0041.6989 79 O9OI-lO45SO?.W~O
CONTRAST
SENSATION: OF STIMULUS
A LINEAR FUNCTION CONTRAST
MARK W. CANNONJR Aerospace Medical Research Laboratory. Human Engineering Division. Visual Display Systems Branch, Wright-Patterson AFB. Ohio 45433. U.S.A. (Receiced 24 July 1978)
Abstract-The method of magnitude estimation was used to determine the relationship between stimulus contrast and contrast sensation for stimulus contrasts from 0.63% to 609; at spatial frequencies of 1, 2, 6.5, and 12 cycles per degree. The relationship between contrast sensation and stimulus contrast was found to be linear over the entire range of stimulus contrasts and spatial frequencies studied. A theoretical function for contrast sensation is proposed and the concept of a contrast sensation surface is introduced. Constant contrast sensation contours derived from this surface are shown to fit data from contrast matching experiments performed in other laboratories.
INTRODUCTION The idea that the contrast sensitivity function is inappropriate for describing human suprathreshold contrast sensation has recieved strong support from a number of papers in the last 12 years. Georgeson and Sullivan (1975) performed contrast matching experiments with sine wave gratings in which the contrast of a test grating was adjusted until its perceived contrast matched that of a 5 c/deg standard grating. Test gratings ranged in spatial frequency from 0.23 c,/deg to 25 cjdeg and the contrast of the standard grating was set at values from about 0.5% to 7.5%. The data points generated for a specific contrast setting of the standard grating were plotted in logarithmic coordinates and connected by line segments to form constant contrast sensation contours. These contours represented luminance contrast values that produced equal contrast sensation as a function of spatial frequency. Although these contours converged to the modulation sensitivity function near threshold, they became effectively flat across spatial frequency when the standard grating contrast was above 300/,. This implies that the contrast sensation becomes independent of spatial frequency as contrast increases. Previous results that support these conclusions were obtained by Bryngdahl(l966). Watanabe, Mori, Nagata, and Hiwatashi (1968) and by Blakemore, Muncey, and Ridely (1973). A similar contrast matching experiment was conducted by Kulikowski (1976) who observed that grating contrast sensations were equal when their suprathreshold contrasts were equal, but he defined this suprathreshold contrast as the actual grating contrast minus its threshold contrast. Constant contrast sensation contours from these data also appeared to flatten at high contrasts if plotted on logarithmic contrast coordinates, but maintained the shape of the threshold function plus a constant if plotted on linear cordinates. In either case, flattening of these contours on a log contrast-log frequency plot implies that the threshold contrast sensitivity function cannot be treated as a multiplicative transfer function for determining suprathreshold contrast sensation. This point is treated in greater detail in the appendix.
Several investigators have used contrast matching techniques to explore the variation in perceived contrast with stimulus contrast. Bryngdahl (1966) and Fiorentini and Maffei (1973) asked subjects to adjust the luminance of a uniform field until it matched in brightness either the peak or trough of an adjacent grating. Both papers showed plots of the difference between the luminance required to match the peak and the luminance required to match the trough as a function of stimulus contrast. Bryngdahl, who used sine wave stimuli and only one subject, found that luminance difference was a power function of contrast whereas Fiorentini and Maffei found that luminance difference was a linear function of log contrast for square wave stimuli. The reason for the difference in functional form between the two sets of data is unknown. It should be noted that neither of these experiments attempted to measure contrast sensation as a function of stimulus contrast. However, two more recent papers have addressed this problem. Kulikowski (1976) used a contrast halving technique and demonstrated a linear relationship between contrast sensation and stimulus contrast for sine wave gratings at 5 c/deg. A similar demonstration of the linear relationship between contrast and contrast sensation was obtained by Hamerly, Quick, and Reichert (1977) using the method of magnitude estimation. They showed data from three subjects as plots of estimated contrast vs. stimulus contrast at spatial frequencies of 4, 6.25, 12, and 16c/deg. However, Hamerly et al., noted. th,rr regression lines drawn through their data did not intercept the contrast axis at the contrast thresholds for any of the spatial frequencies tested. The actual intercepts were an order of magnitude higher than the contrast threshold in each case. This discrepancy may have been caused by their use of a standard 6.25 cycle per degree comparison grating set at ZOO/ocontrast and arbitrarily given a value of 100. Stevens (1956) has demonstrated that if a standard is used in magnitude estimation experiments, assigning a numerically large number to this standard, while placing it at a low stimulus level causes the magnitude estimation function to be steeper than it would be if the
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standard were placed at a higher stimulus level. However, the magnitude estimation technique seems to be ideal for investigating suprathreshold contrast sensation, since the data give a direct relationship between stimulus magnitude and sensation magnitude. Such a relationship permits investigations of the variation in visual system gain (sensation magnitude/stimulus magnitude) as a function of certain stimulus parameters such as spatial frequency, contrast and average luminance. The technique has been successfully used by a number of investigators to measure brightness sensation. for example: Stevens and Stevens (1963). Mansfield (1973, 1976) and Barlow and Verrillo (1976). Therefore, the technique of magnitude estimation without a standard (free modulus magnitude estimationf Stevens (1963) was used to measure contrast sensation in the experiments reported in this paper. In this technique, no number scale is imposed on the subject. who is free to pick a “comfortable” scale. This study was designed to investigate the linearity of contrast sensation across the spatial frequency region where contrast sensitivity function has a maximum and to clarify the relationship between the contrast sensitivity function and suprathreshold contrast sensation in the spatial frequency region between 1 and 12 c/deg. APPARATUS
Sine wave gratings
were presented on two oscilloscopes (Hewlett Packard 1205 A with P-31 phosphor). The CRT faces were IOcm wide by 8 cm high. The CRTs were mounted one above the other with a spacing of 13.6cm between face centers and were constantly illuminated with a uniform luminance level of 5 ft lamberts. Gratings were presented as a sinusoidal intensity modulation. in the horizontal direction. of the 5 ft lambert average luminance. Twelve different grating contrast values could be presented on the upper CRT. They ranged from 5% to 60% and could be varied in 5% increments. The gratings were presented at spatial frequencies of 1;2, 6.5, and 12c/deg. The stimulus contrast of the gratings was defined as:
Percent
contrast
L - Lmn x ,@) = LmJ’ m4, + L”
and minimum where L,,, and L,,, are the maximum luminance values recorded for a particular sine wave grating. The sine wave grating on the lower CRT, when present, was always at a spatial frequency of 4 cjdeg and a contrast of 30”,;. Both CRTs were calibrated using a Pritchard photometer model 1290. The stimulus contrast of both CRTs was found to be linear with rms z axis input voltage up to at least 65% contrast and up to spatial frequencies of I2 c/deg. the highest spatial frequency tested. All stimuli were presented repetitively with 2 sets of grating followed by 9 set of uniformly illuminated screen to minimize adaptation effects that might be caused by high contrast gratings. All gratings had 10 msec rise and fall times and no illuminated surround was used. Subjects were seated in a darkened room with the CRTs as the only lieht sources. Each subject adapted to the 5 It lambert lcminance for 3min before experimentation began. Subjects viewed the CRTs binocularly, with natural pupils. from a distance of 1.9 meters. At this distance, the horizontal width of each CRT subtended 3’ of visual angle. The experimenter and all instrumentation except for the CRTs was located outside the light proof room. Subjects
communicated com system.
with the experimenter
over a two-way
inter-
METHODS
Suprathreshold contrast sensation was determined for sine wave gratings by the free modulus method of magnitude estimation. Subjects were initially shown one example of a high contrast grating (5O”J and one example of a low contrast grating (5”;). They were then told to assign a number that they thought was proportional to the contrast of the stimulus to each grating that would be presented. The numbers were called out over the intercom system and recorded by the experimenter. No standard reference stimulus was displayed during the experiment and no number scale was suggested. Each experimental session consisted of 5 presentations of each of the I2 contrast levels at one spatial frequency. The contrast values were randomly divided into two subgroups of 6 each for presentation. However. four contrast values were reserved so that the minimum contrast in each subgroup was either 5”, or IO’,, while the maximum was either 55”; or 60’?,. Each contrast was presented five times in randomized order with the restriction that no stimulus in a subgroup was presented for the nth time until all stimuli in that subgroup had been presented for the n-1st time. This procedure was followed to assure that the subjects had seen all contrasts early in the presentation sequence and therefore had a well-developed consistent contrast scale for use in estimating subsequent presentations. The numbers assigned to the first two presentations of each contrast were discarded while the last three assigned magnitudes for each contrast were averaged and retained as a measure of the perceived contrast. A matching experiment was performed between presentations of subgroups I and 2. The standard 4cjdeg. 30”; contrast grating was displayed on the lower CRT and the subject WIS asked to adjust the contrast of the grating on the upper CRT to match the contrast of the standard on the lower CRT. Five matches were made by each subject during each session and a mean stimulus contrast was determined from this data. Averages of the pooled data from 9 subjects at each of the four spatial frequencies determined the stimulus contrast for constant contrast sensation as a function of spatial frequency. Since an equivalent function can be determined from the magnitude estimation data, comparison of the function derived from the classical method of adjustment to the magnitude estimation results served to validate the magnitude estimation technique for contrast judgement. M4GSITUDE
ESTlhlATlON
RESULTS
Individual subject data were summarized by computing and plotting the average of the three contrast sensation estimates for each stimulus contrast. This procedure produced 12 estimates per subject for each of the four spatial frequencies. Data points for two subjects are shown in Fig. 1 and demonstrate the typical range of numbers chosen by all subjects (O-12). The open symbols represent the responses to the 6 contrasts presented in subgroup 1. the closed symbols represent responses to the remaining 6 contrasts presented in subgroup 2. The double logarithmic plots of individual subject data demonstrated approximate linearity in all cases. This linearity on double logarithmic coordinates implied a power function relationship between contrast sensation and stimulus contrast. Therefore, the logarithms of the magnitude estimations were averaged across subjects and a least squares regression line was fitted
Contrast sensation: a linear function of stimulus contrast I A 2A
I c/d
0
2c/d
.
SUBJECT
a
Q S.Sc/d .
1047 Q 12c/d .
JS
20 -
PERCENT
CONTRAST
SUBJECT
b
20
PO
t
PERCENT
CONTRASt
Fig. 1. Magnitude estimation responses for two subjects. Closed symbols represent responses to the tirst group of 6 contrasts. Open symbols represent responses to a second set of 6 contrasts randomly interleaved with the first set and presented after all trials on the first set had been completed. Each point represents the average of three estimations. to the means
at each spatial frequency. Average values, standard deviations and least square rcgression lines are all shown in Fig. 2. The slopes of the least squares regression lines on double logarithmic coordinates gave the exponents of the power function relationship between estimated contrast sensation and stimulus contrast. Thus the estimated contrast sensation (S) is expressed in terms of the stimulus contrast (c) as S = AC where A is an arbitrary constant and 01is the slope of the least squares regression line in double logarithmic coordinates. The values of a from the plots in Fig. 2 are given in Table 1. The exponents are very nearly one, indicating that contrast sensation is a linear function of stimulus contrast. Consider the matching experiment performed by the subjects in the middle of each magnitude estimation session. The means and standard deviations of the contrasts at which the test grating had the same “.I. 19/9-F
perceived contrast as the standard grating are shown as the solid circles in Fig. 3. These represent points of constant contrast sensation and a similar set of points can be obtained from the least squares regression lines in Fig. 2. If a horizontal line, representing a constant perceived contrast, is drawn through all four curves the stimulus contrasts at which’ the line intersects the curves are the contrasts that produce constant contrast sensation. These are shown as open circles in Fig. 3, and at each spatial frequency they fall within the experimental uncertainty of the matching values obtained from the matching experiment. Therefore, the constant contrast contour derived from the magnitude estimation results agrees with the matching results. With this agreement established, the analysis can be carried a step further. Since the power function relationship between S and C has exponent of one,
MARK W. CANNONJR
1048 A
I CYCLE
0
2
CYCLES
/
DEGREE
q
6.5
/ DEGREE
v
12
PERCENT
CYCLES/
DEGREE
CYCLES/DEGREE
CONTRAST
Fig. 2. The symbols represent the geometric means of the magnitude estimation responses for nine subjects. Vertical lines show the standard deviations and the solid lines drawn though the points are linear least squares regression lines fitted to the data at each spatial frequency.
Table I. Power function exponent Spatial frequency in c/deg
Exponent (z)
I
1.05
2 6.5 I2
0.97 0.93 0.98
contrast sensation can be expressed as S = kC + 6 for the range of luminance contrasts from 5% to 60%. The parameter k represents the slope of the contrast sensation function if plotted on linear coordinates and is proportional to the gain of the visual system for
NATCNINC OATA -0--
YAON,T”OE
BTMATION
OATA
Fig. 3. The solid circles and vertical bars show the mean and standard deviation of the contrasts set by nine subjects to match the contrast of a grating at 1, 2, 6.5, or 12cpd to a grating of 30% contrast at 4cpd. The open circles are contrasts obtained from the least squares regression lines of Fig. 2 at a sensation level (estimated contrast) of 4.5. These two sets of data demonstrate that the constant contrast sensation contour deduced from the magnitude estimation results is comparable to the contour generated by a matching experiment.
contrast sensations produced by single component sioewave gratings. The values of k at the four spatial frequencies can now be determined. The data were averaged linearly across subjects at each spatial frequency and fitted with least squares regression lines on linear coordinates. The results are shown in Fig. 4. The slopes vary between 0.131 and 0.143, with an average value of 0.137. To test whether the slopes show statistically significant variation with spatial frequency, the four sets of data points from each subject were individually fitted with least squares regression lines. The slopes of these lines were determined and an analysis of variance was performed on them to test the hypothesis that all slopes are equal across spatial frequencies. The slopes are given in Table 2. The analysis of variance shows no statistically significant variation in slope with spatial frequency (P = 0.01). Therefore, the data support the conclusion that visual system gain (change in contrast sensation level divided by change in stimulus contrast) is independent of spatial frequency for single component sine wave gratings and that the threshold contrast sensitivity function is unrelated to the gains of spatial frequency channels for contrast above 5%. These results also suggest that Kulikowski’s interpretation of the linearity of suprathreshold contrast sensation is correct. To investigate this possibility, two further sets of experiments were conducted. Cootrast thresholds were determined for 5 subjects using the method of limits and the standard stimulus presentation. The mean and standard deviations of these measurements are given in Fig. 5. Finally, the suprathreshold magnitude estimates of contrasts from 0.625% to 10% were determined for three subjects. These subjects chose a number scale such that the 10% contrast grating at 6.5 c/deg received an average rating of 5. To make these data comparable to the
Contrast sensation: a linear function of stimulus contrast
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I2 1
lSPATlAL
FREQ.
SLOPE I
STIMULUS
CONTRAST
IN
PERCENT
Fig. 4. The data points are the linear averages of the magnitude estimates of nine subjects. Vertical bars are the standard deviations and the lines through the data points are linear least squares regression lines plotted on linear coordinates. The slopes are indicated in the upper left hand corner and show little variation with spatial frequency. Table 2. Slopes of individual contrast estimation functions Spatial frequency in c/deg
1
2
3
4
5
1 2 6.5 12
0.127 0.130 0.092 0.094
0.080 0.077 0.074 0.083
0.110 0.104 0.168 0.094
0.164 0.155 0.176 0.144
sets all mean estimated magnitudes of the low contrast stimuli were divided by 4. The combined plots of all data are shown in Fig. 6, with the low contrast magnitudes substituted for the 5% and 10%
previous
6
1
a
9
0.111
0.163
0.08 i
0.181
0.169 0.183
0.110 0.177 0.163 0.167
0.182 0.182
0.065 0.047
0.179 0.161 0.158 0.155
0.222 0.207
contrast values of the 9 subject data. Dividing all the low contrast data points by 4 provided a smooth transition between the low and high contrast data -at all spatial frequencies, demonstrating the consistency of the magnitude estimation procedure. DlSCtiSSlON
SunAL FR2wENcY IN CYCLES PER OEGRE6
Fig. 5. Means and standard deviations of thresholds for five subjects. The threshold was determined using the method of limits and the same temporal stimulus sequence used in the magnitude estimation experiment. The grating was present for 2 set followed by 9 set of uniformly illuminated CRT screen. The 2 set interval in which the grating appeared was preceded by a 1 set tone.
The solid curves in Fig. 6 are theoretical functions relating contrast sensation (s) to grating contrast (C) and grating contrast threshold (Q. The function is a simple linear relationship [S = k(C - C,)]. The value chosen for k was the average slope of the least squares regression lines plotted in Fig. 4, and the contrast thresholds which vary with spatial frequency, were obtained from the data of Fig. 5. Using only these two experimentally derived values, thetheoretical contrast sensation functions describe the data very well, demonstrating the linearity of contrast sensation from threshold to at least 65%. By combining contrast sensation, stimulus contrast and spatial frquency in the same plot, a three dimensional surfaa such as that shown in Fig. 7 can be produced. This concept
I050
MARK W. CANNONJR SOLID
CURVES
-
PLOT
OF
o
CDNTRAST 2 c/deg
SENSATION 0
STIMULUS
6.5
= .I37
c/dcg
CONTRAST
(CONTRAST-
V
CONTRAST
THRESHQ_D
)
12 c/deq‘l
IN
1 I
PERCENT
Fig. 6. The data points above 10% contrast are the original nine subject magnitude estimation
data. The points at 10% and below are averaged estimations from three subjects produced in a subsequent low contrast magnitude estimation experiment. The curves drawn through the points are plots of the function S = k(C - C,,) where k is the average slope of the data in Fig. 4. C,, is the contrast threshold (different for each spatial frequency) determined in Fig. 5. The estimated contrast (contrast sensation) predicted by this function fits the experimental data quite well. of a contrast sensation surface is offered as a possible new insight into suprathreshold perception. The contrast threshold function is the intersection of the surface with the contrast-spatial frequency plane. Intersections of the surface with planes parallel to the contrast-spatial frequency plane are constant contrast sensation contours of the type produced in contrast
CONTRAST
SENSATION
SURFACE
Fig. 7. Idealized contrast sensation surface derived from equation S(f) = k[C(l) - C,,(f)] where f is spatial frequency. Note that the co-ordinates are logarithmic on all axes.
matching experiments. The constant contrast sensation contours derived from the theoretical functions of Fig. 6 are plotted in Fig. 8 and clearly demonstrate two similarities to Georgeson and Sullivan’s (1975) constant contrast contours. The first of these is the obvious flattening of the contours at high contrasts, and the second is the crowding together of contours for low contrast at 12c/deg. With the linear relationship between contrast and contrast sensation established, the constacy of k with
Fig. 8. Constant contrast sensation contours derived from the theoretical functions plotted in Fig 6. These curves can be visualized as contours running horixontally across the surface of Fig. 7 when viewed from above.
Contrast sensation: a linear function of stimulus contrast
FREamcf
IN CYCLES PER DEGREE
Fig. 9. Theoretical predictions of constant contrast sensation contours (solid lines) compared to data points obtained in contrast matching experiments by Ginsburg (1977). The method of obtaining the theoretical predictions is explained in the text.
spatial frequency can be verified by comparing predicted constant contrast sensation contours with contrast matching data obtained in other laboratories. First, however, a further discussion of the simplicity of the theoretical relationship between contrast and contrast sensation is appropriate. If f denotes spatial frequency, S(f) = k[C(f) - Clk(fi]. If k is constant with spatial frequency, the values of C(/) that produce a constant contrast sensation, (S(f) = S, for ail /x are C(f) = S/k + C,,(j). This equation simply says that the contrast necessary to produce a constant sensation level S at spatial frequency f is just the threshold contrast function at that spatial frequency plus a constant. If the theory is correct, a constant S/k, determined at any spatial frequencyf, on a given constant contrast sensation contour should, when added to the threshold function C,(fx determine C(fl for every other point on that contour. The required relationship for this constant is S/k = C(fo) - C,,(f,). This relationship was applied to contrast matching data obtained by Ginsburg (1977). The predicted contours are the solid lines in Fig. 9. The individual ooints are Ginsburg’s data. Each contour was derived by simply adding a constant (the same constant for all points on a given contour) to Ginsburg’s threshold
data. The fit of the contours to the data points is quite good verifying that a linear relationship holds between sensation and the suprathreshold contrast and that k is essentially constant with spatial frequency. The theory was also applied to the scotopic data of Georgeson and Sullivan (1975). Their scotopic data points for two subjects are displayed in Figs 1Oa and b. The squares represent the threshold data while the circles and triangles represent suprathreshold matching data. The solid lines are theoretical contours based on the linearity assumption. Again, the fit between theory and data is good. Note that it is the value S(f)/k that determines the shape of the constant contrast sensation contours and as long as k does not vary significantly with spatial frequency or background luminance, the simple linear relationship is a good first order fit for suprathreshold contrast sensation predictions. While it can be inferred from Kulikowski’s (1976) contrast matching data that k is fairly constant over a wide range of luminances, some small deviations in k over spatial frequency were evident from the magnitude estimation data of individual subjects (Table 2). While the model proposed here works well for subjects with normal vision, it is to be expected that it cannot adequately predict contrast sensation for subjects with certain visual abnormalities. For example, the structure of constant contrast sensation contours of an amblyope obtained by Ginsburg (1977) indicated that the gain, k, varied considerably with both spatial frequency and stimulus contrasts for that individual. The relative constancy of k over the spatial frequency range from 1 to 12 cycles per degree has one more important implication. The transfer function for the optics of the eye (Campbell and Green, 1965) must act in a multiplicative manner on the spatial frequency spectrum of the stimulus. The data of Campbell and Green indicate a reduction in gain due to the optics by a factor of 2 between 1 and 12c/deg. This should be reflected directly in a reduction of k by the same amount if no other mechanisms were present. However, no such reduction in k is evident, either in the direct measurement from magnitude estimation or in the application of the theoretical relationship to other psychophysical matching data (Figs 9 and 10). Consequently, this constancy in k supports the hypothesis of Georgeson and Sullivan
SPATIAL fnwUEMcY IN CYCLES PER DEGREE
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IO SPATIAL FREGUENCY
IN CYCLESPER DEGREE
Fig. 10. Theoretical predictions of constant contrast sensation contours (solid lines) compared to data points from two subjects obtained by Georgeson and Sullivan in contrast matching experiments at scotopic light levels. Contrast sensation appears to be predictable at low light levels by the same equation that holds at photopic levels.
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Mfitc
W. CANNON JR
that some type of spatial frequency dependent enhancement mechanism is acting in the human visual system.
Spatial sine-wave responses Vision Rex 8, 1245-1263.
of the human
visual system.
APPENDIX
.-lcknowvledgemenrs-The research reported in this paper was conducted by personnel of the Aerospace Medical Research Laboratory. Aerospace Medical Division, Air Force Systems Command, Wright-Patterson Air Force Base. Ohio. Reprints of this article are identified by Aerosoace Medical Research Laboratory and AMRL-TR-78-56. Further reproduction is authorized to satisfy needs of the U.S. Government. The author wishes to express his gratitude to Lt Gary Sims for the construction of some of the electronic circuitry that made these experiments possible and to Capt. Arthur Ginsburg and Dr Michael Nelson for their constructive criticism of the manuscript. REFERENCES
Barlow R. B. and Verillo R. T. (1976) Brightness sensation in a ganzfeld. vision Res. 16, 1291-1297. Blakemore C., Muncey J. P. J. and Ridely R. M. (1973) Stimulus specificity in the human visual system. Vision Rex 13, 1915-1931. Bryngdahl 0. (1966) Characteristics of the visual system: Psychophysical measurements of the response to spatial sine-wave stimuli in the photopic region. J. opt. Sot. Am. 56. 811-821. Campbell F. W. and Green D. G. (1965) Optical and retinal factors affecting visual resolution. i. Physiol. 181, 576-593. Fiorentini A. and Maffei L. (1973) Contrast perception and electrophysiological correlates. J. Physiol. 231, 61.-69. Georgeson M. A. and Sullivan G. D. (1975) Contrast constancy: deblurring in human vision by spatial frequencv channels. J. Physiol. 252. 627-655. _ _ . . Ginsburg A. P. (1977) Visual information urocessinn based on spatial filters constrained by biological data: Ph.D. thesis Univ. of Cambridge. Hamerly J. R., Quick R. F. Jr and Reichert T. A. (1977) A study of grating contrast judgement. Vision Res. 16, 1419-1431. Mansfield R. J. W. (1976) Visual adaptation: retinal transduction, brightness and sensitivity. Vision Res. 16, 679-690. Stevens S. S. (1956) The direct estimation of sensory magnitudes-loudness. Am. J. Physiol. LXIX, l-25. Stevens J. C. and Stevens S. S. (1963) Brightness function: effects of adaptation. J. op. Sot. Am. 53, 375-385. Watanabe A.. Mori T., Nagata S. and Hiwatashi K. (1968)
Contrast matching experiments are conducted under the assumption that the contrast of a test grating can be adjusted until the contrast sensation produced by this grating is equal to the contrast sensation produced by a standard grating. If the threshold contrast sensitivity function can be treated as a linear multiplicative transfer function. contrast sensation is given by S(f, = ff(fiC(f, where S is contrast sensation, H is the transfer function, C is the stimulus contrast and f is spatial frequency. In contrast matching experiments, S is constant with spatial frequency and the equation becomes: S = !f(flC(fr The contrast to produce constant contrast sensatton across spatial frequency is C(f, = S/H(J) Now consider the values of C(fx at spatial frequencies /I andf,, required to produce constant contrast sensation, S. C(/,)
= S/H(I,)
Wzr) = S,H(J’,) Take
Finally obtain:
the logarithm
to obtain:
) = 1%S - 1%WI)
log C(/,)
= log S - log H(f,).
subtract
log C(f,)
of both equations
log C(/,
the lower equation
from the upper
- log C(fz) = log H(jz)
and
- log H(I,)
This equation shows that the difference between contrasts required to produce constant contrast sensation when these contrasts are plotted in logarithmic coordinates is independent of contrast sensation level S. Therefore. if H(f) was independent of contrast sensation level, the curve C(fl, produced in matching experiments, should have the same shape at all contrast sensation levels on a log contrast vs spatial frequency plot. The data cited in this paper show that this is not the case. In fact log C(f,) - log C(fa) becomes smaller at higher contrast sensation levels. Consequently, the equation C(fl = S/H(fi, where H(f) is independent of contrast sensation level does not hold. While it is possible to describe the data in terms of a function H(j; s) that does vary with contrast sensation this proposed in level, the equation paper. S(/) = /ccc(f) - C,,(fl] appears to describe the data more efficiently.
CONTRAST
SENSATION: OF STIMULUS
A LINEAR FUNCTION CONTRAST
MARK W. CANNONJR Aerospace Medical Research Laboratory. Human Engineering Division. Visual Display Systems Branch, Wright-Patterson AFB. Ohio 45433. U.S.A. (Receiced 24 July 1978)
Abstract-The method of magnitude estimation was used to determine the relationship between stimulus contrast and contrast sensation for stimulus contrasts from 0.63% to 609; at spatial frequencies of 1, 2, 6.5, and 12 cycles per degree. The relationship between contrast sensation and stimulus contrast was found to be linear over the entire range of stimulus contrasts and spatial frequencies studied. A theoretical function for contrast sensation is proposed and the concept of a contrast sensation surface is introduced. Constant contrast sensation contours derived from this surface are shown to fit data from contrast matching experiments performed in other laboratories.
INTRODUCTION The idea that the contrast sensitivity function is inappropriate for describing human suprathreshold contrast sensation has recieved strong support from a number of papers in the last 12 years. Georgeson and Sullivan (1975) performed contrast matching experiments with sine wave gratings in which the contrast of a test grating was adjusted until its perceived contrast matched that of a 5 c/deg standard grating. Test gratings ranged in spatial frequency from 0.23 c,/deg to 25 cjdeg and the contrast of the standard grating was set at values from about 0.5% to 7.5%. The data points generated for a specific contrast setting of the standard grating were plotted in logarithmic coordinates and connected by line segments to form constant contrast sensation contours. These contours represented luminance contrast values that produced equal contrast sensation as a function of spatial frequency. Although these contours converged to the modulation sensitivity function near threshold, they became effectively flat across spatial frequency when the standard grating contrast was above 300/,. This implies that the contrast sensation becomes independent of spatial frequency as contrast increases. Previous results that support these conclusions were obtained by Bryngdahl(l966). Watanabe, Mori, Nagata, and Hiwatashi (1968) and by Blakemore, Muncey, and Ridely (1973). A similar contrast matching experiment was conducted by Kulikowski (1976) who observed that grating contrast sensations were equal when their suprathreshold contrasts were equal, but he defined this suprathreshold contrast as the actual grating contrast minus its threshold contrast. Constant contrast sensation contours from these data also appeared to flatten at high contrasts if plotted on logarithmic contrast coordinates, but maintained the shape of the threshold function plus a constant if plotted on linear cordinates. In either case, flattening of these contours on a log contrast-log frequency plot implies that the threshold contrast sensitivity function cannot be treated as a multiplicative transfer function for determining suprathreshold contrast sensation. This point is treated in greater detail in the appendix.
Several investigators have used contrast matching techniques to explore the variation in perceived contrast with stimulus contrast. Bryngdahl (1966) and Fiorentini and Maffei (1973) asked subjects to adjust the luminance of a uniform field until it matched in brightness either the peak or trough of an adjacent grating. Both papers showed plots of the difference between the luminance required to match the peak and the luminance required to match the trough as a function of stimulus contrast. Bryngdahl, who used sine wave stimuli and only one subject, found that luminance difference was a power function of contrast whereas Fiorentini and Maffei found that luminance difference was a linear function of log contrast for square wave stimuli. The reason for the difference in functional form between the two sets of data is unknown. It should be noted that neither of these experiments attempted to measure contrast sensation as a function of stimulus contrast. However, two more recent papers have addressed this problem. Kulikowski (1976) used a contrast halving technique and demonstrated a linear relationship between contrast sensation and stimulus contrast for sine wave gratings at 5 c/deg. A similar demonstration of the linear relationship between contrast and contrast sensation was obtained by Hamerly, Quick, and Reichert (1977) using the method of magnitude estimation. They showed data from three subjects as plots of estimated contrast vs. stimulus contrast at spatial frequencies of 4, 6.25, 12, and 16c/deg. However, Hamerly et al., noted. th,rr regression lines drawn through their data did not intercept the contrast axis at the contrast thresholds for any of the spatial frequencies tested. The actual intercepts were an order of magnitude higher than the contrast threshold in each case. This discrepancy may have been caused by their use of a standard 6.25 cycle per degree comparison grating set at ZOO/ocontrast and arbitrarily given a value of 100. Stevens (1956) has demonstrated that if a standard is used in magnitude estimation experiments, assigning a numerically large number to this standard, while placing it at a low stimulus level causes the magnitude estimation function to be steeper than it would be if the
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M+.RK W. CASNON JR
IO-t6
standard were placed at a higher stimulus level. However, the magnitude estimation technique seems to be ideal for investigating suprathreshold contrast sensation, since the data give a direct relationship between stimulus magnitude and sensation magnitude. Such a relationship permits investigations of the variation in visual system gain (sensation magnitude/stimulus magnitude) as a function of certain stimulus parameters such as spatial frequency, contrast and average luminance. The technique has been successfully used by a number of investigators to measure brightness sensation. for example: Stevens and Stevens (1963). Mansfield (1973, 1976) and Barlow and Verrillo (1976). Therefore, the technique of magnitude estimation without a standard (free modulus magnitude estimationf Stevens (1963) was used to measure contrast sensation in the experiments reported in this paper. In this technique, no number scale is imposed on the subject. who is free to pick a “comfortable” scale. This study was designed to investigate the linearity of contrast sensation across the spatial frequency region where contrast sensitivity function has a maximum and to clarify the relationship between the contrast sensitivity function and suprathreshold contrast sensation in the spatial frequency region between 1 and 12 c/deg. APPARATUS
Sine wave gratings
were presented on two oscilloscopes (Hewlett Packard 1205 A with P-31 phosphor). The CRT faces were IOcm wide by 8 cm high. The CRTs were mounted one above the other with a spacing of 13.6cm between face centers and were constantly illuminated with a uniform luminance level of 5 ft lamberts. Gratings were presented as a sinusoidal intensity modulation. in the horizontal direction. of the 5 ft lambert average luminance. Twelve different grating contrast values could be presented on the upper CRT. They ranged from 5% to 60% and could be varied in 5% increments. The gratings were presented at spatial frequencies of 1;2, 6.5, and 12c/deg. The stimulus contrast of the gratings was defined as:
Percent
contrast
L - Lmn x ,@) = LmJ’ m4, + L”
and minimum where L,,, and L,,, are the maximum luminance values recorded for a particular sine wave grating. The sine wave grating on the lower CRT, when present, was always at a spatial frequency of 4 cjdeg and a contrast of 30”,;. Both CRTs were calibrated using a Pritchard photometer model 1290. The stimulus contrast of both CRTs was found to be linear with rms z axis input voltage up to at least 65% contrast and up to spatial frequencies of I2 c/deg. the highest spatial frequency tested. All stimuli were presented repetitively with 2 sets of grating followed by 9 set of uniformly illuminated screen to minimize adaptation effects that might be caused by high contrast gratings. All gratings had 10 msec rise and fall times and no illuminated surround was used. Subjects were seated in a darkened room with the CRTs as the only lieht sources. Each subject adapted to the 5 It lambert lcminance for 3min before experimentation began. Subjects viewed the CRTs binocularly, with natural pupils. from a distance of 1.9 meters. At this distance, the horizontal width of each CRT subtended 3’ of visual angle. The experimenter and all instrumentation except for the CRTs was located outside the light proof room. Subjects
communicated com system.
with the experimenter
over a two-way
inter-
METHODS
Suprathreshold contrast sensation was determined for sine wave gratings by the free modulus method of magnitude estimation. Subjects were initially shown one example of a high contrast grating (5O”J and one example of a low contrast grating (5”;). They were then told to assign a number that they thought was proportional to the contrast of the stimulus to each grating that would be presented. The numbers were called out over the intercom system and recorded by the experimenter. No standard reference stimulus was displayed during the experiment and no number scale was suggested. Each experimental session consisted of 5 presentations of each of the I2 contrast levels at one spatial frequency. The contrast values were randomly divided into two subgroups of 6 each for presentation. However. four contrast values were reserved so that the minimum contrast in each subgroup was either 5”, or IO’,, while the maximum was either 55”; or 60’?,. Each contrast was presented five times in randomized order with the restriction that no stimulus in a subgroup was presented for the nth time until all stimuli in that subgroup had been presented for the n-1st time. This procedure was followed to assure that the subjects had seen all contrasts early in the presentation sequence and therefore had a well-developed consistent contrast scale for use in estimating subsequent presentations. The numbers assigned to the first two presentations of each contrast were discarded while the last three assigned magnitudes for each contrast were averaged and retained as a measure of the perceived contrast. A matching experiment was performed between presentations of subgroups I and 2. The standard 4cjdeg. 30”; contrast grating was displayed on the lower CRT and the subject WIS asked to adjust the contrast of the grating on the upper CRT to match the contrast of the standard on the lower CRT. Five matches were made by each subject during each session and a mean stimulus contrast was determined from this data. Averages of the pooled data from 9 subjects at each of the four spatial frequencies determined the stimulus contrast for constant contrast sensation as a function of spatial frequency. Since an equivalent function can be determined from the magnitude estimation data, comparison of the function derived from the classical method of adjustment to the magnitude estimation results served to validate the magnitude estimation technique for contrast judgement. M4GSITUDE
ESTlhlATlON
RESULTS
Individual subject data were summarized by computing and plotting the average of the three contrast sensation estimates for each stimulus contrast. This procedure produced 12 estimates per subject for each of the four spatial frequencies. Data points for two subjects are shown in Fig. 1 and demonstrate the typical range of numbers chosen by all subjects (O-12). The open symbols represent the responses to the 6 contrasts presented in subgroup 1. the closed symbols represent responses to the remaining 6 contrasts presented in subgroup 2. The double logarithmic plots of individual subject data demonstrated approximate linearity in all cases. This linearity on double logarithmic coordinates implied a power function relationship between contrast sensation and stimulus contrast. Therefore, the logarithms of the magnitude estimations were averaged across subjects and a least squares regression line was fitted
Contrast sensation: a linear function of stimulus contrast I A 2A
I c/d
0
2c/d
.
SUBJECT
a
Q S.Sc/d .
1047 Q 12c/d .
JS
20 -
PERCENT
CONTRAST
SUBJECT
b
20
PO
t
PERCENT
CONTRASt
Fig. 1. Magnitude estimation responses for two subjects. Closed symbols represent responses to the tirst group of 6 contrasts. Open symbols represent responses to a second set of 6 contrasts randomly interleaved with the first set and presented after all trials on the first set had been completed. Each point represents the average of three estimations. to the means
at each spatial frequency. Average values, standard deviations and least square rcgression lines are all shown in Fig. 2. The slopes of the least squares regression lines on double logarithmic coordinates gave the exponents of the power function relationship between estimated contrast sensation and stimulus contrast. Thus the estimated contrast sensation (S) is expressed in terms of the stimulus contrast (c) as S = AC where A is an arbitrary constant and 01is the slope of the least squares regression line in double logarithmic coordinates. The values of a from the plots in Fig. 2 are given in Table 1. The exponents are very nearly one, indicating that contrast sensation is a linear function of stimulus contrast. Consider the matching experiment performed by the subjects in the middle of each magnitude estimation session. The means and standard deviations of the contrasts at which the test grating had the same “.I. 19/9-F
perceived contrast as the standard grating are shown as the solid circles in Fig. 3. These represent points of constant contrast sensation and a similar set of points can be obtained from the least squares regression lines in Fig. 2. If a horizontal line, representing a constant perceived contrast, is drawn through all four curves the stimulus contrasts at which’ the line intersects the curves are the contrasts that produce constant contrast sensation. These are shown as open circles in Fig. 3, and at each spatial frequency they fall within the experimental uncertainty of the matching values obtained from the matching experiment. Therefore, the constant contrast contour derived from the magnitude estimation results agrees with the matching results. With this agreement established, the analysis can be carried a step further. Since the power function relationship between S and C has exponent of one,
MARK W. CANNONJR
1048 A
I CYCLE
0
2
CYCLES
/
DEGREE
q
6.5
/ DEGREE
v
12
PERCENT
CYCLES/
DEGREE
CYCLES/DEGREE
CONTRAST
Fig. 2. The symbols represent the geometric means of the magnitude estimation responses for nine subjects. Vertical lines show the standard deviations and the solid lines drawn though the points are linear least squares regression lines fitted to the data at each spatial frequency.
Table I. Power function exponent Spatial frequency in c/deg
Exponent (z)
I
1.05
2 6.5 I2
0.97 0.93 0.98
contrast sensation can be expressed as S = kC + 6 for the range of luminance contrasts from 5% to 60%. The parameter k represents the slope of the contrast sensation function if plotted on linear coordinates and is proportional to the gain of the visual system for
NATCNINC OATA -0--
YAON,T”OE
BTMATION
OATA
Fig. 3. The solid circles and vertical bars show the mean and standard deviation of the contrasts set by nine subjects to match the contrast of a grating at 1, 2, 6.5, or 12cpd to a grating of 30% contrast at 4cpd. The open circles are contrasts obtained from the least squares regression lines of Fig. 2 at a sensation level (estimated contrast) of 4.5. These two sets of data demonstrate that the constant contrast sensation contour deduced from the magnitude estimation results is comparable to the contour generated by a matching experiment.
contrast sensations produced by single component sioewave gratings. The values of k at the four spatial frequencies can now be determined. The data were averaged linearly across subjects at each spatial frequency and fitted with least squares regression lines on linear coordinates. The results are shown in Fig. 4. The slopes vary between 0.131 and 0.143, with an average value of 0.137. To test whether the slopes show statistically significant variation with spatial frequency, the four sets of data points from each subject were individually fitted with least squares regression lines. The slopes of these lines were determined and an analysis of variance was performed on them to test the hypothesis that all slopes are equal across spatial frequencies. The slopes are given in Table 2. The analysis of variance shows no statistically significant variation in slope with spatial frequency (P = 0.01). Therefore, the data support the conclusion that visual system gain (change in contrast sensation level divided by change in stimulus contrast) is independent of spatial frequency for single component sine wave gratings and that the threshold contrast sensitivity function is unrelated to the gains of spatial frequency channels for contrast above 5%. These results also suggest that Kulikowski’s interpretation of the linearity of suprathreshold contrast sensation is correct. To investigate this possibility, two further sets of experiments were conducted. Cootrast thresholds were determined for 5 subjects using the method of limits and the standard stimulus presentation. The mean and standard deviations of these measurements are given in Fig. 5. Finally, the suprathreshold magnitude estimates of contrasts from 0.625% to 10% were determined for three subjects. These subjects chose a number scale such that the 10% contrast grating at 6.5 c/deg received an average rating of 5. To make these data comparable to the
Contrast sensation: a linear function of stimulus contrast
1049
I2 1
lSPATlAL
FREQ.
SLOPE I
STIMULUS
CONTRAST
IN
PERCENT
Fig. 4. The data points are the linear averages of the magnitude estimates of nine subjects. Vertical bars are the standard deviations and the lines through the data points are linear least squares regression lines plotted on linear coordinates. The slopes are indicated in the upper left hand corner and show little variation with spatial frequency. Table 2. Slopes of individual contrast estimation functions Spatial frequency in c/deg
1
2
3
4
5
1 2 6.5 12
0.127 0.130 0.092 0.094
0.080 0.077 0.074 0.083
0.110 0.104 0.168 0.094
0.164 0.155 0.176 0.144
sets all mean estimated magnitudes of the low contrast stimuli were divided by 4. The combined plots of all data are shown in Fig. 6, with the low contrast magnitudes substituted for the 5% and 10%
previous
6
1
a
9
0.111
0.163
0.08 i
0.181
0.169 0.183
0.110 0.177 0.163 0.167
0.182 0.182
0.065 0.047
0.179 0.161 0.158 0.155
0.222 0.207
contrast values of the 9 subject data. Dividing all the low contrast data points by 4 provided a smooth transition between the low and high contrast data -at all spatial frequencies, demonstrating the consistency of the magnitude estimation procedure. DlSCtiSSlON
SunAL FR2wENcY IN CYCLES PER OEGRE6
Fig. 5. Means and standard deviations of thresholds for five subjects. The threshold was determined using the method of limits and the same temporal stimulus sequence used in the magnitude estimation experiment. The grating was present for 2 set followed by 9 set of uniformly illuminated CRT screen. The 2 set interval in which the grating appeared was preceded by a 1 set tone.
The solid curves in Fig. 6 are theoretical functions relating contrast sensation (s) to grating contrast (C) and grating contrast threshold (Q. The function is a simple linear relationship [S = k(C - C,)]. The value chosen for k was the average slope of the least squares regression lines plotted in Fig. 4, and the contrast thresholds which vary with spatial frequency, were obtained from the data of Fig. 5. Using only these two experimentally derived values, thetheoretical contrast sensation functions describe the data very well, demonstrating the linearity of contrast sensation from threshold to at least 65%. By combining contrast sensation, stimulus contrast and spatial frquency in the same plot, a three dimensional surfaa such as that shown in Fig. 7 can be produced. This concept
I050
MARK W. CANNONJR SOLID
CURVES
-
PLOT
OF
o
CDNTRAST 2 c/deg
SENSATION 0
STIMULUS
6.5
= .I37
c/dcg
CONTRAST
(CONTRAST-
V
CONTRAST
THRESHQ_D
)
12 c/deq‘l
IN
1 I
PERCENT
Fig. 6. The data points above 10% contrast are the original nine subject magnitude estimation
data. The points at 10% and below are averaged estimations from three subjects produced in a subsequent low contrast magnitude estimation experiment. The curves drawn through the points are plots of the function S = k(C - C,,) where k is the average slope of the data in Fig. 4. C,, is the contrast threshold (different for each spatial frequency) determined in Fig. 5. The estimated contrast (contrast sensation) predicted by this function fits the experimental data quite well. of a contrast sensation surface is offered as a possible new insight into suprathreshold perception. The contrast threshold function is the intersection of the surface with the contrast-spatial frequency plane. Intersections of the surface with planes parallel to the contrast-spatial frequency plane are constant contrast sensation contours of the type produced in contrast
CONTRAST
SENSATION
SURFACE
Fig. 7. Idealized contrast sensation surface derived from equation S(f) = k[C(l) - C,,(f)] where f is spatial frequency. Note that the co-ordinates are logarithmic on all axes.
matching experiments. The constant contrast sensation contours derived from the theoretical functions of Fig. 6 are plotted in Fig. 8 and clearly demonstrate two similarities to Georgeson and Sullivan’s (1975) constant contrast contours. The first of these is the obvious flattening of the contours at high contrasts, and the second is the crowding together of contours for low contrast at 12c/deg. With the linear relationship between contrast and contrast sensation established, the constacy of k with
Fig. 8. Constant contrast sensation contours derived from the theoretical functions plotted in Fig 6. These curves can be visualized as contours running horixontally across the surface of Fig. 7 when viewed from above.
Contrast sensation: a linear function of stimulus contrast
FREamcf
IN CYCLES PER DEGREE
Fig. 9. Theoretical predictions of constant contrast sensation contours (solid lines) compared to data points obtained in contrast matching experiments by Ginsburg (1977). The method of obtaining the theoretical predictions is explained in the text.
spatial frequency can be verified by comparing predicted constant contrast sensation contours with contrast matching data obtained in other laboratories. First, however, a further discussion of the simplicity of the theoretical relationship between contrast and contrast sensation is appropriate. If f denotes spatial frequency, S(f) = k[C(f) - Clk(fi]. If k is constant with spatial frequency, the values of C(/) that produce a constant contrast sensation, (S(f) = S, for ail /x are C(f) = S/k + C,,(j). This equation simply says that the contrast necessary to produce a constant sensation level S at spatial frequency f is just the threshold contrast function at that spatial frequency plus a constant. If the theory is correct, a constant S/k, determined at any spatial frequencyf, on a given constant contrast sensation contour should, when added to the threshold function C,(fx determine C(fl for every other point on that contour. The required relationship for this constant is S/k = C(fo) - C,,(f,). This relationship was applied to contrast matching data obtained by Ginsburg (1977). The predicted contours are the solid lines in Fig. 9. The individual ooints are Ginsburg’s data. Each contour was derived by simply adding a constant (the same constant for all points on a given contour) to Ginsburg’s threshold
data. The fit of the contours to the data points is quite good verifying that a linear relationship holds between sensation and the suprathreshold contrast and that k is essentially constant with spatial frequency. The theory was also applied to the scotopic data of Georgeson and Sullivan (1975). Their scotopic data points for two subjects are displayed in Figs 1Oa and b. The squares represent the threshold data while the circles and triangles represent suprathreshold matching data. The solid lines are theoretical contours based on the linearity assumption. Again, the fit between theory and data is good. Note that it is the value S(f)/k that determines the shape of the constant contrast sensation contours and as long as k does not vary significantly with spatial frequency or background luminance, the simple linear relationship is a good first order fit for suprathreshold contrast sensation predictions. While it can be inferred from Kulikowski’s (1976) contrast matching data that k is fairly constant over a wide range of luminances, some small deviations in k over spatial frequency were evident from the magnitude estimation data of individual subjects (Table 2). While the model proposed here works well for subjects with normal vision, it is to be expected that it cannot adequately predict contrast sensation for subjects with certain visual abnormalities. For example, the structure of constant contrast sensation contours of an amblyope obtained by Ginsburg (1977) indicated that the gain, k, varied considerably with both spatial frequency and stimulus contrasts for that individual. The relative constancy of k over the spatial frequency range from 1 to 12 cycles per degree has one more important implication. The transfer function for the optics of the eye (Campbell and Green, 1965) must act in a multiplicative manner on the spatial frequency spectrum of the stimulus. The data of Campbell and Green indicate a reduction in gain due to the optics by a factor of 2 between 1 and 12c/deg. This should be reflected directly in a reduction of k by the same amount if no other mechanisms were present. However, no such reduction in k is evident, either in the direct measurement from magnitude estimation or in the application of the theoretical relationship to other psychophysical matching data (Figs 9 and 10). Consequently, this constancy in k supports the hypothesis of Georgeson and Sullivan
SPATIAL fnwUEMcY IN CYCLES PER DEGREE
1051
IO SPATIAL FREGUENCY
IN CYCLESPER DEGREE
Fig. 10. Theoretical predictions of constant contrast sensation contours (solid lines) compared to data points from two subjects obtained by Georgeson and Sullivan in contrast matching experiments at scotopic light levels. Contrast sensation appears to be predictable at low light levels by the same equation that holds at photopic levels.
I052
Mfitc
W. CANNON JR
that some type of spatial frequency dependent enhancement mechanism is acting in the human visual system.
Spatial sine-wave responses Vision Rex 8, 1245-1263.
of the human
visual system.
APPENDIX
.-lcknowvledgemenrs-The research reported in this paper was conducted by personnel of the Aerospace Medical Research Laboratory. Aerospace Medical Division, Air Force Systems Command, Wright-Patterson Air Force Base. Ohio. Reprints of this article are identified by Aerosoace Medical Research Laboratory and AMRL-TR-78-56. Further reproduction is authorized to satisfy needs of the U.S. Government. The author wishes to express his gratitude to Lt Gary Sims for the construction of some of the electronic circuitry that made these experiments possible and to Capt. Arthur Ginsburg and Dr Michael Nelson for their constructive criticism of the manuscript. REFERENCES
Barlow R. B. and Verillo R. T. (1976) Brightness sensation in a ganzfeld. vision Res. 16, 1291-1297. Blakemore C., Muncey J. P. J. and Ridely R. M. (1973) Stimulus specificity in the human visual system. Vision Rex 13, 1915-1931. Bryngdahl 0. (1966) Characteristics of the visual system: Psychophysical measurements of the response to spatial sine-wave stimuli in the photopic region. J. opt. Sot. Am. 56. 811-821. Campbell F. W. and Green D. G. (1965) Optical and retinal factors affecting visual resolution. i. Physiol. 181, 576-593. Fiorentini A. and Maffei L. (1973) Contrast perception and electrophysiological correlates. J. Physiol. 231, 61.-69. Georgeson M. A. and Sullivan G. D. (1975) Contrast constancy: deblurring in human vision by spatial frequencv channels. J. Physiol. 252. 627-655. _ _ . . Ginsburg A. P. (1977) Visual information urocessinn based on spatial filters constrained by biological data: Ph.D. thesis Univ. of Cambridge. Hamerly J. R., Quick R. F. Jr and Reichert T. A. (1977) A study of grating contrast judgement. Vision Res. 16, 1419-1431. Mansfield R. J. W. (1976) Visual adaptation: retinal transduction, brightness and sensitivity. Vision Res. 16, 679-690. Stevens S. S. (1956) The direct estimation of sensory magnitudes-loudness. Am. J. Physiol. LXIX, l-25. Stevens J. C. and Stevens S. S. (1963) Brightness function: effects of adaptation. J. op. Sot. Am. 53, 375-385. Watanabe A.. Mori T., Nagata S. and Hiwatashi K. (1968)
Contrast matching experiments are conducted under the assumption that the contrast of a test grating can be adjusted until the contrast sensation produced by this grating is equal to the contrast sensation produced by a standard grating. If the threshold contrast sensitivity function can be treated as a linear multiplicative transfer function. contrast sensation is given by S(f, = ff(fiC(f, where S is contrast sensation, H is the transfer function, C is the stimulus contrast and f is spatial frequency. In contrast matching experiments, S is constant with spatial frequency and the equation becomes: S = !f(flC(fr The contrast to produce constant contrast sensatton across spatial frequency is C(f, = S/H(J) Now consider the values of C(fx at spatial frequencies /I andf,, required to produce constant contrast sensation, S. C(/,)
= S/H(I,)
Wzr) = S,H(J’,) Take
Finally obtain:
the logarithm
to obtain:
) = 1%S - 1%WI)
log C(/,)
= log S - log H(f,).
subtract
log C(f,)
of both equations
log C(/,
the lower equation
from the upper
- log C(fz) = log H(jz)
and
- log H(I,)
This equation shows that the difference between contrasts required to produce constant contrast sensation when these contrasts are plotted in logarithmic coordinates is independent of contrast sensation level S. Therefore. if H(f) was independent of contrast sensation level, the curve C(fl, produced in matching experiments, should have the same shape at all contrast sensation levels on a log contrast vs spatial frequency plot. The data cited in this paper show that this is not the case. In fact log C(f,) - log C(fa) becomes smaller at higher contrast sensation levels. Consequently, the equation C(fl = S/H(fi, where H(f) is independent of contrast sensation level does not hold. While it is possible to describe the data in terms of a function H(j; s) that does vary with contrast sensation this proposed in level, the equation paper. S(/) = /ccc(f) - C,,(fl] appears to describe the data more efficiently.
