Difference between revisions of Diopters

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* 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.
* 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.
** There are some caveats such as vertex distance, since moving the lens away effectively gives you a weaker negative lens or stronger positive lens. Effects like those become negligible for weaker lenses.
** 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.
* According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.
* According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.
** A lens with a negative diopter sign compensates for [[nearsightedness]] while a lens with a positive diopter sign compensates for [[farsightedness]].
** A lens with a negative diopter sign compensates for [[nearsightedness]] while a lens with a positive diopter sign compensates for [[farsightedness]].

Revision as of 23:36, 28 August 2021

Diopter is a measure of the 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-1.

  • 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 .
  • Lenses in series add their powers: if you're wearing -2 diopter contacts (adjusted for glasses strength) and put +1 diopter reading glasses over the contacts you're in effect wearing -1 diopters.
    • 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.
  • According to the thin lens sign convention, negative focal power is diverging, and positive focal power is converging.
Approximate categorizations of myopia by spherical lens power:
0.00 to -0.75 dpt Probably don't need glasses
-1.00 to -2.00 dpt Mild myopia, no differentials needed
-2.00 to -5.00 dpt Moderate myopia, glasses always needed
-5.00 to -10.00 dpt High myopia
-10.00+ dpt Very high myopia. Field of view significantly reduced.

Gap and ratio

Comparisons between two diopters is typically expressed using one of these terms:

  • diopter gap (or diopter difference): absolute difference in diopters between the values of the two eyes
  • diopter ratio: ratio of the diopters in one eye over the other one (right eye / left eye)

For example,the following correction:

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

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:

|(-1.5 dpt) - (-1.0 dpt)| = 0.5 dpt
|(-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

Note that the term diopter ratio is often used interchangeably for diopter gap[1], for example when talking about reducing a correction while keeping the gap the same. This can also be expressed as a percentage difference between the two diopter values[2] (e.g. the 0.5 dpt difference between the right and left eyes here is equivalent to 0.5 dpt / |-1.5 dpt| = 0.33 or 33%).

Technical Details

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.

Thin Lens Equation

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 the thin lens equation. We can do some further derivation, we arrive at the thin-lens equation:[3]

According to the thin lens sign convention,

  • 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.
  • f is positive for converging lens and negative for diverging.

This is also sometimes presented in the Newtonian form:


Examples

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


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. 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

References