDSY_xBs</youtube>

==Translations==
This guide has been translated to Polish. See [[EndMyopia Translated]]

==See also==
* [[Student content for new members]]
* [https://www.youtube.com/watch?v=xU6mJr16huk Video Version of Getting Started]
* [https://endmyopia.org/how-to-eyesight-improve-five-steps/ How To Improve Your Eyesight: Just 5 Steps]

[[Category:Guides]]