# Quantity and quality of vision: exploration

The quality and quantity of vision are explored by various "metric". These are measures objective or subjective, objective measures merely to predict the quality of the retinal image.

### Visual acuity: General information

The beginner reader is invited to read the page dedicated to 'eye and optical‘. In addition, a specialized page is dedicated to: theVisual acuity is its relationship with the resolving power of eye)

Visual acuity is the ability of the eye to distinguish the details of a scene or a Visual pattern observed: these details are 'ends', and more Visual acuity is high. Acuity Visual, often expressed in tenths, corresponds to the resolving power of the eye. Indeed, apart from the details back to separate them, see them as elements of a scene. There are several tests of Visual acuity (threshold, detection, etc.). The measure of Visual acuity is only one of the parameters used to explore the Visual performance.

This page is essentially devoted to generalities about Visual acuity, defined in terms of power of resolution of the eye, for a target at high contrast (there are other types of Visual acuity as the sharpness of detection, etc.). When we talk about "best corrected Visual acuity", it is assumed that the eye is perfectly corrected for any optical defect (myopia or one astigmatism cause a reduction in Visual acuity). Conversely, Visual acuity 'uncorrected' (or 'uncorrected') corresponds to the Visual acuity of an eye without optical correction. Do not confuse tenths and diopters. Visual acuity can be 'monocular' (one eye, the other being hidden), or "binocular" (both eyes at the same time).

Visual acuity is expressed in France by a number of "tenth" or fraction: ex: 3/10 say "3 tenths. There are several types of scale, the most common being called "Snellen scale." It is made up of letters (or optotypes) of different sizes, black on white background (contrast is high). More letters (optotypes) are small, and more constituent details of these letters are difficult to 'split' the eye who is watching. There are several types of unit for quantified Visual acuity (tenth, fractions,) MAR), which are explained in this page and its related links.

Since the viewing distance Visual acuity is affected (if we approach the observed target, the magnification of the letters makes it easier to identify them because their apparent size grows), it is not wise to define the sharpness as a minimum size of letter discerned. The "tenths" are rather related to the notion of apparent angle of the optotype with the eye: this angle helps to maintain a proportionality between the distance and the size of the optotype seen by the eye.

**Visual acuity: retinal theoretical maximum resolution**

What is the theoretical maximum (to separation) Visual acuity of the human eye? It depends on biological and physical factors.

As the definition of an image depends on a number of pixels per unit area (and therefore the size of the pixels), the maximum definition (finesse) of the retinal image depends on the number of photosensitive elements per unit area (density of retinal photoreceptors). At the center of the fovea (foveola), the density of photoreceptors is maximum. All are cones, joined and hexagonal periphery, whose size (diameter) is around 2 to 2.5 microns, and distance inter slightly lower center, the hexagonal nature of the paving.

Reported to a medium focal length of the human eye (17 mm), this size of photoreceptors allows to sample two points underlying an angle of 30 arcseconds (half a minute of arc, or 1 degree of the rapporteur /(180x60x2= 0.00046))... provided that the eye is "optically perfect' (fixed any optical deficiencies, then limited by diffraction only). In these conditions, each point forms a separate image on two adjacent but separate of a photoreceptor photoreceptors "not simulated.

Some physical factors also imply a reduction of the theoretical maximum visual acuity. If the eye is theoretically perfect, the image of a point on the retina cannot, however, be punctual, and the shape of a focal task is called task of Airy (the spreading of light is caused by diffraction to the edges of the pupil). The diameter of this task is equal to 2.44 x(longueur d'onde de la lumière)/diameter of the pupil.

More the pupil is wide, the larger the diameter of the task of Airy is narrow. For a pupil of 6 mm diameter, the diameter of the task of Airy is less than 2 microns. To separate two points on the retina, that:

(1) the focal tasks of Airy are not superimposed

(2) the images of these Airy tasks themselves each on one or several cones separated from one or several cones not stimulated

What are the terms limits of these two prerequisites?

#### Rayleigh criteria

(1) Rayleigh criterion States that two Airy jobs may be regarded as distinct if they are separated by a distance at least equal to their RADIUS (or 1.22 x(longueur d'onde)/diameter of the pupil - RADIUS angle expressed in radians; obtaining a value in micron (distance) requires the use of the focal length of the eye, or 17 mm on average). In the circumstances of the Rayleigh criterion, Airy duties encroach on the other, but it is possible to distinguish two "peaks" of light intensity.

#### Retinal sampling

As the definition of an image depends on a number of pixels per unit area (and therefore the size of the pixels), the definition of the retinal image depends on the number of photosensitive elements (photoreceptors) retinal. At the center of the fovea (foveola), the density of photoreceptors is maximum. All are cones, whose size is around a little less than 2 microns (for children) to 2.5 microns on average.

The sampling frequency of the mosaic of the retinal cones is related to the density of these cones, which is close to 120 cones by degree angle in the foveola (area located at the center of the fovea, where the cones are fine). The Nyquist theorem predicted that the signal to be sampled must have a frequency at most equal to half of the frequency of the cones, or 60 cycles per degree.

In practice, the human eye is sometimes densities of smaller cones, as well as various "imperfections" (ex: optical aberrations of high degree), resulting in a power separation of the eye (which determines the maximum visual acuity) of adults often less than 30 seconds of arc, even when we correct the eye with the 'best glasses '.

The reduction of the pupillary diameter increases diffraction and therefore the radius of the Airy task, but reduces the effect of optical aberrations of high degree; theoretical considerations set out earlier are so modulated by various factors. Thus, it was decided to set the resolving power of the eye to one minute of arc to define "normal" Visual acuity Please understand this line like the one below which we can consider that Visual acuity is lower than normal.

### Optotypes and Visual acuity

By convention, we choose a distance of 20 feet (6 meters) to serve as a reference distance to measure Visual acuity.

In a corner of a minute of arc, we can register one of the horizontal of a letter 'E', as long as it is for example located 6 meters (20 feet) of the eye, and measures 8 mm. The letter E is made up of 5 horizontal bars (3 black and two white). The letter is part of a total angle of 5 minutes of arc. Each of these bars can be understood as part of a 'cycle', and for an acuteness of 10/10, we could register 30 cycles in an angle of 1 degree under tense by the eye (10/10 is equivalent to solving a spatial frequency of 30 cycles per degree). The size of the optotypes is therefore calculated according to the distance where they are projected (6 meters) and the angle under which their details must be seen.

### Visual acuity, MAR, tenths and Snellen acuity

More letters (optotypes) the scale of measure of acuity are small, and more constituent details of these letters are difficult to 'split' the eye who is watching. As the viewing distance affects Visual acuity (if we approach the observed target, the apparent magnification letter makes it easy to identify them because their apparent size grows), it is not wise to define the sharpness as a minimum size of letter discerned. The "tenths" are related to the apparent angle of the optotype with the eye: this angle helps to maintain a proportionality between the distance and the size of the optotype seen by the eye.

The minimum angle of resolution acceptable to a human eye is 1 minute of arc. The minimum angle of resolution is named after the acronym MAR (Minimum Angle of Resolution). Decimal Visual acuity is equal to the inverse of the Mar. A Visual acuity of 10/10 (minimum angle of resolution of 1 minute of arc, either 1/60th of a degree) "solves" a spatial frequency 30 cycles per degree. Indeed, in these conditions each constituent part of the cycle (which includes two: a clear and dark) is part of an angle of 1 /(2×30) = 1/60th of a degree.

In the Anglo-Saxon countries, Visual acuity is expressed as a fraction whose numerator is fixed and equal to 20. How is calculated the denominator (200 for an acuity of 20/200)? A Visual acuity consistent with a minimum angle of resolution of 1 minute of arc allows a letter which details fit into this angle and at 6 m to be identified. If Visual acuity is decreased (by a myopia, for example), the angle of resolution minimum (MAR) increases. It will take to grow the letter so that it is recognized. To express the corresponding Visual acuity, it assimilates the denominator to the distance that this enlarged letter should be remote to be placed at an angle of 5 minutes of arc. For example, an acuity of 20/200 is to solve 20 feet (6 meters) an 'E' whose size is such (26 mm) to move it back to 200 piers (60 meters) to register it in a corner of 5 minutes of arc

An acuity of 20/40 is better than an acuity of 20/200, allowing it to 'see' an E 17 mm at a distance of 6 meters (20 feet), and there is no need to back this letter to 12 meters (40 feet) to register it in a corner of 5 minutes of arc.

These fractions can be expressed with an another numerator (6 meters), or converted to our famous "tenths". 20/20 is so 10/10 (1 in decimal notation), 20/200 is equal to 1/10 (0.1 in decimal notation).

This is the meaning of these tenths of Visual acuity, which are the decimal expression of a fraction. The fraction is a ratio of distances, and this fraction is the reciprocal of a minimum angle of resolution.

It should also never forget that Visual acuity depends on the minimum angle of resolution)MAR). This minimum resolution angle (Minimum Angle of Resolution) determines the Visual acuity. Performing calculations of average or standard deviation range on measures of Visual acuity justifies the use of another unit for these statistical calculations: the log MAR.

[…] Visual by far will be reduced. The tenths allow to quantify the distance vision Visual acuity (ex: 10/10, 8/10, [...])

[…] days to regularize themselves. This explains the vision fluctuations during the first days. Visual acuity uncorrected operated patients is generally between 8/10 and 10/10 on the fifth day [...]