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Visual acuity, resolution and resolving power

All about Visual acuity

Visual acuity as resolving power is measured as the ability to separate visually two separate objects. It's this kind of acuity that commonly explored in Ophthalmology (by read more small letters), to measure eye refraction, before and after refractive surgery, for example. For a same distance of observation, more objects to distinguish are close, more Visual angle (angle whose top is the eye) that they form is weak, and more the resolving power is high. Visual acuity described here is central Visual acuity, IE to the Foveal vision (the fovea is at the center of the macula, and is the seat of the fine vision). The Visual acuity of an eye corresponds to the so-called Visual acuity 'monocular '.  Visual acuity can also be measured in binocular vision.  The material provided on this page are mainly monocular Visual acuity. Visual acuity is important to appreciate the Visual function, but he is not alone. The sensation of contrast, relief)stereoscopic acuity) are other factors which contribute to ensure a good visual performance. However, they require the presence of a good visual acuity.

How to quantify the maximum visual acuity? What maximum visual acuity an eye can achieve? What are the parameters that influence Visual acuity? This page is intended to provide answers to these questions.


minimum angle of separation and Visual acuity

The resolving power is inversely proportional to the minimum angle that can form two sources with the eye while their retinal images are "just separated". These images are formed after refraction (diffraction) waves light issued by sources and captured by the eye. The notion of 'separation' of these images is less trivial than it seems: it depends on factors related to the image, as well as of physical parameters (diffraction in the case of an eye perfectly corrected) and neuro-biological (the density of the photoreceptors of the retina, which sample the retinal image)

Visual acuity expresses this ability to separate, that is to say form a separate image of each object on the retina. In France, it is commonly expressed in «» ", rather than a minimum angle of separation ().minimum separabile), or MAR (Minimum Angle of Resolution). Visual acuity usually considered as 'normal' is 10/10″, which corresponds to a minimum angle of resolution (MAR) of 1 minute of arc (1/60th of a degree of Visual angle). This threshold is not really functional or anatomical justification as discussed: it was probably held for historical reasons: astronomer Hooke (17th century), known to have been the rival of Newton, had issued the note that most observers could just separate from the stars in the sky, the apparent angle with the eye is of one minute of arc.

Visual acuity and resolving power

Visual acuity (resolving power) 10/10th to solve a couple of stars, the apparent angle with the eye is of one minute of arc. In practice, Visual acuity may cross that line, and separate patterns still fine (up to 30 seconds of arc, about 20/10). This ability is linked among other things to the conjunction of physical phenomena (diffraction) and anatomical (spatial density of photoreceptors). Separate the respective star images assumes that their retinal projection is separate, and the retina to sampling, that is to say separate these images: therefore, that between the stimulated photoreceptors, some are not: If the image of every star was projected on two contiguous photoreceptors, it would be difficult to interpret the image formed like that of two separate points. These concepts will be developed further.

Visual acuity of the simplified eye

To estimate the resolving power of the eye (and deduce the Visual acuity), it is useful to make some simplifications:

-We're interested in the power of optical resolution (the retinal resolution, related to the density of retinal photoreceptors of the fovea, is supposed to be sufficient to sample the signal: this is the case in practice).

-the source objects to separate are basic (S1 and S2) points

-the eye is considered to be a simplified, optical system which is 17 mm focal length from the nodal point (the retina is located in the focal plane: the eye is Emmetropic, it accommodates not). The eye forms an image perfectly focused on the plan of the fovea (Emmetropic eye). The optical eye (horny and crystalline) may be simplified and likened to a paraxial system equipped with two nodal points, but their anatomic proximity (they are located toward the back of the lens) allows in this context to confuse them into a single nodal point. The length from the nodal point is not equal to the axial length: this length is therefore defined since this nodal point (N), located towards the back of the lens, or about 17 mm from the fovea.

-the constraints related to the need to sample the light signal are not addressed at this stage.

We are trying to estimate the resolving power of the eye: this is to determine the distance between two sources S1 and S2 so that their images I1 and I2 are "resolved" on the fovea. Each source emits rays in all directions, including a parts is captured by the eye.

nodal point acuity rays

Sources S1 and S2 are such that they form after refractions by the cornea and the lens each image (respectively I1 and I2), these images should be just "separated" or resolved at the level of the fovea (these images must not encroach on the other, because otherwise they will not be separated.) There among the refracted rays from S1 a ray which is "not deviate", and goes through the nodal point N. This construction (theoretical) can also be performed for source S2. These rays are traced in bold on the schema

When an incident Ray passes through the nodal point, he emerges not 'deviated' (it forms the same angle to the entrance and exit of the optical system). So restricting our schema to the record of these rays.

acuity Visual axis nodal point

The previous schema is restricted to the rays through the nodal point N. Its distance from the fovea is 17 mm. The goal is to calculate alpha, the minimum angle that can form two separate sources to be resolved at the level of the retina. If it is determined the minimum distance between I1 and I2, we can then deduce the alpha angle through a minimum of knowledge in trigonometry (this angle is equal to the tangent arc between I1I2 distance divided by 17!)


To determine the minimum distance between I1 and I2, address the problem of the diffractionrelated to the passage of the light through the IRIS pupil, whose diameter can vary between 2 and 7 mm approximately. Diffraction induces a "spread" of the image of a point source, even when the optical system has no aberration.


Diffraction, stigma, power of separation

In geometric optics, we consider the light as consisting of rays, and images of point sources can be point, located at the intersection of some rays.  The stigma is said to be rigorous, we neglect the effects of diffraction. However, the calculation of the resolving power of the eye must consider diffraction, related to the wave of light appearance, and the fact that the presence of a natural aperture of the eye (the pupil) necessary to hold account of diffraction.

We can calculate that due to diffraction, the image of a point can be a point because light always spreads after crossing an obstacle (pupil), and this proportion to the wave length used, and pupillary diameter.

The wavelength is large, the pupillary diameter is small, and more sprawl is important. The light spread in the form of a luminous disc surrounded by concentric bright. In practice, the central disc has almost all of the light intensity.

A formula to get the diameter of the central disk of this sprawl: diameter = 2.44 x wavelength x focal length / pupillary diameter.

sharpness diffraction Airy Pupil

The distribution of light intensity in concentric surfaces is related to diffraction by edges of the pupil of the indecent light waves. The diameter of the central peak (which concentrates the light) is given by the formula: 2.44 F λ / D.

The eye can therefore form actually spot images of point sources: in the best of the case, it forms almost one-off images, which we will call focal tasks, and whose diameter is of the order of a few microns (see examples more away: we could also call these focal tasks of PSF, for "Point Spread Function, the Point spread function).

We notice that in the case of the ideal eye (not), for a given wavelength, only the pupillary diameter can vary the focal spot diameter: more the pupil is wide, and more (theoretically) the focal spot is small.

In fact, for real normalsighted same eyes, pupillary dilatation induced the increase in the rate of aberrations of high degree, which tends to expand the focal spot.

In case of myopia, the focal spot is more so extended that the diameter of the pupil is wide: the light rays cross in front of the retina, and diverge to form by her meeting a disk on the retina. The dilation of the pupil induces a rapid additional increase in the diameter of the focal spot, that's why in part that the myopic eyes see less well when the brightness decreases and the pupil dilates (see role of the pupil). That is also why the myopic "blink", pucker or knitted the eyes to improve their Visual acuity (the folded eyelids reduce the diameter of the beam allowed by the eye).

However, we can apply the reasoning based on an Emmetropic eye for a nearsighted eye provided that one has a correction (glasses or lens). Surgery (refractive)LASIK(, PKR) aims to reduce the diameter of the focal task of an affected eye optical defect so that it reaches at least the minimum imposed by diffraction.

acuity eye simple lens pupil

A simplified average eye has a distance between simplified single nodal point and 17 mm fovea, a pupil of variable diameter. The wavelength is located in the green yellow (ex: 0.580 microns)

We know that a point is imaged as a bright drive (the peak of intensity width) on the retina. The resolving power is based on the ability of the eye separate these spikes of light intensity. The following diagram shows, in virtue of the Rayleigh criterion, we can separate these spikes as long as their spacing is equal to half of the diameter of each (either their RADIUS, equal to 1.22 λ F / D). In this situation, the focal tasks encroach a little on the other, but the sum of the intensities of each focal spot is between the center of the peaks of intensity and the point between these, there is an intensity of 20% differential, which is enough to 'split' the focal tasks.

The ability to separate two focal tasks (called Airy tasks when bright sprawl depends only on diffraction) is based on their spacing, which must at least be equal to their RADIUS (Rayleigh criterion). In these conditions, the tasks are 'just separate': there is a difference of detectable intensity between the peaks (maximum) and the space between the (minimum) peaks. Closer, the images would appear confused.


The calculation reported on the illustration shows that space (the distance) minimum between light intensity peaks formed on the retina must be of 4 microns for their 'resolution' according to the Rayleigh criterion, and this for the following conditions: a pupil diameter of 3mm and a wavelength of 580 microns (and a length from the nodal point to the fovea of 17 mm). This (4 microns) is achieved by calculating: 1.22*0.580/17000 (distances expressed in microns). Note that if you had considered a more important pupillary diameter, it would have calculated a minimum distance between the peaks more restricted (through the reduction of the effects of diffraction).

Knowing the minimum distance between the peaks of intensity to their resolution, we can calculate the minimum angle that must underlie the two light sources points to be separated at the level of the retina, according to the constraints due to light diffraction (sampling constraints will be considered further).

The angle formed by the two sources and the eye (which occupies the vertex of the angle) is called 'minimum angle of resolution')Minimum Angle of Resolution: MAR)

angle resolution resolving power

A minimum spacing of 4 microns the retinal plane requires an angle of the source separation equal to 0.0135 degrees, that is 0.8 minutes of arc (1 degree = 60 minutes of arc). The minimum resolution angle (Minimum Angle of Resolution MAR) is equal to 0.8 arc minutes. Visual acuity in tenths is equal to the inverse of the MAR: 1/0.8 = 1.25 = 12.5 / 10 approximately 12/10.


Decimal Visual acuity is expressed as a fraction of which the numerator is equal to 10.

Visual acuity is equal to the inverse of the value of the MAR angle expressed in minutes of arc.

Visual acuity = 1/MAR

MAR one minute of angle equals an acuity of 1/1 = 1 = 10/10. If the angle MAR double (2 minutes of arc) Visual acuity is logically divided by 2 (1/2=0.5=5/10).

In our example, an angular resolution of 0.8 arc minutes is equivalent to a Visual acuity of 1/0.8=1.25= 12.5/10.  The MAR angle is reduced by 20% (0.8 minutes of arc), Visual acuity increases by 20% (or 12/10 rather than 8/10). It is easier to think in MAR that in tenths, this decimal notation is in fact more away from the physical reality of what is the Visual acuity of resolution (resolving power). The MAR is growing in a geometric way (if it doubles: Visual acuity is divided by 2, if it triple, 3, etc.). For statistical calculations, we use the logarithm of the MAR (logMAR), whose growth is arithmetic.

Back to our Visual acuity of resolution. The most common test used in ophthalmology offices do not use points to separate, but a system of projection of letters or numbers)optotypes).

The recognition of a letter guess to distinguish details that make it up. To recognize an 'E', 5 horizontal bars (alternately black and white). The power of resolution should for example resolve (separate) two adjacent bars. in the following example. the first bar is black, and the second bar is white. The black bar and white bar must be separated - this implies that the black bar is one of the images to separate, even if its luminance is zero.

measure Visual acuity

The measurement of Visual acuity tests the ability of the eye to "solve" geometric patterns (mostly letters). Depending on the distance of the test, and its size, we can calculate the angle only under tends the smallest details of this test (here, the distance between a horizontal component of the 'E' of the adjacent bar).

Knowing the resolving power of the eye (minimum angle of resolution), one can calculate the angular size of the details to identify a letter.

A letter as the 'E' is a series of black and white horizontal interleaved (3 white bars separated by 2 black bars). For example, an eye whose visual acuity is such that 5 metres, the smallest he could identify the size of the letter 'E' is 5.5 millimetres.

The E is made up of 2 black bars and 3 white bars. Each bar measures so 1.1 mm (the vertical dimension is 5.5 mm for the letter E). We know the distance where the letter is displayed, and its size: by a simple trigonometric calculation involving the tangent we can calculate the angle in which fits this letter: it is 4 minutes of arc. The first white horizontal bar is separated from the first black bar by an angle of 0.8 arc minutes. This angle is the minimum angle of resolution (MAR). An angle MAR 0.8 arc minutes corresponds to a decimal acuity of 1/0.8 12.5/10 =. The size of the image of a bar on the retina is 2 microns: a white bar and a black bar so occupy 4 microns, and the image of the E 10 microns.

The tables of letters and numbers used to measure Visual acuity are designed so that at a distance of 5 metres about the height (vertical dimension) of the letter corresponding to a Visual acuity of 10/10 (minimum angle of resolution equal to one minute of arc) is 7.3 mm. This size corresponds to an apparent angle of 5 minutes of arc, with traits or the gaps (for example, the horizontal bars of the 'E') of 1 minute of arc (since these details must be seen when they meet at an angle of less than 1 minute of arc). The size of the retinal image to view letter in these conditions is close to 25 microns.

The first white bar of the E and the adjacent dark bar form a close pattern of what is called a «» cycle«: a sinusoidal variation of luminance, with a maximum and a minimum.»

diagram linking acuity resolution and cycle

Two adjacent bars of the letter 'E' have the same spatial extension than a cycle. The angle in which fits the cycle in full is equal to twice the angle necessary to the resolution of the cycle.


Visual acuity can be expressed in cycles per degree angle it is possible to solve. More you can enter a degree cycles, more these cycles are 'ends' (for a same distance), and greater the power of resolution (sharpness).

Visual acuity and cycles per degree

The power of resolution can be expressed in numbers of cycles solved by degree. The minimum angle of resolution is equal to 30 /(nombres de cycles par degré). Solve 30 cycles per degree (angle of minimum resolution: a minute of arc is 1/60th of a degree) is equivalent to a Visual acuity of 10/10. Solve 5 cycles per degree is equivalent to a minimum angle of resolution of 6 minutes of arc, an acuity of 1.6/10

If a cycle is requires an angle of 0.8 minutes of arc to be resolved, he enrolled in an angle equal to the double of this angle of resolution (2 x 0.8 = 1.6 minutes of arc). A degree has 60 minutes of arc: in a degree angle can then register 60/1.6=37.5 of these cycles. Expressed in cycles per degree, the resolution of the eye in this example is therefore 37.5 cycles per degree, which correspond to a sharpness of 12/10. This conversion in the cycle can convert decimal acuity, or MAR in number of cycles per degree.

Visual acuity measured at 10/10 allows in theory to solve 30 cycles per degree. When 30 cycles are enrolled in a degree angle, each cycle is an angle of 1 minute of arc (ago 60 minutes of arc in a degree). Visual acuity in tenth corresponds to the inverse of the minimum angle of resolution (expressed in minutes of arc).

Visual acuity in tenths is calculated as the inverse of the minimum angle of resolution expressed in minutes of arc. 30 cycles per degree correspond to a resolving power of 1 minute of arc, is 10/10.

Visual acuity in tenths is calculated as the inverse of the minimum angle of resolution (MAR) expressed in minutes of arc. 30 cycles per degree correspond to a resolving power of 1 minute of arc, is 10/10.

This unit (cycles per degree) is convenient to calculate visual acuity needed to identify some of the reasons (ex: urban display), or calculate the required resolution for best use Visual acuity and the power of resolution of the eye)see these examples page). The number of cycles per degree allows to quantify the period for the spatial frequency.
The progression of the visual acuity scales of type Monoyer (in tenths) is of geometric type. The transition from a visual acuity of 1/10 to 2/10 is equivalent in terms of gain at the transition from a sharpness of 5/10 to 10/10 (in both case, there is a doubling of the visual acuity, since the angle of resolution minimum-MAR – is divided by two!).

The interval between the lines of the scale is not constant, the use of this notation is unsuitable for performing statistical calculations, requiring the prior converted to logarithms acuity figures expressed in tenths or minimum resolution (MAR) angle. The following figure shows schematically the progression of Visual acuity in tenths (AV) according to that of the minimum angle of resolution (MAR). Observed that the closer the 1 min of arc MAR 10/10 (angle), more progression in tenths is fast: there is little difference between a Visual acuity of 8/10 and a Visual acuity of 10/10...

Representation of Visual acuity that is divided into 10 sectors each corresponding to a MAR of a minute of arc angle (whose width has been exaggerated for didactic reasons). From a sea of 1 minute (10/10) a reduction in Visual acuity (AV) of half logically corresponds to doubling the angle MAR (value: 2 minutes of arc), which corresponds to a decimal AV in 1/2 or 0.5. For statistical calculations of average type, refers to the value of the logarithm of the angle MAR (MAR log)
The following figure corresponds to the schematic graphical presentation of the geometric progression of the decimal visual acuity – i.e. expressed in tenths (the angular sectors between the acuitys of 10/10 and 5/10 were slightly magnified For the clarity of the illustration). The minimum resolution is the minimum angle for separating two points. In this illustration, one of the dots is located on the horizontal axis, and the maximum visual acuity (10/10) corresponds to a resolution (MAR) of 1 minute of arc (red sector).

increase decimal acuity

The progression of the decimal acuity is geometrical: between each tenth, the reduction of the MAR (minimum angle of resolution) is not constant. All the "tenths" is not the same! The angle corresponding to the Red sector is equal to 1 minute of arc (the drawing is of course not scaling, and minimum resolution corresponding to each decimal acuity angles are formed with the horizontal direction)

To compensate for this problem, it is necessary to convert decimal acuity in a unit whose growth is arithmetic.

LogMAR scale:

The decimal logarithm of a number N is the value of the exponent as N = 10 exp (x) x. The decimal logarithm of 10 is 1 since 10 (exp1) = 10. The decimal logarithm of 1 is 0, since 10 exp (0) = 1.

LogMAR scale uses the decimal logarithm of the minimum angle of resolution (MAR).

Acuity LogMAR =-log(dixieme Visual acuity)

Decimal Visual acuity = 1 10 acuity LogMAR

This scale has a constant interval between lines, and doesn't depend on the measured Visual acuity levels. It allows the calculation of averages, of the standard deviation on a series of measures: the value of the average obtained from acuity logMAR (geometric mean) is always less than that obtained from the decimal acuity of because of the difference in growth between the two scales.
The calculation of the gain or loss of lines of Visual acuity is the result of the subtraction between the initial and final acuities in logMAR (arithmetic scale) multiplied by ten. The passage of acuity from 2/10 to 1/10 is actually a loss of 3 lines: [log (0.1) - log (0.2)] x 10 = - 3. However, the passage of a sharpness from 10/10 to 9/10 is less than half a line of Visual acuity [log (0.9) - log (1)] x 10 = - 0, 45).

There are many factors of variation of Visual acuity measurement conditions. In addition to the form test (scale of Monoyer, Landolt rings...) and the distance of presentation, the average luminance and contrast sensitivity are two particularly important parameters in the assessment of the quality of vision and can affect the measurement of Visual acuity.

In theory, these two parameters must be adjusted around values defined by convention: 85 + / 5 cd/m2 for maximum luminance, and 0.85 for the contrast for maximum visual acuity measurement. The increase in retinal illuminance improves the contrast sensitivity. The contrast should not be less than 0.70; When Visual acuity is tested with a low (less than 0.3) contrast, it decreases sharply, the reduction of contrast primarily affecting the perception of the high spatial frequencies. The calculation of the curve of MTF informs about the theoretical contrast of the retinal image.


Theoretical consideration, practical consequences

It is customary to consider that 10/10 is a "normal" Visual acuity Using our forms for pupillary diameter 2.4 mm, a minimum distance of 5 microns would have been calculated for I1I2 distance, and the alpha angle would have been equal to one minute of arc (1/60th of a degree). Visual acuity of 10/10 is a "standard", which corresponds to an arbitrary decision: can be seen in practice that this acuteness is a minimum below which we can consider that Visual acuity is reduced toward normal.

We can calculate the theoretical limit for the optical resolution of the human eye is close to 20/10 (or 120 cycles per degree), by increasing the diameter of the pupil (ex 5 mm). This is quite theoretical because it is assumed that this expansion does not too pronounced degradation of the optical quality of the eye by the induction of optical aberrations of high degree.

In these conditions, the distance I1I2 corresponds to a retinal spacing of 2.5 microns for the focal tasks. It is interesting to note that the minimum diameter of a cone of the fovea is of the same order of magnitude than this value (between 1.5 and 2.5 microns). Evolution has selected optimal size of photoreceptor: smaller, it would be useless (on sampling), bigger, she would not allow to properly sample the finer details (under sampling). Indeed, measured in some patients an acuity near or equal to 20/10, without (emmetropes) or with (myopic/astigmatic/hypermetropia) appropriate optical correction. There are significant variations in the density (size) of the cones in the fovea to the eye, which explains the maximum Visual acuities may vary from one individual to the next.

The optical correction by glasses glass can significantly change the size of the retinal image of an ametropic eye (with respect to the size of the "fuzzy" retinal image of this same eye when it is not corrected). This can affect visual acuity as the reduction in the size of the retinal image causes a reduction in the maximum visual acuity, it is possible to get to a same capacity of sampling of retinal photoreceptors.

Size of photoreceptors and Visual acuity

The size of the photoreceptors (spacing) is the ultimate limit of Visual acuity, for a Visual system whose perspective is perfectly corrected for the aberrations of low and high degree: even if the light signal from two separate sources points is transmitted accurately to the retinal level, it remains necessary whether well "interpreted" and transmitted to the Visual areas: the interpretation of the signal by the photoreceptor cells is called "sampling".

The perceived signal sampling is accomplished by the mosaic of photoreceptors (the central area of the fovea, whose diameter is close to 400 microns, contains only cones, and not stick). More this mosaic is dense, and it allows sampling without loss of the high spatial frequencies. The density of cones in the central region of the fovea of the human eyes (foveola) is between 120,000 and 200,000 cones/mm2. Such a high density corresponds to an ability to close sampling of 60 cycles per degree, but there are variations according to the eyes, related to the minimum size of these photoreceptors, which can be around 1.6 microns for the smallest. The paving of the fovea by cones is a polygonal overall hexagonal, what makes that the distance between the centers of cones is somewhat lower than their maximum diameter. The cones of the Central fovea are connected each to a single ganglion cell, a cell to transition the expansion of which joined the optic nerve.


Visual acuity and density of the photoreceptors

The density of photoreceptors determines the theoretical maximum visual acuity. To sample a cycle, its retinal image size must not exceed a couple of contiguous photoreceptors. The maximum visual acuity (power of separation) is the angle in which fits the smallest echantillonnable cycle. As It takes two photoreceptors to sample a cyclethe limit of sampling in cycles per degree angle (Nyquist limit) is equal to half of the spatial frequency of the cones in the fovea. For the human eye, this limit is close to 60 cycles per degree (120 cones by degree), which corresponds to an angle of resolution of a half minute of arc (or 30 arc seconds) - either 1 degree angle divided by 120 - and a decimal acuity of 20/10.

Finally, other factors of neuro-cognitive order affect visual acuity; the Organization of the retinal receptors fields (wiring between photoreceptors and cell relay) is designed to promote the perception of 'edges', details (ex: bars of the E). In addition, it is sometimes easier to "guess" a letter that describe an abstract pattern. Some tests of Visual acuity using the same motive which only orientation varies (ex: a Landolt ring, a = C E we moving way vertical, horizontal, oblique, etc.).

Visual acuity: eyes human vs. animal eyes

Maximum visual acuity of the human eye is in the order of 60 cycles per degree, or 30 seconds of arc (1/2 minute of arc = 0.5 minutes of arc: in tenths corresponding Visual acuity is 20/10 as it corresponds to the inverse of the maximum of resolution angle or MAR for Maximum Angle of Resolution: or 1/0.5 = 2 = 20/10). The calculation of the maximum resolution retinal angle is equal to the tangent arc between the photoreceptor inter distance and the distance between the nodal point and the fovea. If the eye is bigger, the distance between the nodal point and the fovea is larger, and the angle of lower resolution (best visual acuity). In addition to a greater density of photoreceptors, a bigger look allows also to benefit from a better resolving power.

The Eagles have thethe highest Visual acuity of the animal Kingdom. Compared to human eyes, the Eagles have a double vision, that is to say that the maximum angle of resolution is twice smaller, due to a more higher density of photoreceptors at the level of the fovea, and also a bigger eye (the dimensions of the Eagle's eye is approximately equal to that of the horse's eye) While the size of these animals is very different). The Visual acuity of Eagles in the tenth is estimated at 40/10, and this has been confirmed by behavioural studies.

Based on anatomical studies of the animal retinas, the maximum visual acuity of octopi is close to 12/10, while that of cats struggles to reach 3 to 4/10. The case of the cat eye is interesting: these eyes have indeed fewer cones (photoreceptors bit sensitive in low light) than those of men, but many more sticks (in low light sensitive photoreceptors). Unlike the human eye, the fine vision of the eyes of cats area contains sticks, and not only cones. The eyes of our feline friends are so more sensitive in the dark, but less able to discern fine detail in the light of the day (this feature is also present in the dog). Compared to the human eye, the eye of the cat also has a larger angular field (his cornea and her lens have a shorter focal length, such as photo targets wide angle). Their retina is equipped with a special tunic, called "tapetum", which plays the role of a mirror pointing to the photoreceptors a part of incident light that goes through the retina. The cat's eye is optimized to capture the light in low light conditions. His pupil is able to expand strongly in the dark: if she remained dilated in light of day, this would make the retina at risk: it is important that this pupillary opening can be strongly reduced in case of high brightness. The circular pupils can close beyond a certain limit, slit-shaped pupils allow a higher closing. It explains the oblong-shaped vertical slot of the pupil of the cat: such a geometry can vary by a factor of 130 the collector surface (pupillary opening), while in humans, this factor is close to 16. the cat pupil dilates and closes much more than human when lighting conditions require it.

In insects, Visual acuity is necessarily reduced because of the dimensions of the eyes of these animals: at dragonflies. It is 40 times lower, and in the Drosophila fly hundreds of times less than that of human eyes.

 Factors affecting acuity

The main factors affecting acuity have been explored: optical and retinal. Other neuro-cognitive parameters are certainly able to influence the measurement of Visual acuity, as the degree of attention, this type of task training, etc. Next to these, are the main factors that can modulate the value of measured Visual acuity:

Diameter of the pupil

When the diameter of the pupil is less than 2 mm, the diffraction degrades the optical quality of the retinal image. Beyond 5-6 mm, these are the optical aberrations of high degree that reduce this quality.

Visual acuity and refractive error (ametropia)

It seems obvious that the refractive errors such as nearsightedness, farsightedness and theastigmatism, by increasing the diameter of the retinal focal spot (the rays cutting in front or back of the retina, the focal spot extends), necessarily lead to a reduction in the resolving power of the eye. This reduction is conditioned by various factors, such as the diameter of the pupil. Unlike our theoretical perfectly Emmetropic eye, an eye have a slight myopia (ex :-0.50 D) sees always sharper when the brightness is important (in these conditions, the pupil is close: myosis) that when it decreases (wide pupil: Mydriasis). After the examination of the fundus, when the pupil is dilated, the vision is fuzzier because in addition to "unmask" certain optical aberrations, the presence of myopia or hyperopia an induces a more marked enlargement of the focal tasks with the expansion.

The glass bezel correction can modulate the size of the retinal image ametropia forts.


The wavelength of the stimulus affects the width of the retinal focal spot, and chromatic aberrations of the eye affect the quality of the retinal image to a poly-chromatique stimulus.

Retinal eccentricity

Visual acuity drops with distance from the center of the fovea — the "retinal grain" (density of cones) fall quickly (by a factor of 10 to 1 mm of the fovea). This fall is more rapid in nasal and temporal Visual field. Binocular Visual acuity is usually better than the best visual acuity in each eye, due to phenomena of summons.


Visual acuity is usually measured with black symbols on white background with high contrast (100%). In these conditions, Visual acuity is constant beyond 10 cd-m-2. Below 1 cd-m-2, visual perception is based more on the cones that on sticks they need some time to adapt to work optimally. They are absent from the central part of the fovea (Central 600 microns about).


The contrast of the observed target determines Visual acuity, especially when the eyes examined show optical defects such as light (beginner cataract, etc.). In such circumstances, the reversal of the contrast of the target (optotypes white on black background) may induce an increase of Visual acuity.


Brief (less than 20 ms) stimuli are more difficult to identify than the longer stimulus, especially if the stimulus intensity is low.


Measures of Visual acuity training doesn't seem to affect the performance in Central acuity, but can improve peripheral vision.


It seems that the power splitter final of the human eye, which increases rapidly after birth, is acquired at the age of three or four years, but clinical measures are unreliable due to the lack of cooperation or understanding of young children.



The resolving power of the eye should be distinguished from the power of discernment, which is based on the ability to discern if two thin lines are aligned (type Vernier acuity), if a trait is slightly tilted with respect to the vertical direction of reference; etc. acuity measured for tasks of this type is greater than the resolving power. For example, it is possible to identify shifts in the order of a few seconds of arc between two lines (while the power of resolution linked to retinal sampling cannot fall below 30 arc seconds). These performances are not in contradiction with the laws of optics; He comes here to compare the spatial distribution of centroids at the level of the light intensity of the retinal image. Furthermore, Vernier Visual exercises based on a transmission of information (the lines are aligned or not), and this requirement allows the Visual system to be more 'sensitive' to the comparison of the distribution of small changes of light intensities.


Close Visual acuity

Close Visual acuity is interesting to study the accommodative function, IE the ability to the point on the retina an image located at a distance closer to the eye. Accommodation allows you to develop a target close on the retina, through the curvature of the lens. In France we use a scale called Parinaud. Presbyopia is responsible for a gradual reduction of the accommodation, which occurs around 40. The measurement of Visual acuity is almost systematic for the elderly of forty years, as part of a review of refractive surgery.

Scale of Parinaud

It includes paragraphs of text each assigned a number, between 28 (larger font) and 1.5 (small characters). Read 3 Parinaud is read (usually to a close reading of 35 cm distance) the affected text to a number 3. Reading distance affects Visual acuity closely: the scales are designed to be read at a distance that is stipulated by the manufacturer. Close Visual acuity is considered normal when the subject read Parinaud 2 to 33 cm. At an Emmetropic (patient with normal uncorrected far Visual acuity without correction), Visual acuity is closely influenced by the quality of the accommodation, the diameter of the pupil, and the distance reading.



example of plank Parinaud and logarithmic Visual acuity for near vision Board.

Example of Visual acuity of reading boards. Left, a logarithmic scale, designed for a reading at 40 cm. Right, a Board of Parinaud, generally used in France, and designed for 33 cm reading distance. Two boards are represented "at scale".

It is possible to calculate the decimal equivalent of the vision expressed by the achelle Parinaud (ex: Parinaud 4). The number of Parinaud (ex: N) of the text is as Visual acuity (in minute of arc) is equal to 1/N, when the text read is located at 25 cm from the eye.

For example, read Parinaud 2 to 25 cm assumes a Visual acuity (resolving power) of 1/2 = 5/10 (or a minimum angle of resolution of 2 minutes of arc).

A distance D is usually mentioned on career tests (for example, Parinaud 4 is associated with D = 1 m). This means that noted test Parinaud 4 (D = 1 meter) would be registered in an angle of 4 minute of arc to 2 meter. A career 2 (D = 0.25 meter) test is registered in an angle of 4 minute of arc at 0.5 meter. The relationship between D and N is in fact: D = 0.25 N.

In general, the reading distance is not 25 cm: it is rather between 33cm and 40 cm (depending on the size of the arms and... of the accommodative function, presbyopes tend to back their book). Nevertheless, one can recalculate decimal acuity for playback from a test of Parinaud 3 to 40 cm for example by performing the following reasoning:

If the subject read Parinaud 3 to 25 cm (and not 40 cm) decimal acuity would be 1/3 = 0.33 (minimum angle of resolution is 3 minute of arc). In fact, this test is read by the patient to 40 cm, which is to reduce the resolution by a factor of 25/40 minimum angle. Because of this (remembering that decimal acuity is the opposite of the angle minium resolution in minutes of arc).

Parinaud 3 to 40 cm corresponds to a decimal AV close = (40/25) x 1/3 = 0.53 or 5.3/10

Similarly, Parinaud 2-33 cm equals a decimal acuity of some (33/25) x 1/2 = 0.66 or 6.6/10


 Development of Visual acuity

It is possible to estimate Visual acuity in infants and children, using techniques adapted, as the preferential use of the look when presented to the right or to the left of the maps of acuities, which consist of networks of spatial frequencies (ex: say maps 'Baby vision', Teller acuity maps..). Infants seem to look on things that they see, and designed according to a strict protocol review can quite appreciate their ability to distinguish some basic patterns, and deduce a Visual acuity (in number of cycles per degree). The maps baby vision consist of concentric circular patterns, whose average luminance is the same as that of the gray background of the Board who represents them, and which is shown about 40 cm of the child.

Visual acuity increase shortly after birth, fairly linearly, to achieve a near acuity of 12 cycles per degree (about 4/10) to a year (1/10th to 3 months, 6 months 2/10th).

Once the child has the maturity to name objects (around 2 years to 2 years 1.2), the use of boards of optotypes (drawings) is possible. Maximum visual acuity is close to 7/10, and reached 10/10 until the age of 5 years. It was during the following years Visual acuity may gradually reach the limit imposed by the retinal resolution (after the age of 10 years).



THEVisual acuity measured routinely in ophthalmology corresponds to the eye resolving power, i.e. the ability to the eye to separate two distinct but close maximum"points" unless they be confused at a single point. Visual angle underpinned by points (their apparent Exxx_xxx_5197ment) sets the minimum angle of resolution. The minimum angle under tense by two points seen as distinct can be used to define the Visual acuity)MAR: Minimum Angle of Resolution). THEVisual acuity is related to the MARis expressed in tenths and corresponds to the inverse of the MAR. 1/10 corresponds to a MAR of 10 minutes of arc. 10/10 corresponds to an angle of one minute of arc (which is 1/60th of a degree). It is measured with various types of scales (Snellen, etc.) of far away, but also closely (career), made up of reasons as for the letters, figures, drawings, etc. These reasons are grouped under the term of optotypes. Visual acuity depends on the optical quality of the eye, the pupillary diameter and the 'retinal resolution' (number of 'pixels' or rather 'photosites"retinal, which are cones at the level of the retina foveolaire, dedicated to"fine"vision). When you show a letter as an 'E', the retinal image of it must be able to be resolved (or sampled) by the retinal cones. This assumes that the bars forming the letter E (five alternating luminance horizontal bars) are imaged as such at the level of the retina and that there is at least one row of cones for each of these bars. Of course, (or corrected in case of myopia, hyperopia or astigmatism), an eye must have a Visual acuity of at least 10/10. The resolution of the mosaic of the retinal cones (photosensitive cells allowing precise central vision) allows a theoretical acuity close to 20/10: tantamount to discern the edges of a piece of 10 cents to 130 meters. Do not confuse tenths and diopters. Them diopters (D) allow to quantify an optical Visual defect (ex: myopia of-2 D). The optical defect results in a reduction of Visual acuity. Classically, a myopia of 1 D reduced Visual acuity to 5/10. A myopia of 1.25 D reduced Visual acuity at 1/10. There is no linearity between optical defect (number of diopters) and the number of tenths. Visual acuity closely explores the accommodative function. It is done through specific scales (Parinaud in France).



11 responses to "Visual acuity, resolution and separator power"

  1. Daniel BEVERAGGI says:

    Vivid compliments for the pedagogical qualities for your presentation and for his illustrations.

    Would you great kindness to tell me what is the diameter of the smaller black circle on a white background, under excellent lighting, a naked eye in good health, with a sharpness of 10/10, is able to see, in careful observation, optimal remotely?

    My view of octogenarian (1934) has lost its sharpness but, thank heaven, my curiosity has not yet been reached.

    Thank you for the attention you want to lend to my approach and I you to accept my very best wishes.
    Daniel Beveraggi

  2. Dr. Damien Gatinel says:

    Thanks for your compliments. The answer to your question is not simple. Detection of a reason any on a uniform background appeals to the Visual acuity of detection, and not to the power of resolution. The Visual acuity of the human eye detection is superior to Visual acuity of "separation". It is easier to distinguish a "unique design", even very end, on uniform background, to separate two points or two loosely spaced lines. The Visual acuity of detection is the order of a few arc seconds (one second of arc = PI/180/3600 in radians). With optimal correction, assuming that detection is possible for an apparent size of 10 arcseconds in excellent conditions, simply multiply the previous figure by 10 (or about 0.00005) and the viewing distance (ex: 30 cm) to get a dimension of the order of 0.0015 cm or 15 microns.

  3. Thanks Damien
    Very nice article


    Frédéric Hehn

  4. Daniel Pietri says:

    Thanks for this review which allowed me to better understand these phenomena.
    However, I did not find the answer to the problem that led me to read it and thank you in advance to read more.

    You explain very well the theoretical maximum sharpness, without so far for example consider the maximum sharpness achievable "no negative effect" (I understand very well the imprecise side of this constraint - but it just allows you to better identify the notion of achievable).
    For example, imagine the case of an athlete for whom his visual acuity may be decisive (aiming) or his ability to distinguish more precisely the movement of an object at a good distance (événtuellement variable), would it Possible to consider wearing a device (glasses or lenses) that could improve its visual performance (bearing its acuity of 10/10 by example to 12/10 or 14/10), without causing too much unwanted side effects (headaches...).

    Thank you for your answer

  5. Dr. Damien Gatinel says:

    Most young adults reach a Visual acuity of 12 or even 16 tenths and up to 20/10, when they are normalsighted, or well corrected for their optical failure. Theoretical maximum visual acuity is 20/10 (resolving power of 30 arc seconds), and "healthy" eyes that do not reach this sharpness present either an optical aberration of high rate (astigmatism said irregular, that cannot be corrected by glasses), or retinal abnormality (density of photoreceptors at the strong myopic), or a sensory pathology (amblyopia). It is possible to correct optical aberrations of high degree in experimental conditions (with a mirror for adaptive optics), in refractive surgery (guided by the Wavefront custom treatment), or even adapting rigid lenses. The correction of the aberrations of high degree gives no headaches, and for an athlete wishing to perfect his visual acuity, refractive surgery or adaptation of a pair of rigid lenses are possible solutions. Yet once, acuity greater than 10/10 must be obtained in routine with a suitable correction glasses or lenses.

  6. Jimmy Coat says:


    I want to thank you first of all for your site which allows us to learn more about ourselves and especially about our eyes.

    You seem to say that the maximum acuity of an eye is 20/10 even if one could perceive smaller according to certain factors of conditioning (cf Hyperacuity and commentary of 14 Feb 2016).

    I was operated by LASIK on 23 January 2018 and the day after my surgery, in consultation with the Cabinet, I had a sharpness of 20/10 in both eyes. However I feel I can read even smaller letters. So I wonder about my true acuity. To be honest, I even ask myself the question whether what I read at the ophthalmologist was really from the 20/10 of the coup...

    20/10 is it indeed a maximum and read smaller letters would be due to the recognition of form by my brain (which would make me say that it is a C for example) or would it be possible to go even further than the 20/10, by having for example bcp more D Receptor that of reason, a bigger eye, etc. (being myopic basic, I guess my eye is necessarily bigger than average), etc.? Is there a way to measure a finer acuity, like 25/10 or 30/10? In a center for example.


  7. Dr. Damien Gatinel says:

    There are case where visual acuity greater than 20/10 could be measured. When the optical correction of the eye is perfect, the visual acuity depends on the density of photoreceptors (cones) at the level of the Fovéola (central retinal zone used for fixation). However, physical (diffraction) and biological (minimum size of photoreceptors) constraints do not allow the presence of a sharpness much higher than 20/10 to be considered. The acuity test scales are limited to 20/10 for the finer acuity, but it is theoretically possible to use them by moving them away (or away from the target). According to Thalès's theorem, if you still perceive by being placed at 10 meters the letters of acuity (optotypes) of 20/10 designed to be read at 5 meters, it is that your visual acuity reaches 40/10. This will make you a successful candidate for the Guinness Book Records!

  8. Michael hospital says:

    Hello Mr. Gatinel,

    Thank you for your articles that are very well made and well illustrated.

    Is it possible to find an ophthalmology instrument that allows to observe the fovea this area of about 1.5 mm in diameter with a resolution of 500 * 500 to 10000 * 1000 pixels which would provide pixels from 1.5 UM to 3um.

    This would allow you to start distinguishing the cones.

    Thanks for your response

  9. Dr. Damien Gatinel says:

    The observation of the cones is limited by the pupillary diffraction and optical aberrations of the eye. Even by dilating the pupil to the maximum and by correcting these aberrations, the laws of Physics (diffraction) limit the theoretical resolution to about 2 microns, which inherently limits the ability to distinguish the finer cones.

  10. Caussidery says:

    I have a Visual acuity measured last year at 20/10 (I have 41 years, soon 42).
    However, for about 6 months, I have ophthalmic pains, type of tightness, daily (especially when I drive).
    Last ophthalmic exam performed on April 1st 2019 is quite normal (not had the examination with dilation drops) and the ophthalmo did not know how to explain these pains and discomfort. She prescribed corrections of + 0.50 OD and OG by speculated that it might be "resting" my eyes.
    So I find myself with glasses since this morning while I see it too well, aberrant!
    I wish I had a 2nd opinion but the ophthalmos appointments in my area are 10 months waiting. In the worst case , failing to solve my problem, I would not want these corrections to "ruin" my vision.
    Having understood many things with your very complete article, I therefore appeal to your informed opinion to advise me.
    Thanking you
    David C

  11. Dr. Damien Gatinel says:

    The slight hyperopia is compatible with an excellent vision from afar, but sometimes at the cost of a small fatigue, especially towards the quarantine (reduction of the accommodative power of the eye). Wearing this slight positive correction can be beneficial even if it is often judged as useless by patients.

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