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CONTRAST SENSITIVITY FUNCTION 2
CONTRAST SENSITIVITY FUNCTION
BACKGROUND
The most widely used measure of visual resolution is visual acuity. It is used both for clinical diagnosis and
evaluation and for legal screening and selection. (See the report of another working group, National Research
Council 1980, for a discussion of methods and standards for the measurement of visual acuity.) Acuity is based
on the size of the smallest detail in a visual target (optotype) that permits some criterion level of identification or
detection performance (75 percent correct, for example). The smaller the size of this critical detail, the better the
vision of the observer. The value of visual acuity measurements is well proven for correcting refractive errors.
Under some conditions, however, individual variation in standard measurements of visual acuity often is not able
to predict individual variation in performance on some visual tasks, such as target detection and identification
(Ginsburg, 1983; Ginsburg et al., 1982, 1983).
A considerable body of empirical knowledge has been gained about the stimulus factors, such as size,
exposure duration, contrast, and adaptation level, that influence detection of simple disk-shaped targets (Graham
and Margaria, 1935; Lukiesch and Moss, 1940; Blackwell, 1946). Although these data in some circumstances do
quite well in predicting detection of more complex targets, they often are inadequate in predicting recognition
and identification of these targets. In addition, individual differences in performance with simple targets are not
easily related to any measured characteristics of vision, nor were they related via any satisfactory theoretical
framework.
In the past two decades, a new method of assessing vision has emerged that may provide a universal
language. This method is the measurement of the contrast sensitivity function and, for some purposes (described
below), it complements visual acuity. The first study that demonstrated the power of contrast sensitivity to
supplement acuity measures employed low contrast Landolt C target (Hecht et al., 1949). Today, however, the
contrast sensitivity function is typically measured using sinusoidal grating patterns as targets. This use of sine
wave gratings was first introduced in vision by Schade (1956) and was subsequently used by early investigators
to measure basic visual sensitivity (Westheimer, 1960; DePalma and Lowry, 1962; Campbell and Robson, 1968).
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Sinusoidal gratings vary in frequency, contrast, and phase. In Figure 1 the left side shows such a grating
pattern, and the right side shows the sinusoidal variation in luminance across space. The number of light-dark
cycles of the grating that subtend 1 deg visual angle is a measure of the spatial frequency of the grating,
expressed in cycles per degree (cpd). The human visual system is able to detect spatial frequencies up to about
60 cpd. There is no lower limit, but gener ally measurements are not made below about 0.1 cpd, often because of
practical limits of display size. Borrowing the term octave (a doubling of frequency) from audition, the range of
spatial frequencies usually measured by the contrast sensitivity function is about 10 octaves. A low spatial
frequency consists of broad black and white bands; a high spatial
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CONTRAST SENSITIVITY FUNCTION 3
frequency grating has thin black and white bands. Spatial frequency is therefore related to the size of
conventional objects. When viewing distance and slant are held constant, higher spatia frequencies correspond to
smaller objects.
FIGURE 1 Photographs (left) and horizontal luminance profiles (right) of vertical sinusoidal grating patterns,
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electronically generated at three levels of contrast. The contrasts of the gratings were 0.85 (A), 0.50 (B), and 0.10
(C).
SOURCE: Photographs taken from transparencies provided by Michael Miller, Department of Neurology, Mount
Sinai School of Medicine, and Wolkstein et al., 1980. Reprinted with permission from I. Bodis-Wollner. Copyright
1980 by J. B. Lippincott Company.
The contrast of a sinusoidal grating is based on the maximum luminance (Lmax) and the minimum
luminance (Lmin) in the grating (see Appendix A). It is a dimensionless variable having values ranging from 0.0
(a uniform field) to 1.0, the maximum possible. The phase of a grating measures its position in space relative to
some predetermined reference point.
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CONTRAST SENSITIVITY FUNCTION 4
The minimum contrast at which a grating can be distinguished from a uniform field with some fixed level of
accuracy is the contrast threshold. The reciprocal of threshold contrast is called contrast sensitivity. The contrast
sensitivity function is obtained by measuring contrast thresholds over a range of spatial frequencies. A typical
photopic contrast sensitivity function is shown in Figure 2. What is important about the contrast sensitivity
function seen in Figure 2 is that there is a range of spatial frequencies around 2 to 5 cpd where sensitivity is
maximum. Sensitivity falls off for lower spatial frequencies and rapidly falls off for higher spatial frequencies.
Eventually a high spatial frequency is reached that requires a contrast of 1.0 to detect (the high frequency cutoff).
Spatial frequencies higher than this cutoff frequency cannot be detected by an observer.
Relationship Between Acuity and Contrast Sensitivity
Visual acuity, because it is measured in terms of the smallest identifiable, high-contrast target, and because
small sizes correspond to high spatial frequencies, measures visual sensitivity largely in the higher frequency
regions of the contrast sensitivity function. In brief, visual acuity is measured in terms of the size of the critical
detail (stroke width of the Snellen letter, for example), but this feature is
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FIGURE 2 Photopic contrast sensitivity function of the human visual system for sinusoidal gratings. Both
coordinates are logarithmic.
SOURCE: Campbell and Robson, 1968. Reprinted with permission from F. W. Campbell and J. G. Robson.
Copyright 1968 by The Physiological Society.
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CONTRAST SENSITIVITY FUNCTION 5
not the only important one. Snellen acuity letters corresponding to acuity of 1.0 have a height of 5 min arc. The
spatial frequencies necessary (but not sufficient) for correct identification after detection of these small letters
fall in the approximate range from 18 to 30 cpd (Ginsburg, 1981a). This range of critical spatial frequencies
necessary for identification of letters at a visual acuity of 1.0 is shown with the contrast sensitivity function in
Figure 3. Does the measurement of sensitivity within this range of spatial frequencies (as with visual acuity)
adequately describe the rest of the contrast sensitivity function? Extensive psychophysical data that deal with
abnormal contrast sensitivity and individual differences in contrast sensitivity functions, independence of
contrast thresholds at different spatial frequencies, and masking and adaptation experiments lead us to conclude
that the answer is no.
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FIGURE 3 Photopic contrast sensitivity function showing the range of spatial frequencies necessary to achieve a
visual acuity of 1.0 with Snellen letters.
SOURCE: Ginsburg, 1981a. Reprinted with permission from A. P. Ginsburg. Copyright 1981 by Cambridge
University Press.
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CONTRAST SENSITIVITY FUNCTION 6
Visual acuity measurements, which are related primarily to high spatial frequency sensitivity, cannot predict
contrast sensitivity to low spatial frequencies because thresholds of spatial frequencies separated by more than
about a factor of 2 (one octave) are statistically independent of each other (Blakemore and Campbell, 1969;
Graham and Nachmias, 1971; Sekuler et al., 1984). This independence of widely separated spatial frequencies is
consistent with a model of the visual system containing separate mechanisms, each of which is selectively
sensitive to a limited range of spatial frequencies (Campbell and Robson, 1968; Blakemore and Campbell, 1969;
Graham and Nachmias, 1971; Stromeyer and Julesz, 1972; Ginsburg, 1984a). The contrast sensitivity function
has the potential of adding more information about the functioning of the visual system than that given by visual
acuity, because it assesses sensitivity over a wide range of spatial frequencies, while visual acuity measures
primarily sensitivity at the high spatial frequencies. A primary source of evidence showing that visual acuity
measurements do not characterize the whole contrast sensitivity function comes from clinical studies of people
having abnormal visual function. People with identical high spatial frequency sensitivity may have very different
low spatial frequency sensitivity (Bodis-Wollner, 1972; Bodis-Wollner and Diamond, 1976; Regan et al., 1981).
The clinical applications of contrast sensitivity function are summarized in Proenza et al. (1981).
This dissociation between visual acuity and the contrast sensitivity function was first established in patients
with cerebral lesions who, although they had visual acuity of 0.5 or better, complained of blurred vision. The
contrast sensitivity functions of these patients are shown in Figure 4. A convenient way to illustrate the changes
of sensitivity seen in Figure 4 is by plotting deviations from the “normal” contrast sensitivity, as shown in
Figure 5. In the upper part of Figure 5 are two contrast sensitivity functions: one for normal observers and one
from a patient complaining of reduced vision. The contrast sensitivity function of this patient shows that
sensitivity is reduced at all spatial frequencies. The difference between the normal sensitivity curve and that of
the patient is plotted in the lower part of Figure 5.
This plot of the difference (on a logarithmic scale) between the normal sensitivity and that obtained for an
individual is called a visuogram (see Lundh and Arlinger, 1984, for a discussion of three different ways to
construct a visuogram). A visuogram is the visual equivalent of an audiogram, used by audiologists and
otologists to illustrate deviations from normal auditory sensitivity at different frequencies. The audiogram has
proved valuable in identifying different types of deafness and in making diagnoses about their causes (Davis and
Silverman, 1960). Perhaps this same value will be realized in vision
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CONTRAST SENSITIVITY FUNCTION 7
once a large enough demographic data base for the contrast sensitivity function becomes available.
FIGURE 4 The normal contrast sensitivity function, shown with heavy lines, based on data from 10 observers. The
two other curves represent patients having the same visual acuity, but vastly different contrast sensitivity functions.
SOURCE: Bodis-Wollner and Diamond, 1976. Reprinted with permission from I. Bodis-Wollner. Copyright 1976
by Oxford University Press.
Pathophysiological studies of contrast sensitivity function reveal that loss of sensitivity can occur at all
spatial frequencies or at only restricted bands of spatial frequencies (e.g., Bodis-Wollner and Diamond, 1976;
Proenza et al., 1981). The major point to be taken from these data is that identical visual acuity may be found in
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people with different contrast sensitivity and that a single measure, such as visual acuity, cannot predict
sensitivity at other sizes or spatial frequencies. This dissociation between visual acuity and contrast sensitivity
has been found in patients; but what about people with “normal” vision?
Figure 6 illustrates three different contrast sensitivity functions from three Air Force pilots having visual
acuities of 1.33, 1.00, and 0.80. The visual acuities of the pilots are predicted from the contrast sensitivity in the
high spatial frequency range. The higher the high frequency sensitivity, the higher the visual acuity. Note the wide
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CONTRAST SENSITIVITY FUNCTION 8
variations in low and high frequency sensitivity, and that a low sensitivity at high frequencies does not
necessarily imply a low sensitivity at low spatial frequencies.
FIGURE 5 Contrast sensitivity function (top) and visuogram (bottom). The upper plot shows two contrast
sensitivity functions: the average contrast sensitivity functions of normal subjects with acuity of 1.0 (smooth
curve), and a contrast sensitivity of a patient with visual defects (open circles). Contrast sensitivity (ordinate of
upper plot) is specified on a logarithmic scale in decibels. The lower plot is a visuogram. It shows the contrast
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sensitivity deficit (downward arrow) at each of the tested spatial frequencies for the patient whose contrast
sensitivity is given above. A loss of 6 db signifies a twofold reduction of contrast sensitivity; a loss of 20 db
signifies a tenfold reduction. The spatial frequency scale (abscissa) of the visuogram is the same as that of the
contrast sensitivity function above it.
SOURCE: Wolkstein et al., 1980. Reprinted with permission from I. Bodis-Wollner. Copyright 1980 by J. B.
Lippincott Company.
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CONTRAST SENSITIVITY FUNCTION 9
FIGURE 6 The contrast sensitivity function of three pilots having visual acuities of 1.33, 1.00, and 0.80. Note the
variation of sensitivity below 7 cpd.
SOURCE: Ginsburg, 1981b. Reprinted with permission from A. P. Ginsburg. Copyright 1981 by the Air Force
Aerospace Medical Research Laboratory.
Visual Acuity and Contrast Sensitivity Function in Normal Vision
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While visual acuity cannot predict the spatial contrast sensitivity function in people with abnormal vision,
visual acuity also cannot predict contrast sensitivity in people with assumed normal vision. There are individual
differences in contrast sensitivity as well as changes in the contrast sensitivity function with age (Ginsburg,
1981a, 1984b; Ginsburg et al., 1984; Owsley et al., 1983). These findings raise important questions: Does an
observer with 1.33 acuity have a correspondingly higher contrast sensitivity function than one having acuity of
1.0? Or does the first have a slightly wider contrast sensitivity function? Is it better to have a higher peak contrast
sensitivity function or a broader one for performing various visual tasks? There is some experimental evidence
that under some conditions
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CONTRAST SENSITIVITY FUNCTION 10
peak contrast sensitivity may be more important than visual acuity for predicting detection and identification of
objects (Ginsburg, 1981b).
Contrast sensitivity functions are measured with sinusoidal grating patterns. Although contrast sensitivity
functions could be measured with a wide assortment of targets differing systematically in size and contrast, the
human visual system seems to be especially sensitive to sinusoidal targets (Guth and McNelis, 1969; Watson et
al., 1983; Ginsburg, 1984b). These sinusiodal gratings have important mathematical properties (see Appendix A
and Appendix C) that allow the application of linear systems analysis to the human visual system. This approach
allows both the visual stimulus and the visual system to be described with the same language: that of sinusoidal
spatial frequencies. The visual system is not completely linear, however, and there may be other types of visual
targets (low contrast letter optotypes, for example) that may be particularly effective in detecting certain types of
visual defects (Regan and Neima, 1983, 1984). The working group does not wish to preclude the use of other
types of visual targets if their utility can be demonstrated.
Contrast Sensitivity Function and Visual Performance
Because the image of any object can be described as a set of spatial frequencies at various orientations,
amplitudes, and phases (see Appendix C), there is the potential that an observers contrast sensitivity function can
be used to predict visual performance with more complex visual material. The working group evaluated the
evidence that the contrast sensitivity function can predict visual performance with complex stimuli and found
that considerably more research in this area is needed. If the potential of these early experiments is verified by
further studies, we believe that we will have a powerful way of studying individual differences in vision and
accounting for some of the variability of individual performance on a wide variety of tasks that are primarily
dependent on vision.
There is some experimental evidence suggesting that the contrast sensitivity function can predict certain
types of visual performance better than other measures can. In one series of experiments, subjects were asked to
judge the visual similarity between all possible pairs of random complex grating patterns. These studies found
that the similarity judgments were accurately predicted by using the spatial frequency content of the gratings in
conjunction with the human contrast sensitivity function (Harvey and Gervais, 1978, 1981; Gervais, 1978). In
another study, subjects were required to identify letters of the alphabet 6 min arc high presented for 30 msec
(Gervais, 1978; Gervais et al., 1984). The researchers tried several models of visual processing to predict the
pattern of identification confusions found among all 26 letters of the alphabet. The model with the greatest
predictive power was one based on the amplitude and phase information in the spatial frequency content of each
letter filtered by the human contrast sensitivity function. Gervais et al. (1984) also provide a critical review of
other studies that have failed to find an advantage in spatial frequency models.
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CONTRAST SENSITIVITY FUNCTION 11
The contrast sensitivity function of infants has been used to successfully predict the amount of time that
infants spend looking at different types of visual stimuli. Prior to using contrast sensitivity measures, the best
predictor of looking time was thought to be the amount of contour in the stimulus, the contour density (Karmel,
1969). One study demonstrated that when stimuli were equated for contour density, infants still preferred some
stimuli over others. These preferences were predicted by the spatial frequency characteristics of the stimuli
(Banks and Stephens, 1981). Another study showed that when the spatial frequency content of the stimulus
patterns were combined with the infant's contrast sensitivity function, both the infant's looking preferences and
looking times were better predicted than by the contour density measure (Gayl et al., 1983).
Finally, individual differences in contrast sensitivity functions may be the basis of individual differences in
performance on complex tasks. Figure 7 shows the contrast sensitivity functions of three observers having visual
acuities of 1.00, 0.66, and 0.40 (Ginsburg, 1981b). The two subjects with the acuity below 1.00 required optical
correction but were tested without their glasses. These observers had their contrast thresholds measured for the
detection and identification of both letters of the alphabet and airplanes of different angular size. The individual
differences seen in the detection and identification of letters and planes were predictable from the relevant spatial
frequencies of those targets required for detection and identification and the individual contrast sensitivity
functions. Note in Figure 7 that the observer having the highest contrast sensitivity in the middle spatial
frequencies also was best at the target detection and identification tasks, even though his visual acuity was not
the best of the three. A second study of 11 Air Force pilots (Ginsburg et al., 1982) indicated that contrast
sensitivity, not visual acuity, predicted simulated air-to-ground target detection. Visual acuity and contrast
sensitivity functions were measured under high and low photopic levels of luminance. The correlations between
the acuity measures and detection range was not statistically significant. There was a significant correlation
(0.83, p < 0.01) between detection range and the peak sensitivity of the contrast sensitivity functions measured at
low photopic levels. In a third study (Ginsburg et al., 1983), 84 Air Force pilots took part in field trials that
required them to detect an approaching airplane from the ground; 10 sets of field trials were run under widely
differing visibility conditions, with about 8 pilots participating in each set. An interesting pattern of correlations
emerged between the distance of target detection and the contrast sensitivity at six different spatial frequencies.
These correlations tended to be significant for frequencies greater than 8 cycles per degree under high visibility
conditions. In contrast, the correlations tended to be significant at 8 cycles per degree and below under low
visibility conditions. These results suggest that contrast sensitivity measurements taken over a range of spatial
frequencies has potential for predicting detection performance under a variety of visibility conditions. Further
studies are needed to determine the full potential for predicting this important kind of performance.
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CONTRAST SENSITIVITY FUNCTION
Aerospace Medical Research Laboratory.
subjects having 0.4 and 0.6 Snellen acuity without their glasses and one subject having uncorrected acuity of 1.0.
FIGURE 7 Contrast sensitivity to sine wave gratings, detecting and identifying letter and aircraft silhouettes for two
SOURCE: Ginsburg, 1981b. Reprinted with permission from A.P. Ginsburg. Copyright 1981 by the Air Force
12
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CONTRAST SENSITIVITY FUNCTION 13
Suprathreshold Contrast Functions
The human visual system responds to suprathreshold grating patterns quite differently than it does to
threshold patterns. Although the amount of contrast required for detection of gratings is heavily dependent on the
spatial frequency of the grating, this dependency breaks down in the perception of apparent contrast of
suprathreshold gratings (Georgeson and Sullivan, 1975; Cannon, 1979; Ginsburg et al., 1980). This effect, called
contrast constancy, is found when subjects adjust the physical contrast of different frequency gratings in order to
achieve the perception of equal apparent contrast. Particularly at high levels of physical contrast, the contrast
required for constant apparent contrast is virtually independent of spatial frequency.
There also can be a dissociation between detection sensitivity and spatial frequency discrimination (Began
et al., 1982). Following adaptation to a suprathreshold sine wave grating, although detection threshold is greatly
elevated at the adaptation spatial frequency, discrimination threshold is unaffected. Discrimination threshold is
maximally affected at a frequency about twice that of the adapting frequency (Regan and Beverley, 1983).
Studies using visual evoked potentials have also found a dissociation between the response to low contrast
gratings and the response to high contrast gratings (Bodis-Wollner et al., 1979). We cite this evidence to point
out that extrapolation from threshold measurements of contrast sensitivity to predictions of responses to
suprathreshold patterns is theoretically and practically a complicated issue. This complication does not deter the
working group from looking at the empirical evidence relating to the usefulness of the contrast sensitivity
function in predicting visual processing of complex targets.
Sensitivity to Phase
The spatial phases of the sinusoidal components of complex patterns are as important as their amplitudes.
There is growing evidence that the contrast sensitivity function does not capture all important individual
differences, that phase sensitivity must be considered as well. The abnormal vision of some amblyopic patients is
not well explained by changes in the contrast sensitivity function (Hess, 1984). These patients report perceptual
distortions that seem like phase distortion effects when viewing sinusoidal gratings. The ability to discriminate
between gratings containing two harmonically related spatial frequencies that differ only in their phase
relationships is markedly reduced in the amblyopic eye.
The ability of the human observer to recognize or identify an object is remarkably robust to distortions of
the spatial frequency amplitude spectrum of the object but not to a distortion of its phase. A small amount of
phase distortion renders the picture unrecognizable. Sensitivity to phase distortions both in photographs of
objects and in random checkerboard textures is relatively independent of spatial frequency (Caelli and Bevan,
1982).
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