Diopters - Revision history

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

2023-03-26T09:37:28Z

Gap and ratio: fixed refs

← Older revision		Revision as of 09:37, 26 March 2023
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	, 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 -		, 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>		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 - ~~topic~~ - ~~manage~~ - ~~your~~ -~~maximum - diopter - deviation~~/ </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:		It is often useful to disambiguate what is being compared:
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	** 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.		** 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.		** The axis is ignored.
	** This quantity is usually positive, because more positive sphere is needed for [[ close-up ]] than for [[ distance vision ]] .		** This quantity is usually positive, because more positive sphere is needed for [[ close-up ]] than for [[ distance vision ]] .

	==Technical Details==		==Technical Details==

Endmpiauser: added alternative notation for calculating diopter from the newsletter

2023-03-26T09:24:58Z

added alternative notation for calculating diopter from the newsletter

← Older revision		Revision as of 09:24, 26 March 2023
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	<math>P = \frac{1}{f} = - \frac{1}{d}</math>		<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>.		* 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.		* 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.

Endmpiauser: fix section formatting again

2023-03-26T09:21:09Z

fix section formatting again

← Older revision		Revision as of 09:21, 26 March 2023
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	* http://billauer.co.il/simulator.html		* http://billauer.co.il/simulator.html

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









	~~See [[ Vertex distance#Calculation ]]~~

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

Endmpiauser: fix formatting

2023-03-26T09:13:36Z

fix formatting

← Older revision		Revision as of 09:13, 26 March 2023
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	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 <sup> - 1 </sup> .		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 <sup> - 1 </sup> .

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

	==Gap and ratio==		== Gap and ratio ==

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

Ninebalasan at 12:49, 2 August 2022

2022-08-02T12:49:14Z

Show changes

Ninebalasan at 12:48, 2 August 2022

2022-08-02T12:48:16Z

Show changes

User: /* Examples */

2022-03-28T16:18:24Z

Examples

← Older revision		Revision as of 16:18, 28 March 2022
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	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		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

	<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>		<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>

User: /* Decentration */

2022-03-28T16:16:55Z

Decentration

← Older revision		Revision as of 16:16, 28 March 2022
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	Induced prism can be calculated using Prentice's rule. Similar to Vertex Distance, decentration is less of an issue for smaller power lenses.		Induced prism can be calculated using Prentice's rule. Similar to Vertex Distance, decentration is less of an issue for smaller power lenses.

	The amount of prism P induced by decentration c of a lens of power f is		The amount of prism power P induced by decentration c of a lens of power f is

	<math>P=cf</math>		<math>P=cf</math>

User: /* Cylinder */ change variable to P for power, instead of F for focal power, since f is used for focal length

2022-03-28T16:16:10Z

Cylinder: change variable to P for power, instead of F for focal power, since f is used for focal length

← Older revision		Revision as of 16:16, 28 March 2022
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	=== Cylinder ===		=== Cylinder ===
	A cylindrical lens of power F<sub>c</sub> has ~~focal~~ power F at angle θ from its axis:		A cylindrical lens of focal power P<sub>cyl</sub> has power P at angle θ from its axis:

	<math>F = F_{cyl} (\sin\theta)^2</math>		<math>P = P_{cyl} (\sin\theta)^2</math>

			==== Axis ====
			Axis is usually in degrees modulo 180. It is popular for 0 to be written as 180 in some areas.

	==== Transposition ====		==== Transposition ====
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	<math>F = F_{cyl} \left( 1 - (\cos\theta)^2 \right) = F_{cyl} + \left(-F_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math>		<math>P = P_{cyl} \left( 1 - (\cos\theta)^2 \right) = P_{cyl} + \left(-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 (same as subtracting 90 degrees, since the axis is in modulo 180 degrees) to the axis, we get an equivalent combination.		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.
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	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		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

	<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>		<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>

	This is why the spherical equivalent has power equal to half of the cylinder's power.		This is why the spherical equivalent has power equal to half of the cylinder's power.
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	<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>		<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 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.		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.

User: /* Gap and ratio */

2022-03-28T16:12:11Z

Gap and ratio

← Older revision		Revision as of 16:12, 28 March 2022
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	** The axis is ignored, and the cylinder powers are subtracted without using [[Diopters#Adding/Combining Lenses\|lens combination calculations]].		** The axis is ignored, and the cylinder powers are subtracted without using [[Diopters#Adding/Combining Lenses\|lens combination calculations]].
	* ''diff-norm gap'': differentials diopter minus normalized diopters, ignoring axis		* ''diff-norm gap'': differentials diopter minus normalized diopters, ignoring axis
	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.		** 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.
	** This quantity is generally positive, as more plus sphere is needed for [[close-up]] than [[distance vision]].		** This quantity is generally positive, as more plus sphere is needed for [[close-up]] than [[distance vision]].