# Eyeglass prescription

Using a phoropter to determine a prescription for eyeglasses

An eyeglass prescription is an order written by an eyewear prescriber, such as an optometrist or ophthalmologist, that specifies the value of all parameters the prescriber has deemed necessary to construct and/or dispense corrective lenses appropriate for a patient.

If an examination indicates that corrective lenses are appropriate, the prescriber generally provides the patient with an eyewear prescription at the conclusion of the exam. In the United States, the FTC (Federal Trade Commission) requires eyewear prescribers to give each patient a copy of their prescription, immediately following the concluding exam, even if the patient doesn't ask for a copy.[1][2]

The parameters specified on spectacle prescriptions vary, but typically include the power to which each lens should be made in order to correct blurred vision due to refractive errors, including myopia, hyperopia, astigmatism, and presbyopia. It is typically determined using a phoropter asking the patient which lens is best, computer automated refractor, and through the technique of retinoscopy. Opticians are not eye doctors and, therefore, are not licensed to write an eyeglass prescription. A dispensing optician will take a prescription written by an optometrist or ophthalmologist and order and/or assemble the frames and lenses to then be dispensed and sold to the patient.

## Abbreviations and terms

Similar to medical prescriptions, eyeglass prescriptions are written on paper pads that frequently contain a number of different abbreviations and terms:

• DV is an abbreviation for distance vision. This specifies the part of the prescription designed primarily to improve far vision. In a bifocal lens, this generally indicates what is to be placed in the top segment.
• NV is an abbreviation for near vision. This may represent a single-vision lens prescription to improve near work, or the reading portion of a bifocal lens. Some prescription forms use ADD in place of NV with a single box to indicate the additional refractive power to be added to the spherical of each eye.
• OD is an abbreviation for oculus dexter, Latin for right eye from the patient's point of view. Oculus means eye. In some countries, such as the United Kingdom RE (right eye), LE (left eye), and BE (both eyes) are used. Sometimes, just right and left are used.
• OS is an abbreviation for oculus sinister, Latin for left eye from the patient's point of view.
• OU is an abbreviation for oculi uterque, Latin for both eyes.
• A spherical correction corrects refractive error of the eye with a single convergent or divergent refractive power in all meridians.
• A cylindrical correction corrects astigmatic refractive error of the eye by adding or subtracting power cylindrically in a meridian specified by the prescribed axis.
• The axis indicates the angle in degrees of one of two major meridians the prescribed cylindrical power is in. Which major meridian is referenced is indicated by the cylindrical correction being in plus or minus notation. The axis is measured on an imaginary semicircle with a horizontal baseline that starts with zero degrees in the 3 o'clock (or east) direction, and increases to 180 degrees in a counter-clockwise direction.

Most eyeglass prescriptions will contain values here. The spherical and cylindrical columns contain lens powers in diopters (see below).

• Prism and Base are usually left empty, as they are not seen in most prescriptions. Prism refers to a displacement of the image through the lens, and is used to treat eye muscle imbalances or other conditions (see vergence dysfunction) that cause errors in eye orientation or fixation. Prism correction is measured in "prism diopters", and Base refers to the direction of displacement.
• Pupillary Distance (PD) is the distance between pupil centers, usually expressed in millimeters. It is sometimes known as the interpupillary Distance (IPD). It is written as two values if the prescription is for bifocals or progressive lenses - these are the pupillary distances for the distance and near fixation (essentially, the upper and lower part of the lenses). They differ due to pupillary convergence when looking at near objects. Additionally, an eyeglasses prescription may include a monocular pupillary distance ("monocular PD"). These measurements indicate, in millimeters, the distances from the center of each pupil to the center of the nose where the center of the frame bridge rests. PD measurements are essential for all spectacle dispensings, monocular PDs being essential in progressive lenses and for those with high prescription. PDs can be measured using a pupilometer or by using a ruler. In some countries, such as the United Kingdom, PD measurement is not a legal requirement as part of the prescription and is often not included.
• Back vertex distance (BVD ) is the distance between the back of the spectacle lens and the front of the cornea (the front surface of the eye). This is essential in higher prescriptions (usually above ±4.00D) as slight changes in the distance between the spectacles and the eyes above this level can cause the patient to perceive a different power, leading to blur and/or other symptoms.

## Background

Blur is the subjective experience or perception of a defocus aberration within the eye. Blur may appear differently depending on the amount and type of refractive error. The following are some examples of blurred images that may result from refractive errors:

Blur is corrected by focusing light on the retina. This may be done with eyeglasses or contact lenses, or by altering the shape of various eye structures via refractive surgery or special contact lenses.

Eyeglasses sometimes have unwanted effects including magnification or reduction, distortion, color fringes, altered depth perception, etc. Although many people think of lenses as magnifiers, the lenses within eyeglasses improve vision primarily by reducing blur. Depending on the optical setup, they may also produce magnification or reduction of images which may or may not be intentional or desirable. Often, magnifiers are part of a regimen prescribed by low vision optometrists to help people with reduced vision.

The visual acuity is measured with an eye chart. The eye chart is the background used by eye doctors to compare the patient's visual acuity with the one of other human beings. Although there are many variations of the eye chart, the standard one is the Snellen eye chart, which was developed by Dutch eye doctor Hermann Snellen in the 1860s.[3] Usually, these charts show 11 rows of capital letters and it is common that the first row contains one letter (the "big E") and the other rows contain letters that are progressively smaller. Other types of eye charts are the Landolt C and the Lea test.

With individuals who are unable to read letters for various reasons, including being too young to know the alphabet or having a handicap, eye doctors may use what is called the tumbling E chart. This type of chart is a variation of the Snellen chart and shows the capital letter E at different sizes and rotated in increments of 90 degrees. The scale of the tumbling E chart is the same as with the standard Snellen chart. The eye doctor, in this case, will ask the person being tested to use either hand (with fingers extended) to show in which direction the "fingers" of the E are pointing: right, left, up or down.[3]

In the United States, a 20/20 visual acuity is considered normal. This means that the chart is normally placed at 20 feet distance from the person who is being tested. 20/20 visual acuity is considered normal vision for individuals, but not perfect, as some individuals, although rare, can see at 20 feet what others can see at 10. While vision can be poorer than 20/200, a person with the best-corrected vision (once wearing corrective lenses) of 20/200 is normally considered legally blind. Individuals with 20/200 vision are normally able to read only the first letter on the chart. Usually the 20/20 line of letters is fourth from the bottom, with 20/15, 20/10 and 20/5 below that. Not many people have 20/10 or better visual acuity, but many animals do, especially birds of prey, which have been estimated to have an acuity of 20/5 or even better.[3] In the United States, individuals who want to get their driver's licenses without corrective lens restrictions must have at least 20/40 visual acuity.

Eye charts do not provide information on peripheral vision, depth perception or color perception and therefore do not sufficiently characterize the quality of vision, nor assess the health of the eyes. A complete eye examination will include other tests. However, eye charts are useful in deciding whether the patients need eyeglasses or contact lenses to correct their distance visions, and assessing how effective their refractive corrections are.

## Lens power

The values indicated in the sphere and cylinder columns of an eyeglass prescription specify the optical power of the lenses in diopters, abbreviated D. The higher the number of diopters, the more the lens refracts or bends light. A diopter is the reciprocal of the focal length in meters. If a lens has a focal length of 13 meters, it is a 3 diopter lens.

A +10 diopter lens, which has a focal length of 10 centimeters, would make a good magnifying glass. Eyeglass lenses are usually much weaker, because eyeglasses do not work by magnifying; they work by correcting focus. A typical human eye without refractive error has a refractive power of approximately 60 diopters.

Stacking lenses combines their power by simple addition of diopter strength, if their separation is negligible. A +1 diopter lens combined with a +2 diopter lens forms a +3 diopter system.

Lenses come in positive (plus) and negative (minus) powers. Given that a positive power lens will magnify an object and a negative power lens will minify it, it is often possible to tell whether a lens is positive or negative by looking through it.

Positive lenses cause light rays to converge and negative lenses cause light rays to diverge. A −2 lens combined with a +5 lens forms a +3 diopter system.

A −3 lens stacked on top of a +3 lens looks almost like flat glass, because the combined power is 0.

In science textbooks, positive lenses are usually diagrammed as convex on both sides; negative lenses are usually diagrammed as concave on both sides. In a real optical system, the best optical quality is usually achieved where most rays of light are roughly normal (i.e., at a right angle) to the lens surface. In the case of an eyeglass lens, this means that the lens should be roughly shaped like a cup with the hollow side toward the eye, so most eyeglass lenses are menisci in shape.

The most important characteristic of a lens is its principal focal length, or its inverse which is called the lens strength or lens power. The principal focal length of a lens is determined by the index of refraction of the glass, the radii of curvature of the surfaces, and the medium in which the lens resides. For a thin double convex lens, all parallel rays will be focused to a point referred to as the principal focal point. The distance from the lens to that point is the principal focal length of the lens. For a double concave lens where the rays are diverged, the principal focal length is the distance at which the back-projected rays would come together and it is given a negative sign. For a thick lens made from spherical surfaces, the focal distance will differ for different rays, and this change is called spherical aberration. The focal length for different wavelengths will also differ slightly, and this is called chromatic aberration.[4]

## Spherical lenses and spherical correction

Usually:

• the spherical component is the main correction
• the cylindrical component is "fine tuning".

Depending on the optical setup, lenses can act as magnifiers, lenses can introduce blur, and lenses can correct blur.

Whatever the setup, spherical lenses act equally in all meridians: they magnify, introduce blur, or correct blur the same amount in every direction.

An ordinary magnifying glass is a kind of spherical lens. In a simple spherical lens, each surface is a portion of a sphere. When a spherical lens acts as a magnifier, it magnifies equally in all meridians. Here, note that the magnified letters are magnified both in height and in width.

Similarly, when a spherical lens puts an optical system out of focus and introduces blur, it blurs equally in all meridians:

Here is how this kind of blur looks when viewing an eye chart. This kind of blur involves no astigmatism at all; it is equally blurred in all meridians.

Spherical equivalent refraction is normally used to determine soft lens power and spherical glasses power. Individuals who are applying for different positions in police or military may be given a certain maximum spherical equivalent they can have.

## Amount of refractive error and degree of blur

Approximation of blur seen by a patient. (In actuality, defocus blur is much less "soft" than the Gaussian blur shown.)

The leftmost image here shows a Snellen eye chart as it might be seen by a person who needs no correction, or by a person who is wearing eyeglasses or contacts that properly correct any refractive errors he or she has.

The images labelled 1D, 2D, and 3D give a very rough impression of the degree of blur that might be seen by someone who has one, two, or three diopters of refractive error. For example, a nearsighted person who needs a −2.0 diopter corrective lens will see something like the 2D image when viewing a standard eye chart at the standard 20-foot distance without glasses.

A very rough rule of thumb is that there is a loss of about one line on an eye chart for each additional 0.25 to 0.5 diopters of refractive error.

The top letter on many eye charts represents 20/200 vision. This is the boundary for legal blindness; the US Social Security administration, for example, states that "we consider you to be legally blind if your vision cannot be corrected to better than 20/200 in your better eye." Note that the definition of legal blindness is based on corrected vision (vision when wearing glasses or contacts). It's not at all unusual for people to have uncorrected vision that's worse than 20/200.

## Cylindrical lenses and cylindrical correction

Some kinds of magnifying glasses, made specifically for reading wide columns of print, are cylindrical lenses. For a simple cylindrical lens, the surfaces of the lens are portions of a cylinder's surface. Consider how this would refract light. When a cylindrical lens acts as a magnifier, it magnifies only in one direction. For example, the magnifier shown magnifies letters only in height, not in width.

Similarly when a cylindrical lens puts an optical system out of focus and introduces blur, it blurs only in one direction.

This is the kind of blur that results from uncorrected astigmatism. The letters are smeared out directionally, as if an artist had rubbed his thumb across a charcoal drawing. A cylindrical lens of the right power can correct this kind of blur. When viewing an eye chart, this is how this kind of blur might appear:

Compare it to the kind of blur that is equally blurred in all directions:

When an eye doctor measures an eye—a procedure known as refraction—usually he begins by finding the best spherical correction. If there is astigmatism, the next step is to compensate it by adding the right amount of cylindrical correction.

## Axis

Spherical lenses have a single power in all meridians of the lens, such as +1.00 D, or −2.50 D.

Astigmatism, however, causes a directional blur. Below are two examples of the kind of blur you get from astigmatism. The letters are smeared out directionally, as if an artist had rubbed his or her thumb across a charcoal drawing.

A cylindrical lens of the right power and orientation can correct this kind of blur. The second example is a little bit more blurred, and needs a stronger cylindrical lens.

But notice that in addition to being smeared more, the second example is smeared out in a different direction.

A spherical lens is the same in all directions; you can turn it around, and it doesn't change the way it magnifies, or the way it blurs:

A cylindrical lens has refractive power in one direction, like a bar reading magnifier. The rotational orientation of that power is indicated in a prescription with an axis notation.

The axis in a prescription describes orientation of the axis of the cylindrical lens. The direction of the axis is in degrees measured anti-clockwise from the horizontal line through the centers of the pupils when viewed from front side of the glasses (i.e., when viewed from the point of view the person making the measurement). It varies from 1 to 180 degrees.

In the illustration below, viewed from the point of view of the person making the measurement, the axis is 20° if written in plus notation or 110° if written in minus notation.

The total power of a cylindrical lens varies from zero in the axis meridian to its maximal value in the power meridian, 90° away. in the example above the axis meridian is located in the 20th meridian, and the power meridian is located in the 110th meridian.

The total power of a lens with a spherical and cylindrical correction changes accordingly: in the meridian specified by axis in the prescription, the power is equal to the value listed under "sphere". As you move around the clock face, the power in a given meridian will get steadily closer to the sum of the values given for sphere and cylinder until you reach the meridian 90° from the meridian specified by the axis, where the power is equal to the sum of sphere and cylinder.

## Spherical equivalent refraction (SER)

Eye care professionals use the term spherical equivalent refraction (SER) to refer to an eye's effective focusing power if only spherical aberration were present. SER can be defined as:

$SER = \text{sph.} + \frac{1}{2}*\text{cyl.}$

## Distant vision (DV) and near vision (NV)

The DV portion of the prescription describes the corrections for seeing far away objects. The NV portion is used in prescriptions for bifocals to see very close objects. For most people under forty years of age, the NV or near-vision portion of the prescription is blank because a separate correction for near vision is not needed. In younger people, the lens of the eye is still flexible enough to accommodate over a wide range of distances. With age, the lens hardens and becomes less and less able to accommodate. This is called "presbyopia"; the presby- root means "old" or "elder". (It is the same root as in the words priest and presbyterian.)

The hardening of the lens is a continuous process, not something that suddenly happens abruptly in middle age. Though it is typically by the middle age when the process has progressed to the point where it starts to interfere with reading. Therefore almost everybody needs glasses for reading from the age of 40–45. Because young children have a wider range of accommodation than adults, they sometimes examine objects by holding them much closer to the eye than an adult would.

This chart (which is approximate) shows that a schoolchild has over ten diopters of accommodation, while a fifty-year-old has only two. This means that a schoolchild is able to focus on an object about 10 cm (3.9 in) from the eye, a task for which an adult needs a magnifying glass with a magnification of about 3.5.[citation needed]

The NV correction due to presbyopia can be predicted using the parameter age only. The accuracy of such a prediction is sufficient in many practical cases, especially when the total correction is less than 3 diopters. See also the following calculator for computing this correction.

When someone accommodates, they also converge their eyes. There is a measurable ratio between how much this effect takes place (AC:A ratio, CA:C ratio). Abnormalities with this can lead to many orthoptic problems.

## Optical axis and visual axis

The optical axis is the centre of a lens where light travels through and is not bent. The visual axis is where light travels through the eye to the retina and is essentially understood to not be bent.

Sometimes glasses are given with the optical axis shifted away from the visual axis. This creates a prismatic effect. Prisms can be used to diagnose and treat binocular vision and other orthoptics problems which cause diplopia such as:

## Variations in prescription writing

There is a surprising amount of variation in the way prescriptions are written; the layout and terminology used is not uniform.

When no correction is needed, the spherical power will sometimes be written as 0.00 and sometimes as plano (pl.). The lens, although not flat, is optically equivalent to a flat piece of glass, and has no refractive power.

When cylindrical correction is needed, the mathematics used to denote the combination of spherical and cylindrical power in a lens can be notated two different ways to indicate the same correction. One is called the plus-cylinder notation (or "plus cyl") and the other the minus-cylinder notation (or "minus cyl"), based upon whether the axis chosen makes the cylindrical correction a positive or negative number.

For example, these two prescriptions are equivalent:

NotationSphericalCylindricalAxis
Plus-cylinder notation+2.00+1.00150°
Minus-cylinder notation+3.00−1.0060°

The plus-cylinder notation shows the prescription as a correction of +2.00 diopters along an axis of 150° and an additional correction of +1.00 diopters, giving a total correction of (+2.00) + (+1.00) = +3.00 diopters, at 90 degrees from that meridian (= 60°).

The minus-cylinder notation shows the prescription as a correction of +3.00 diopters along an axis of 60° and an additional correction of −1.00 diopters, giving a total correction of (+3.00) + (−1.00) = +2.00 diopters, at 90 degrees from that meridian (= 150°).

The result in both cases is +2.00 diopters at the 150th meridian and +3.00 diopters at the 60th meridian.

The method to transform one format to another is called flat transposition:

• Add cylindrical value to the spherical one
• Invert the sign of cylindrical value
• Add 90° to axis value, and if the new axis value equals or exceeds 180°, subtract 180° from the result

In practice, optometrists tend to use minus-cylinder notation, whereas ophthalmologists and orthoptists tend to prescribe using plus-cylinder notation. However, some ophthalmologists and orthoptists (such as in Australia) are changing to using minus-cylinder notation.[citation needed]

In addition to the plus and minus cylinder notations, some countries use slight variations for special purposes. For example, the National Health Service of the United Kingdom uses the term Greatest Spherical Power when looking up the amount of state optical benefits that can apply to a particular prescription. This is simply the transposition of the prescription format so that the magnitude of the sphere is greatest. In the examples given earlier this would be the minus-cylinder version; that is, +3.00 −1.00 x 60° as opposed to +2.00 +1.00 x 150°.

## References

1. ^ The Contact Lens Rule (16 C.F.R. Part 315) and the Eyeglass Rule (16 C.F.R. Part 456). Ftc.gov (2011-06-24). Retrieved on 2013-07-21.
2. ^ http://www.ftc.gov/opa/2004/10/BUS63-contactfaq.pdf
3. ^ a b c "The Eye Chart and 20/20 Vision". Retrieved 2010-06-18.
4. ^ "Principal Focal Length". Retrieved 2010-06-18.