Ординатура / Офтальмология / Английские материалы / Ocular Periphery and Disorders_Dartt, Bex, Amore_2011

Test–retest variability of the Snellen chart is around0.3 logMAR, while the ETDRS chart has far better repeatability (test–retest variability 0.1–0.2 logMAR). Despite the many limitations of the Snellen chart, it is still widely used in clinical practice. While this is likely to be largely due to clinicians’ familiarity with the Snellen chart, there is also a perception that Snellen acuity measurement is quicker than that on the Bailey–Lovie or ETDRS charts.

Various modified versions of the ETDRS chart exist: for example, a version with an altered letter set (A, B, E, H, N, O, P, T, X, and Y) has been developed for use by readers of most European languages, including those based on Cyrillic or Hellenic alphabets.

For observers unable to report letters on a sight chart, other frequently used optotypes include the tumbling E chart (formerly and less politically correctly known as the illiterate E chart), where a letter E is shown in each of four rotations; the HOTV chart, where only these four letters are used; symbols such as the Lea or Kay pictures; and simple shapes, such as the Cardiff card.

Reporting Visual Acuity

Clinicians have traditionally used Snellen fractions to record visual acuity, where the numerator is the test distance and the denominator the target size. The target size is expressed, counterintuitively, as the distance from which the target has an MAR of 1 min of arc. Therefore, a visual acuity of 6/6 indicates that from 6 m, letters with MAR 1-min arc are correctly identified, while a visual acuity of 3/36 indicates that from 3 m, the targets identified have a MAR of 1 min of arc when viewed from 36 m. The reciprocal of the Snellen fraction gives the visual acuity in MAR: so a visual acuity of 3/36 indicates a MAR of 12 min of arc.

In much of Europe, the Snellen fraction is reduced into a decimal fraction.

A further confusion with the Snellen system is that in countries not using the metric system, distances are expressed in feet rather than meters, with 20/20 being exactly equivalent to 6/6 but with a test distance of 20 ft rather than 6 m. Although Snellen recommended adoption of the metric system in 1875 and, in 1980, the US National Academy of Sciences favored adoption of a standard defined in meters, given the imminent adoption of the metric system, the feet system is still widely used in the USA, and among lay people in the UK.

The accepted standard for expressing visual acuity in clinical research, and increasingly in clinical practice, is to use the base 10 logarithm of the MAR (logMAR), such that 0.0 logMAR is equivalent to 6/6 or 20/20, and 1.0 logMAR is the same as 6/60 or 20/200. Table 1 gives approximately equivalent values in MAR, cycles per degree, Snellen fractions in meters and feet, decimal acuity, and logMAR for a range of visual acuities.

Optical and Neural Limits on Visual Acuity

Visual acuity is limited by many factors: the optics and refraction of the eye; the clarity of the optical media; the spacing and function of the retinal photoreceptors; the ratio of retinal ganglion cells to photoreceptors; and the resolution of the primary visual cortex and higher areas of visual processing.

Each diopter of myopia reduces visual acuity: a –1.00DS myope will typically have uncorrected visual acuity of around 0.5 logMAR (6/18; 20/60) and a two-diopter myope will have vision of around 0.8 logMAR on a distance test. Hypermetropia can often be relieved by accommodation in young people, but each diopter of hypermetropia

Nonfoveal vision is limited by many elements. First, the eye’s optics are not optimized for viewing off the visual axis, and peripheral vision is subject to greater aberration than central vision. Second, the size of photoreceptors increases and their density falls with increasing eccentricity. The number of photoreceptors per retinal ganglion cell also increases, from less than one photoreceptor per ganglion cell in the fovea to more than 20 photoreceptors per ganglion cell in the far periphery. The volume of visual cortex devoted to noncentral retina is also proportionally lower. It is unsurprising, therefore, that visual acuity falls quickly with increasing distance from the fovea (Figure 4). This is one reason for the severely reduced visual acuity of people with central vision loss from diseases such as age-related macular disease.

Visual Acuity over Life

Over the first year of life, visual acuity assessed by a preferential looking test appears to be reasonably stable

Visual Standards

In most countries, there is a visual-acuity requirement for car drivers. While the level and measurement technique varies between countries, the acuity limit is usually approximately 0.3 logMAR. Commercial airline pilots are required to have a binocular visual acuity of 0.0 logMAR.

Best corrected binocular visual acuity of 1.0 logMAR or poorer is used as a definition of low vision or partial sight in many countries, with acuity of worse than 1.3 logMAR being described as severe sight impairment.

Hyperacuity

Some visual tasks can be performed with a far greater degree of precision than would be suggested by the MAR. Alignment tasks such as Vernier discrimination (where the offset of one line with respect to another is detected, Figure 6(a)) can be performed with misalignment of less

Age (years)

Figure 5 Variation in visual acuity over life. From Mayer, D. L. and Dobson, V. (1982). Visual acuity development in infants and young children, as assessed by operant preferential looking.

Data from Vision Research 22(9): 1141–1151 and Klein, R., Klein, B. E., Linton, K. L., and De Mets, D. L. (1991). The beaver dam eye study: Visual acuity. Ophthalmology 98(8): 1310–1315.

must be for it to be seen. If a target moves with velocity of 40 s 1, the MAR is increased to about 2 min of arc, while at 80 s 1, acuity is about 3 min of arc.

In peripheral vision, slow image motion (less than 10 s 1) slightly improves visual acuity for peripherally presented targets, perhaps because it breaks the phenomenon of Troxler fading.

Target motion at the retina can be induced by target movement, by eye motion, or by head motion. Many eye diseases, particularly those of the macula, are associated with poor fixation stability of the eye. This poor eye stability increases retinal image motion, and is significantly associated with poorer visual function. Small degrees of head motion do not significantly decrease visual acuity under normal conditions, but have a marked deleterious effect for subjects viewing through telescopic spectacles. Therefore, subjects with macular disease who have poor fixation stability and who view through telescopic low-vision aids have a marked impairment in their dynamic visual acuity.

See also: Amblyopia; Contrast Sensitivity; Pupil.

(b)

(a)

Figure 6 Examples of hyperacuity tasks. Misalignment of the lower element is easily visible. (a) Vernier alignment; (b) dot alignment: the offset of the middle dot with respect to the upper and lower dot is easily discerned.

than 5 s of arc – considerably less than the center-to- center spacing of a foveal photoreceptor. This is thought to be due to interpolation of the inputs of two or more adjacent neural elements.

Dynamic Visual Acuity

Throughout this article, visual acuity has been discussed for static targets. If the target is moved, central visual acuity decreases: the faster the target moves, the larger it

Further Reading

Anstis, S. M. (1974). Letter: A chart demonstrating variations in acuity with retinal position. Vision Research 14(7): 589–592.

Bailey, I. L. and Lovie, J. E. (1976). New design principles for visual acuity letter charts. American Journal of Optometry and Physiological Optics 53: 740–745.

Bennett, A. G. and Rabbetts, R. B. (eds.) (1989). Visual acuity and contrast sensitivity. In: Clinical Visual Optics, pp. 23–72. Oxford: Butterworth-Heinemann.

Brown, B. (1972). Resolution thresholds for moving targets at the fovea and in the peripheral retina. Vision Research 12(2): 293–304.

Committee on vision. (1980). Recommended standard procedures for the clinical measurement and specification of visual acuity. Report of working group 39. Advances in Ophthalmology ¼ Fortschritte der Augenheilkunde ¼ Progres en Ophtalmologie

41: 103–148. Assembly of Behavioral and Social Sciences, National Research Council, National Academy of Sciences, Washington, DC

Crossland, M. D., Culham, L. E., and Rubin, G. S. (2004). Fixation stability and reading speed in patients with newly

developed macular disease. Ophthalmic and Physiological Optics

24: 327–333.

Demer, J. L. and Amjadi, F. (1993). Dynamic visual acuity of normal subjects during vertical optotype and head motion. Investigative Ophthalmology and Visual Science 34(6): 1894–1906.

Klein, R., Klein, B. E., Linton, K. L., and De Mets, D. L. (1991). The beaver dam eye study: Visual acuity. Ophthalmology 98(8): 1310–1315.

Liang, J., Williams, D. R., and Miller, D. T. (1997). Supernormal vision and high-resolution retinal imaging through adaptive optics. Journal of the Optical Society of America. A, Optics, Image Science, and Vision 14: 2884–2892.

Mayer, D. L. and Dobson, V. (1982). Visual acuity development in infants and young children, as assessed by operant preferential looking. Vision Research 22(9): 1141–1151.

Plainis, S., Tzatzala, P., Orphanos, Y., and Tsilimbaris, M. K. (2007). A modified ETDRS visual acuity chart for European-wide use.

Optometry and Vision Science 84(7): 647–653.

Rosser, D. A., Cousens, S. N., Murdoch, I. E., Fitzke, F. W., and Laidlaw, D. A. (2003). How sensitive to clinical change are ETDRS logMAR visual acuity measurements? Investigative Ophthalmology and Visual Science 44: 3278–3281.

Thibos, L. N., Cheney, F. E., and Walsh, D. J. (1987). Retinal limits to the detection and resolution of gratings. Journal of the Optical

Society of America. A, Optics, Image Science, and Vision

4: 1524–1529.

Westheimer, G. (1987). Visual acuity. In: Moses, R. A. and Hart, W. M. (eds.) Adler’s Physiology of the Eye: Clinical Application,

pp. 415–428. St Louis, MO: Mosby.

Glossary

Channels – The groups of visual sensors that are selective for a narrow range of image spatial or temporal structure.

Contrast constancy – At high contrasts, apparent contrast is relatively independent of the parameters that strongly influence contrast-detection threshold.

Contrast-detection threshold – The statistical contrast boundary below which contrast is too low for an image to be detected reliably and above which contrast is high enough for frequent image detection. Often defined as the contrast that produces 75% correct target identifications in forced-choice paradigms.

Contrast sensitivity – The reciprocal of contrastdetection threshold that also represents the transition between visible and invisible images.

Critical flicker frequency – The highest flicker rate of a full contrast image that can be detected reliably.

Forced-choice paradigms – Robust behavioral method used to measure detection or discrimination thresholds. Observers are forced to select between two or more intervals, of which only one contains

a target.

Fourier analysis – Analytical method that calculates the simple sine-wave components whose linear sum forms a given complex image.

Resolution limit – The highest spatial frequency of a full contrast image that can be detected reliably. Spatial frequency – The number of image cycles that fall within a given spatial distance, typically 1 of visual angle.

Temporal frequency – The number of image cycles that fall within 1 s.

Wavelets/gabors – A local filter that is the point-wise product of a two-dimensional (2D) spatial sine wave and a 2D Gaussian envelope.

Most people are familiar with image brightness and contrast from their controls on computer and television displays. The brightness control adjusts the mean luminance of the display uniformly, in order that the intensity of every point in the image increases when brightness is increased or decreases when brightness is reduced. The contrast control adjusts the difference between the lightest and darkest areas of the image. Increasing contrast

makes areas that are below mean luminance darker and areas that are above mean luminance lighter, without changing the mean value. Decreasing contrast draws all values toward the mean, thus making the whole image fainter, similar to viewing the image through fog.

Figure 1 illustrates the effect of changing the contrast of a sine-wave striped pattern (the reasons for using a sine-wave pattern are described below). The top panel shows images of gratings whose contrast increases from 12.5% on the left to 100% on the right. The mean luminance of each image is the same. The traces in the bottom row plot luminance versus position for a horizontal slice through each image.

Contrast-Detection Threshold

A powerful measure of visual sensitivity can be obtained by finding the minimum contrast that is necessary for an image to be detected. This minimum contrast is referred to as contrast-detection threshold (Cthresh) and it is important because it defines the transition at which an image moves

from invisible to visible. One method to estimate Cthresh might be to allow a subject to adjust the contrast until an

image is just visible. However, this method is highly subjective and large differences in individual criteria for just visible make this measure unreliable.

Psychophysical Assessment of Vision

To overcome these problems, most researchers employ forced-choice procedures that require an observer to identify which of two or more intervals (the more the better) contain the target. An example of a four-alternative forcedchoice (4AFC) detection task is shown in Figure 2(a). In this case, a computer presents a target in one of four positions at random around a central fixation point. The observer’s task is to fixate the central dot and to indicate the location of the target, usually by pressing a computer button. Targets that are below Cthresh (sub-threshold) are rarely detected, whereas targets that are above Cthresh (supra-threshold) are usually detected. Contrast-detection thresholds are therefore probabilistic and are defined as the contrast at which they are correctly detected midway between chance and perfect performance.

It is difficult to cheat on forced-choice methods or to change criteria – the target is either seen, in which case its position is correctly identified, or it is not seen, in which

Proportion correct

1

0.75

0.5

0.25

Contrast

75% correct at approximately 2.5% contrast. The slope (s) can be used to infer how easily nearby contrasts can be discriminated from one another – a shallow slope means that a large contrast difference is required to achieve a given change in performance, whereas a steep slope means that a small change in the stimulus produces a large change in performance.

Figure 2 Contrast detection. (a) Example of a four-alternative forced-choice (4 AFC) task. The observer is required to fixate the central dot and to indicate whether the target appeared top left, top right, bottom left, or bottom right. The target contrast is adjusted by computer to a level that produces 75% correct detection. (b) A typical psychometric function. Circles show the proportion of trials the target was detected (ordinate) as a function of the target contrast (abscissa). Error bars show 1 standard deviation. The curve shows the best-fitting cumulative normal function, from which the interpolated 75% correct point is taken as contrast-detection threshold.

case the subject is forced to guess. Notice that when guessing, the subject is still correct sometimes (25% if there are four alternatives, 33% if there are three, or 50% if there are two, etc.), as shown in the frequency of seeing curve in Figure 2(b), where, at low contrasts, performance is 25% correct. The data have been fit with a curve known as a psychometric function, in this case a cumulative Gaussian:

Y ¼ g þ ð1 gÞ erf ðz=sqrtð2ÞÞ=2

where z ¼ (X – m)/s; g is the guess rate (0.25 in a 4AFC experiment). The mid-point (m) of the psychometric function is often taken as Cthresh – for a 2AFC task, this is 75% correct. In the example shown, the observer achieved

Spatial Frequency Channels

Based on behavioral observations in humans and single unit recordings in mammalian visual systems, researchers discovered around half a century ago that the visual system analyses images at a series of relatively narrow spatial scales and orientations known as channels. Thus, fine and coarse image details are encoded separately and Fourier analysis can be used to study the image structure that is encoded by different visual processing channels. Fourier analysis computes the sum of basic sine waves whose linear sum produces the image. To illustrate the representations of an image that are available at different spatial scales, Figure 3(a) shows a typical image, together with its coarse (Figure 3(b)) and fine (Figure 3(c)) spatial structure.

Visually responsive neurons in primary visual cortex, the first cortical projection from the retina through the lateral geniculate nucleus of the thalamus, respond to images only within a limited area of the visual field, known as the classical receptive field, and are selective for a limited range of spatial frequencies and orientations. These receptive fields are now routinely modeled as Gabor or wavelet functions, defined as:

l represents the wavelength, y the orientation, and c the phase of the sine-wave component. For the Gaussian window, s is the standard deviation and g is the spatial aspect ratio. Examples of Gabors are illustrated in Figure 4. On the top row, spatial frequency increases from left to right and all Gabors are of the same orientation 0 and contrast. On the bottom row, spatial frequency is fixed, but orientation is 45 , 90 , or 135 (from left to right). The visual system encodes image structure with a bank of such wavelet filters that represent the retinal image through patchwise local analysis.

Figure 5 provides compelling demonstrations that our visual system employs a set of spatial frequency and orientation-selective channels. These demonstrations show that after prolonged viewing of a particular pattern (termed adaptation) the appearance of other patterns can be altered (termed an aftereffect). In these demonstrations, adapting to a pattern of one spatial frequency or orientation produces a loss in sensitivity in the channel that responds most to that pattern, but little change in channels tuned to other spatial frequencies or orientations. This localized loss in sensitivity produces a relative shift in the responses of our visual channels that cause us to experience changes in the appearance of the image.

These observations have led to the widespread use of sine-wave grating patterns in basic and clinical vision research. In order to derive a measure of vision that reflects the sensitivity across our set of visual channels and to reflect the fact that functional vision requires us to detect and interact with objects of various sizes, contrastdetection thresholds are measured for gratings of a range of bar widths, expressed as spatial frequency or the number of grating cycles per unit distance. Figure 4 illustrates Gabors of differing spatial frequency; however, the size of one grating cycle on the retina depends on the distance

Figure 4 Gabor (wavelets) of differing spatial frequency and orientation. Top row: spatial frequency increases from left to right, orientation is fixed at 0 . Bottom row: Orientation increases from left to right: 45 , 90 , and 135 , spatial frequency is fixed.

from which it is viewed. Therefore, image sizes are usually calculated in terms of visual angle, which specifies the retinal image size. Figure 6 shows how visual angle is calculated and its relationship to image size and viewing distance. A convenient rule is that 1 cm viewed from 57 cm subtends a visual angle of 1 and roughly corresponds to a finger nail viewed at arm’s length.

Contrast Sensitivity Function

Many researchers have shown that for sine-grating patterns, Cthresh strongly depends on spatial frequency. This fundamental observation is demonstrated in the classic image shown in Figure 7. Spatial frequency increases from left to right and contrast increases from top to bottom, so that contrast is constant across any horizontal line. Contrast-detection thresholds can be visualized on this figure as the imaginary curve along

Figure 5 Demonstration of spatial frequencyand orientationselective aftereffects. First note that when you fixate the centre gray dot, the gratings in the middle row are of the same spatial frequency and orientation. Next, look back and forth between the black dots in the top row for around 10 s. Now, when you look at the center gray dot, the grating on the left appears to be of higher spatial frequency than the grating on the right. Next, look back and forth between the white dots in the bottom row for around 10 s. Now, when you look at the center gray dot, the grating on the left appears tilted counterclockwise, while the grating on the right appears tilted clockwise. These aftereffects are robust even though you know that the gratings in the middle row are the same. These demonstrations provide compelling evidence that visual processing involves channels that are narrowly tuned for spatial frequency and orientation.

which the grating changes from invisible (toward the top of the figure) to visible (toward the bottom of the figure). Most people report that the function peaks somewhere near the middle of the figure. Notice that the peak shifts as you move the figure closer or further away. This demonstrates the importance of visual angle rather than physical image size. Note that the highest spatial frequency that can be detected at maximum contrast is given by the rightmost point on a contrast sensitivity function (CSF). This is referred to as the resolution limit and is a quick and convenient method of assessing visual sensitivity than measuring the entire CSF.

When measured with forced-choice procedures, (Figure 2) contrast-detection thresholds are lowest for

gratings around 2–5 cycles per degree of visual angle (c deg–1). By convention, the inverse of Cthresh (1/Cthresh) is usually reported and is termed contrast sensitivity. The rationale for the use of contrast sensitivity over contrastdetection threshold is most likely because the shape of the CSF is the same as that of the underlying modulation transfer function of the system. The circles in Figure 8 show the author’s contrast sensitivity as a function of spatial frequency measured with a forced-choice procedure. Error bars show 95% confidence intervals. The data have been fit (green curve) with the outputs of a set of spatial frequency channels shown by the colored curves. The channels are log spaced in spatial frequency (with peaks at 0.5, 1, 2, 4, 8, 16, or 32 c deg–1) and have the same bandwidth (1.4 octaves). The summed outputs of the set of filters provide a good fit to the data and this channel-based system is now a widely accepted model of early visual processing.

The spatial frequency aftereffect shown in Figure 5 is easily explained with this channel-based model. Adapting to one spatial frequency reduces the responses of the channel that is most sensitive to that spatial frequency, but has little effect on the responses of other channels. When a different spatial frequency is subsequently viewed, the overall activity across the channels is shifted away from the adapted channel. This shift in the population response produces a shift in apparent spatial frequency away from the adapting frequency. An analogous model explains the shifts in orientation in the lower row of Figure 5, except that orientation-selective channels are adapted rather than spatial-frequency-selective channels.

The CSF is highly dependent on the mean luminance of the display on which it is measured. This can easily be experienced by viewing Figure 7 with a pair of dark sunglasses (possibly two pairs), which moves the curve down (reducing sensitivity) and shifts the peak to lower spatial frequencies. The data in Figure 8 were collected on a standard computer monitor that has a mean luminance of 50 cd m–2 (candelas per square meter). Photopic, mesopic, and scotopic vision and changes in visual performance show that sensitivity to high spatial frequencies increases with mean luminance. This property is important because CSFs are routinely measured on relatively dim displays (e.g., 50–100 cd m–2) in the laboratory and in the clinic; however, the luminance of the real world is typically much greater. For example, the luminance of a cloudy sky is around 35 000 cd m–2, suggesting that standard experimental conditions may underestimate sensitivity to fine spatial structure.

Temporal Contrast Sensitivity

In addition to a dependence on spatial frequency, contrast sensitivity also depends strongly on temporal frequency. Figure 1 illustrates spatial variation in luminance, but

Figure 7 Illustration of the contrast sensitivity function (CSF). Spatial frequency increases from left to right, contrast increases from top to bottom. The contrast along any horizontal line is fixed. Different spatial frequencies become visible at different contrasts and define an imaginary curve that separates seen from unseen structure. Notice that if you move the image closer to your eye, the peak moves to the right and if you move it further away, the peak moves to the left. This demonstrates that contrast sensitivity depends on retinal not physical image size. If you wear one or two pairs of dark sunglasses, the curve shifts down and the peaks moves left, which demonstrates the dependence of the CSF on mean luminance.

imagine instead that the x-axis represents time, rather than space. Now the figure illustrates flicker. Flicker frequency can be varied in the same way as spatial frequency is varied in Figures 3 and 7. The circles in Figure 9 show how the author’s contrast sensitivity varies as a function of temporal frequency for a 2 c deg 1 grating pattern. Sensitivity peaks around 5 Hz, at the mean luminance

200

150

Sensitivity 100

50

Spatial frequency (c deg–1)

Figure 8 Spatial contrast sensitivity. Circles show contrast sensitivity (the reciprocal of contrast-detection threshold) for sine gratings of a range of spatial frequencies. Sensitivity peaks at around 2 c deg–1 under the conditions employed here and decreases at lower or higher spatial frequencies. The black curve is the summed sensitivity of the set of log-scaled channels shown by the colored curves and provides a good fit to the data.

used here (50 cd m 2) and decreases at lower or higher temporal frequencies. These data are well fit (black curve) by a model with only two temporal channels, compared with the multiple channels that support spatial contrast sensitivity. One channel (red curve) is low-pass or sustained and is most sensitive to structure that is stationary or slowly changing over time. The second channel (blue curve) is band-pass or transient and is most sensitive to structure that changes at around 5 Hz.

The spatial resolution limit falls steadily with distance from the fovea, an effect that can be experienced by viewing Figure 7 while fixating away from the center of the image. As you fixate further away, the threshold curve moves further down the figure and its peak shifts further to the left. Unlike spatial resolution, temporal resolution (the highest flicker rate that can be detected at any contrast, often called critical flicker fusion frequency)

Temporal frequency (Hz)

Figure 9 Temporal contrast sensitivity. Circles show contrast sensitivity (the reciprocal of contrast-detection threshold) for sine gratings of a range of temporal frequencies. The black curve is the summed sensitivity of the two log-scaled channels shown by the red and blue curves. The red curve has peak sensitivity at low temporal frequencies – that is, static images – and is termed a sustained channel. The blue curve has peak sensitivity around 6 Hz and is termed a transient channel.

increases moderately with distance from the fovea. This explains why older, 60-Hz computer displays can sometimes be seen to flicker when seen in the peripheral visual field, but not when viewed directly. Just as spatial contrast sensitivity depends on luminance, so does temporal contrast sensitivity. A 35-mm film is generally recorded at 24 frames per second, a refresh rate that could be easily detected at moderate light levels, as can be seen from Figure 9. For this reason, movie theaters are generally dark because sensitivity to high flicker rates is poor under those conditions. In addition, the visible 24-Hz image update rate is masked by flashing the illuminant at 48 Hz, so each frame is flashed twice.

At supra-threshold contrasts, apparent contrast is relatively independent of spatial or temporal frequency,

a phenomenon termed contrast constancy.Contrast constancy can be experienced in Figure 7 – while the transition between visible and invisible gratings has a curved shape, toward the bottom of the figure, the gratings appear to have similar contrast regardless of spatial frequency. This has important implications for image enhancement, which should therefore target only image components that are below their Cthresh.

See also: Acuity.

Further Reading

Bracewell, R. (1999). The Fourier Transform and Its Applications, 3rd edn. London: McGraw-Hill.

Campbell, F. W. and Robson, J. G. (1968). Application of Fourier analysis to the visibility of gratings. Journal of Physiology 197: 551–566.

Field, D. J. and Tolhurst, D. J. (1986). The structure and symmetry of simple-cell receptive-field profiles in the cat’s visual cortex.

Proceedings of the Royal Society of London. Series B. Biological Sciences 228(1253): 379–400.

Georgeson, M. A. (1990). Over the limit: Encoding contrast above threshold in human vision. In: Kulikowski, J. J. (ed.) Limits of Vision, pp. 106–119. London: Erlbaum.

Hubel, D. H. and Wiesel, T. N. (1959). Receptive fields of single neurones in the cat’s striate cortex. Journal of Physiology 148: 574–591.

Kelly, D. H. (1961). Visual responses to time-dependent stimuli. 1. Amplitude sensitivity measurements. Journal of the Optical Society of America. A, Optics, Image Science, and Vision 51: 422–429.

Kulikowski, J. J. and Tolhurst, D. J. (1973). Psychophysical evidence for sustained and transient detectors in human vision. Journal of Physiology 232(1): 149–162.

Landis, C. (1954). Determinants of the critical flicker-fusion threshold.

Physiological Reviews 34(2): 259–286.

O’Shea, R. P. (1991). Thumb’s rule tested: Visual angle of thumb’s width is about 2 deg. Perception 20(3): 415–418.

Rovamo, J., Virsu, V., Laurinen, P., and Hyvarinen, L. (1982). Resolution of gratings oriented along and across meridians in peripheral vision.

Investigative Ophthalmology and Visual Science 23: 666–670.