the effects of photopig~ent depletion on brightness ... - ScienceDirect
Yisron RPS VoL 18. pp. 269 to 278. Pqamon
Preu
1978. tinted
m Great Britain
THE EFFECTS OF PHOTOPIG~ENT DEPLETION ON BRIGHTNESS AND THRESHOLD’ WILSONS. G~tstnn Depoirtmeat of Psychology. University of Texas. Austin. TX 78712, U.S.A. (Received 10 January 1977; in reuisedform 6 June 1977) Abstract-Viewing an intense light depletes the store of regenerated photopigment within the receptors, thereby reducing the proportion of quanta in a subsequent stimulus that can be absorbed by the regenerated photopigment. This effect of photopigment depletion is often thought to play an insignifL cant roie in the adaptation process. Although this appears to be true in the scotopic system, Rushton’s densitome~y measurements of the bleaching and regeneration of cone pigments are used here to show that in the photopic system photopigment depletion plays a substantial role in determining (a) darkadaptation ihresholds, (b) the brightness of steady lights, (c) increment thresholds obtained against continuous backgrounds, and (d) simultaneous brightness contrast at high test- and inducing-field intensities. The effects of photopigment depletion on brightness were examined using a modified version of Craik’s (1940) experiment.
it is a well-known fact that viewing an intense light depletes the store of regenerated photopigment within the receptors and that it takes many minutes in darkness before all the photopigment regenerates. Bleaching must, therefore, reduce the quantum-catching ability of the receptors In particular, if a pro~~on p of the photopigment is in the regenerated state, then (assuming self-screening effects are negligible) the rate of quantum absorptions is the proportion p of what it would have been if all the pigment were regenerated. This reduction in quantum-catching ability due to bleaching will be referred to here as the depletion effect. He&t (1934,1937) attempted to explain essentially all of visual adaptation on the basis of photopigment retinal-densitometry Unfortunately, depletion. measurements have shown that it plays a negligible role in rod vision (Campbell and Rushton, 1955; Weale, 1962; Rushton, 1961). On the other hand, photopigment depletion may account for some important aspects of cone vision. In particular, there is some evidence that the depletion effect can account for the changes in hue of intense lights (Brindley, 1955; Comsweet, 19623, for the fact that cone saturation is not observed with intense continuous backgrounds (Alpem, Rushton and Torii. 1970), and for some effects of light adaptation on the cone late-receptor potential in the macaque monkey (Boynton and Whitten, 1970) In this paper, the results of Rushton’s densitometry measurements (Rushton. 1963b. 1964, 1965; Rushton and Henry, 1968) are used to analyze, for the photopie system the effects of p~otopi~~t depletion on
(a) dark-adaptation thresholds, (b) the brightness of continuous lights, (c) increment thresholds obtained against continuous backgrounds, and (d) simultaneous brightness contrast at high test- and inducing-geld intensities I. DARK-AOAFTAl?ON
THRESHOLDS
To what extent can the cone thresholds obtained during dark adaptation be accounted for by the depletion effect? Consider the data in Fig 1, taken from Rushton (1964). The solid circles (scale on the left) are photopic &rk-a~p~tion ~~01~ obtained after bleaching away 99% of all cone pigment with an intense white light of 2min duration. The open circles (scale on the right) show the proportion, q. of bleached cone pigment present during the course of dark adaptation, for the same bleaching light The correspondence of the solid and open circles in Fig 1 demonstrates the well-~0~ linear relation-
‘This paper is based, in large part, upon a doctoral dissertation, “Visual Adaptation and Inhibition”, submitted to the Department of Psychology at Indiana University in August, 1975 (University Microfilms No. 76-2816, 137). I thank Dr. Sherman L. Guth and Dr. Richard M, Shiffrin for advice and criticisms while this research was being carried out 269
TIME (HIN) Fig 1. Analysis of the relationship between cone darkadaptation thresholds (solid circles) and the proportion of bl&ed cone pigment (open circles). gee text for exphmation of theoretical curvea (Data from Rushton, 1964.)
270
WILSW.
ship between log relative threshold and the proportion of pigment bleached.
,og$=zq
(1)
S. GEISLER
for the effects of photop~~ent depletion. The refationship between relative threshold in quantum absorptions and relative threshold in intensity is given by the equation
0
where, in this case, z is about 3.0. Although equation (if is used in the analysis below, it should be noted that it cannot hold in the limit as y approaches 1.0 since threshold must approach infinity-not a constant. Furthermore, there is even some debate as to whether equation (i) provides the best empirical description of the cone thresholds obtained over the ranges of photopigmenr bleaching covered in Fig. 1. Hollins and Alpem (1973) show that both equation (I) and the equation. log
A$=rq 0
log(l - 4).
provide a reasonable fit to their replication of Rushton’s experiment. [In order to obtain a good fit with equation (2). x must be made smaller than is needed with equation (I).] The predictions of the two equations differ primarily for bleaches above 80% and there is enough variability in the data to prevent rejection of either equation. Unfortunately, one of the potentially important implications of the analysis that fofiows depends upon the a~umption that equation (1) hoids for levels of bleaching in the range of so-90%. Neither equation (1) nor (2) is a relationship that one would expect to obtain if the only effect of bleaching were to reduce that q~t~~atchin~ ability of the receptors. This is illustrated by the dashed curve (lowest curve in Fig. 1). which is the photopic dark-adaptation curve that would have been obtained if only the depletion effect were operating. It was obtained by assuming that self-screening effects are negligible and, therefore, that threshold is inversely proportional to the proportion of unbleached pigment2 Clearly, simple photopigment depletion does not provide an adequate account of the data; thus there must be at least one other adaptation mechanism responsible for the observed thresholds. The dotted curve in Fig. 1 is the dark-adaptation curve that would be obtained if there were only this other adap tation mechanism(s). It was derived simply by plotting relative thresholds in terms of effective quantum absorptions rather than in terms of intensity, since this transformation corrects the observed thresholds
’ For the following reasons it is assumed throughout this paper that self-screening effects are negligible, First, the actual maximum optical densities (&,.,f of the cone pigments are not known; estimates vary from less than 0.2 up to 1.0 (Brindley, 1955; Enoch and Stiles. 1961; Rushton, 1963a; King-Smith, 1973).Second. in the experiments described here, the stimuli were composed of white light from a tungsten source. We have carried out calculations showing that the errors introduced by ignoring seff-screening effects are much less for white light than for monochromatic light of wavelength Amax. In fact, the calcuiations show that even if the maximum optical densities of the cones are as high as 1.0, the conclusions arrived at in this paper would remain essentially unchanged.
Taking the logarithms of both sides of this equation shows that the dotted curve in Fig. 1 is the difference between the solid and dashed curves. The equation that describes the dotted curve as a function of the proportion of pigment bleached can easily be derived by combining equations (I) and (3); thus, log
.s!.=rq i- log(I
420
-qi,
However, since equation (1) cannot hold at high levels of bleaching neither can equation (4). For this reason the dotted curve in Fig. 1 is not extended back before the point in time when the first threshotd (solid circfe) was obtained. To summarize Fig. 1, the dashed curve gives the threshold elevations due to the depletion effect. The dotted curve gives the threshold elevations produced by the other m~hanism. Finally, these two mechanisms combine to produce the sold curve that approximately describes the obtained thresholds. From this rather simple analysis there appear to be three important implications The f&t and third impiications are essentialfy independent of whether it is equation (1) or (2) that best describes the relationship between threshold and the proportion of pigment bleached. The second implication depends critically upon which equation is correct: 1. The depletion effect apparently does play an important role in determining cone ok-a~p~tion thresholds-it raises threshold from the dotted curve up to the solid curve. This means that the dark-adap tation function in need of explanation is not the solid curve. but the dotted curve (or the similar curve that would be obtained if equation (2) should prove to be correct). 2. The dotted function flattens out at high levels
of bleaching (i.e. within the first minute of dark-a&p tation). Thus, the threshold-elevating effect of the underlying adaptation mechanism seems to increase steadily until about 75% of the pigment is bleached, but further increases produce no additional increases in threshold This suggests that the underlying a&p tation mechanism (perhaps Barlow’s (1964) dark light) is saturating. As can be seen from Fig. 1. the v&lity of this conclusion depends totally upon the data obtained within the first JSsec after beans If equation (21, instead of equation (i), should prove to be correct for bleaches in the range of SO-90% then the derived dotted function would not flatten out. 3. It is incorrect to use photopic dark-adaptation curves like the soiid curve in Fig. 1 to calculate the equivalent backgrounds that are needed to test certain current explanations of dark adaptation. such as Barlow’s (1964) dark-light hypothesis. Rather, equivalent backgrounds should be calculated using darkadaptation curves, like the dotted curve in Fig. I. that
The effects of photopigment
depletion on brightness and threshold
271
have heen corrected for the effects of photopigment depletion. The particular case of estimating equivalent hackgrounds in order to test Barlow’s dark-light hypothesis is bri&y considered Mow.
conditions) that differ by a factor of nearly P. even though the dark-fight hypothesis is correct (On the other hand if g, and gr are both linear functions or are both squareroot functions then equations (5) and (6) are equivalent for testing the dark-light hypothesis, aithough they stiD
Let I, and f1 be photopic dark-adaptation curves obtained under two conditions, for example, test fields of two different diameters. and let g, and g2 be the incrementthreshold iunctions obtained with this same pair of testfields T&e equivalent backgrounds, It and iI, for these
would not produce the same estimates of the equivabmt backgrounds.)
two conditions would normahy be given by the following equations,
Barlow’s (1964) dark-light hypothesis is usually taken to be supported if I, = I2 for aU values of t. The above method for testing the hypothesis assumes that dark Light is the only adaptation mechanism goveming the sensitivity of the eye during dark adaptation. However. since the depletion effect plays a substantial role in cone dark adaptation, the dark-light hypothesis should be
tested with dark-adaptation curves that have been corrected for the effects of photopigment depletion (e.g. the dotted curve in Fig. 1) Therefore, the equivalent backgrounds should be calculated from the following equations, 1, = G;‘C(F/P,).f&)l 12 = 9;’ CWP,);fl(r)l
(6)
where p is the proportion of pigment bleached at time t. and P, and p2 are the proportions of pigment not bleached by II and IL. Cafculating equivakmt backgrounds with equation (5) instead of (6) should. under some circumstances, lead to apparent failures of Barlow’s hypothesis even when it is correct. For example, it is easy to show that if g, is a square-root function (square-root faw). and g2 is finear
(Weber’s law) then using equation (5) instead of (6) would result in estimated equivalent backgrounds (for the two
0)
0 RIGHT
LEFT
EYE
EYE
II. APPAREM’
BRiCHTiWSS
Subjectively, adaptation effects on brightness are even more dramatic than the threshold effects. Thus, when an intense tight is first presented to the &rkadapted eye it appears extremely bright, but it decreases greatly in brightness within a few minutes. What role does photopigment depletion play in the production of these brightness changes? In order to answer this question we need some relevant data.
A natural starting point in the study of these brightness changes is to compare the brightness of lights presented to the dark-adapted eye with their brightness after they have been viewed for a long time. This important experiment was carried out by Craik (1940). Craik used the successive, bmocularmatching procedure shown in Fig. 2a. I-ie first had subjects view a large field (45” in dia) continuously with the right eye until adaptation to it was complete; during this time the left eye was kept dark adapted. The stimulus-presentation sequence consisted of tuming off the adapting light and immediately pulsing the matching field (also 4.5” in dia) for I second. in the dark-adapted left eye. After this, the adapting field was also flashed on and off for 1 sec.and then turned back on until the next trial. Trials were spaced far enough apart to ensure that the left eye remained retatively dark adapted. The intensity of the light pulsed to the dark-adapted eye was adjusted until it
T 45’
1
j
I
I
I
i *I
u
SEC+
Fig. 2. Stimulus displays and stimulus presentation sequences for brightness matching experiments: (a) Craik (194Oh(b) the experiment described in the text.
WILSON S. GEISLER
313
had the same apparent brightness as the adapted light. (It should be noted that light adaptation produced color differences between the adapted and matching fields which, of course, increased the difficuity that subjects had in deciding when the two fields matched.) Craik’s results, for the condition just described, are shown in the lower curve (solid circles) in Fig. 3. Now, if there were no adaptation effects on brightness then an adapted light and a pulsed matching light of the same intensity would have the same brightness, and Craik’s data would fall along the diagonal line of slope 1 drawn in the figure. What Craik found was that for low to moderate intensities of the adapted light, the intensity of the matching light pulsed to the dark-adapted eye, increased linearly on this loglog plot. But, at high intensities the function breaks sharply indicating that little increase in brightness of the adapted light occurs with further increases in its intensity. The range of intensities over which brightness remains constant in Craik’s data corresponds roughly to the range of normal daylight intensities obtained out-of-doors. According to LeGrand (1957), the retinal illu~ation produced by a light colored object viewed in daylight will vary roughly from 3.5 to 5 log td-5 log td if viewed in direct sunlight. The difference between the diagonal line and Craik’s curve in Fig. 3 is a measure of the change in brightness due to adaptation. For exampfe, we see that a&pting to a light of 3.5 log td is approx~tely eq’uivalent to reducing its intensity by a factor of 100. Craik also reported similar conditions in which the pulsed, matching field was presented not to a darkadapted eye, but to a partially light-adapted eye. This was accomplished by filling the gap between successive presentations of the matching field with an adapting. background field whose intensity was fixed for all levels of the adapted field presented to the other eye. The open circles in Fig. 3 were obtained with a preadaptation field of 1.1 log td. The obvious feature of these data, and the other conditions not shown, is that they fali along a curve of approximately the same shape as that obtained with a dark-adapted eye,
rz
’
3-
i
/”
-I
0
I
2
LOG ADAPTEO
3
4
5
WfOLANDS)
Fig. 3. Intensit) of a light pulsed in a relatively darkadapted eye (solid circles) and in an eye adapted to I.1 log td (open circles) that matches the brighmess of a tight to which the other eye has become adapted, as a function of adapted-light intensity. See text for explanation of theoretical curves. (Data from Craik, 1940.)
but now the entire curve is shifted vertically. This is an important result that we will return to later. Craik’s experiment is very important. but it has never been fully replicated or extended. (Some of the data obtained by Onley and Boynton (1962) do provide a partial replication of one of Craik’s conditions in which the matching eye was preadapted to a fixed level. This experiment will be described later.] Furthermore, C&k mentioned in his paper that he had some problems in his experiment with stray light, with intensity control, and with variations in pupil size. For these reasons, we decided to replicate the base condition (the lower curve in Fig. 3). However, in order that this experiment might be more comparable to the increment-threshold experiments described in a subsequent paper (Geisler, 1977). a slightly different stimulus con~guration and procedure were used. Instead of using a successive. brightness-matching technique with large 45” fields, smaller adjacent fields were simultaneously presented for comparison. Method
The stimulus con~guratio~ shown at the top of Fig. tb was seen by the subject in Maxwellian view. It was comprised of two semicircles, one presented to the left eye and the other to the right eye, and a pattern of 5 dim red fixation lights presented to both eyes to help maintain binocular fusion. Together, the semicircles subtended a visual angle of 5’. and were composed of white light (color temp. 3ooO”Kj. Subjects were instructed to fixate the center fixation light. The image of the filament at the pupil was less than 1.7 mm in dia. The stimulus presentation sequence, which was computer-controlled. is shown in the bottom half of Fig. 2b. After dark-adapting for IOmin, the right-eye field was turned on and the subject adapted to it for 2 min. lhis was followed by presentation of a series of trials that consisted of turning off the continuous right-eye field for 0.5 see, pulsing the left- and rig&eye fields on and off together for 0.5 see, and then, 0.5 set later, turning the right-eye field back on until the next trial. The stimulus fields were turned on and off by electromagnetic shutters whose rise and decay times were less than I msec. The interval between trials was IOsec. It was hoped that this was enough time between presentations for the left eye to remain relatively dark-adapted. (Results of threshold studies (e.g. Crawford, 1947) suggest that at least for the intensities of the left-eye field reached in this study, this is approximately true.) Subjects controlled the intensity of the field pulsed to the dark-adapted left eye, and adjusted it to have the same brightness as the field simuItaneously pulsed in the right eye. The computer recorded the subject’s final setting, and then the subject began adapting to the next right-eye field intensity. In ail experimental sessions. the field in the right eye started at the lowest intensity and worked upward to the highest, (As in Craik’s experiment, slight color differences developed between the lights presented to the adapted and dark-adapted eyes.)
Figure 4 shows the results for two subjects. Each data point is the average of at least three brightness matches. Despite the differences in procedure and stimuli, these results are very similar to Craik’s (compare Figs.. 3 and 4). The slope of the linear portion of the curve is 0.70, as compared with Craik’s slope of 0.65, and both curves begin to flatten out for adapted-field intensities above 3.0 to 3.5 log td.
The effects of photopigment depletion on brightness and threshold
-I
0
I
2
3
273
5
4
LOG ADAPTED (BINDS) eye that matches the brightness of intensity. The closed and open .symbols are, respectively, the data for subjects S.J. and W.G. (the author). See text for explanation of theoretical curves Fig. 4. Intensity of a light pulsed in a relatively dark-adapted
a light to which the other eye has become adapted, as a function of adapted-light
To what extent can the large changes in apparent brightness shown in Figs 3 and 4 be accounted for by photopigment depletion? To begin with, suppose that the depletion effect is the only adaptation process in operation. If this were the case, a matching field of intensity I’, and an adapted field of intensity I, would have the same brightness if the quantum absorptions per set for each field were the same; that is, 1’
mr.4, P
where p’ and p are the proportions of pigment present in the hrvo eyes. In or&r to make predictions we need, of course, to estimate the values of p’ and p. These estimates can be obtained from the results of Rushton’s densitometry measurements In particular, Rushton and his colleagues (e.g. R&&n and Henry, 1968) have shown that the steady-state proportion of unbleached photo-
3 This equation is based upon measurements of the density of all cone pigments together. However, blue cone pig-
ment (choke) apparently is so scarce that the measurements p&nariIy rctlat the kinetics of the red (crythrolabc) and green (chlorolabc) cone pigments Rushton (1963b. 1965) has shown that these two pigments regenerate at the same rate, and furthermore, that with the white (tungsten) tight he used for bleaching, they aiso bicach at the same rate. Rushton’s measurements should apply to the bleadring and regeneration of cone pigments in all of the experiments described or presented. here, sina in atl cases the stimuli were dso comprised of white light from a tungsten source.
pigment
is given by, P
10 ==+
where lo, which is the intensity of a steady white light (from a ~n~ten soura) needed to bleach half the photopigment in cones, is about 4.3 log td.j Rushton’s results also imply that negligible amounts of pigment are bleached by the matching field at any of the intensities shown in Fig. 3; therefore, we can set P’ = 1.0. Finally, using equation (8) to replace p in equation (7) gives,
The &shed line in Fig. 4 shows the predictions of equation (9). Again, as was the case for dark-adap tation thresholds, it is seen that most of the observed changes in brightness are due to some adaptation process other than the depletion of photopigment. However, an interesting aspect of the depletion effect is its prediction that the brightness-matching function should break over sharply in the neighborhood of 3.5 to 4.5 log td. Is this, in facf the reason that the data show a similar flattening out for adapted lights above 3.5 log tds? One way to test this hypothesis is to partial out the depletion effect, as before, by plotting the data in terms of effective quantum absorp tions However, it is more instructive to assume instead that without the depletion effect the data would have continued along the straight line that describes the data at low intensities Then the depletion effect can be added back in, to see how we11 the resultant function agrees with the data.
271
WILSONS.
First. note that the data in Fig. 1 are approximately linear on a log-log plot for intensities below 3.5 log td In other words, the data are de&bed by a function of the form,
log I’ = a.log I + 6.
(10)
The “depletion effect alone” curve shows that photopigment depletion plays essentially no role at these lower intensities; therefore, equation (10) is totally the result of other adaptation processes. Suppose equation (10) also describes the effect of these other adap tation processes at higher intensities. In other words, suppose that the data would be described by equation (10) at all intensities if there were no photopigment depletion. This is shown by the dotted line in Fig. 4. which was obtained by setting a = 0.70 and 6 = -0.70 in equation (10). Now, as mentioned earlier, depleting all but proportion p of the available photopigment is equivalent to reducing a light of intensity I to p.1. Therefore, the predicted relationship between a light pulsed in the dark-adapted eye and a light to which the other eye had become completely adapted is given by. log I’ = a. log(p.1)+ 6,
(11)
where p is given by equation (8). The dotted/dashed line in Fig. 4 is a plot of this function. The same analysis was carried out for Craik’s data, and the predicted functions are shown in Fig. 3. The depletion effect does correctly predict the shape of the curve, but the asymptotic brightness of the adapted lights is “over-predicted” by about l/3 log unit. There are two possible reasons for this. One possibility is that the effect of the other adaptation process alone is not described by equation (10) at high adapted-light intensities. If the dotted function in Fig. 4 were to decelerate somewhat at high intensities, then the combined processes would more accurately account for the results. The other possibility is that the half-bleaching constant, I,. is really smaller than 4.3 log td. If it is assumed that equation (11) is correct. then I, can be estimated from the data by forcing equation (11) to predict the correct asymptotic brightness. Doing this gives an average value for I0 of about 3.8 log td which is l/2 log unit lower than Rushton and Henry’s (1968) estimate. This value may be reasonable since Rushton and Henry estimated I,, under the assumption ‘that the optical densities of the cone pigments are negligible at the wavelength of the measuring light (56Onm). When Rushton (1963b. 1965) assumed that the optical densities of the cone pigments were substantial (in the range of 0.35-0.2), he then estimated I0 to be 4.1
4 Rushton (1963b) notes that these values of f ,,, together with his finding that the time constant of regeneration (to) is between 120-14Osec. implies that the maximum (effective) photosensitivity of the cone pigments is quite high, around 7 x 10-‘6cm’/quantum for chloroiabe. Rushton. and later Alpern and Pugh (1974). argue that this value is reasonable even though it is about 2.5 times greater than that obtained for rhodopsin in uiuo. which in turn is about 2-4 times greater than the estimates obtained for cattle rhodopsin in vitro. Their explanation is based upon two factors--orientation of the pigment molecules and optical funneling by the inner segments.
GEISLER
and 3.8 log td. respectively.’ Unfortunately, the actual optical densities of the cone pigments is still a controversial issue (see footnote 1). Regardless of which explanation is correct. the analysis presented here shows that for daylight intensity levels. the depletion effect may play an important role in visual perception-it may be the primary reason that brightness remains constant for all steadystate retinal illumination levels above 1 log td. Most of the brightness changes that occur during light adaptation are the result of a mechanism other than photopigment depletion. An important property of this other adaptation mechanism is revealed by the experimental conditions in which Craik lightadapted the matching eye to a fixed level. As mentioned earlier, the effect of this manipulation is to shift vertically by some amount the curve obtained with a dark-adapted matching eye (see Fig. 3). As Craik realized, he would have obtained essentially the same results if he simply ran the dark-adapted condition (solid circles) with an appropriate neutral density filter over the subject’s left (matching) eye. In other words, it appears that the effect of pre-adapting to a fixed level is to reduce visual response to all lights as if multiplying their intensities by a factor between
0 and I. Craik’s data (and that of Onley and Boynton (1962) described below) show that this characterization of the adaptation effect is onl! approximately correct; however, it is accurate enou& to sene as a rough rule-of-thumb. In particular. it allows us to write a simple formula that approximately describes all the data. Let I represent the intensity of a white light presented to the left eye and let I’ be the intensity of a white light presented to the right eye. The two will approximately match in brightness when. I.n.11 ,’
-
-
f
-.
p’ u’
.
(12)
where p' and p are the proportions of pigment present in the left and right eyes, respectively. and u’ and u are the corresponding factors (both between 0 and 1.0) resulting from the other adaptation mechanism. Rushton and Henry’s (1968) results can be used to calculate p' and p under a wide variety of conditions. (However, as demonstrated above, the predictions of equation (12) will be best when the half-bleaching constant, lo, is approximately 3.8 log td) Unfortunately, there are no general formulae like those described by Rushton and Henry for calculating IA’and u under all conditions. However, for fixedintensity adapting fields u (or u’) can be obtained from Fig. 4. In particular, if we let J be the intensity of the preadapting field in the right (left) eye, then -log u (-log u')is the difference between the solid, diagonal line and the dotted line at 1ogJ. The results of a brightness-matching study carried out by Onley and Boynton (1962) are in general agreement with the analysis presented above. The data for their subject J.O. are shown in Fig. 5. (These data have been replotted to facilitate comparison with Figs. 3 and 4.) The vertical axis shows that intensity of one half of a 5” bipartite field, pulsed for 300 msec to the right eye, that has the same apparent brightness as the other half which was presented simultaneously to the left eye, and whose intensity is given along
The effects of photopigment
depletion on brightness and threshold
JO 3-
-I
0
~1 2 3 tOG TEST (mL)
4
Fig. 5. Luminance of the matching field. presented to an eye adapted to 1 mL. that has the same apparent brightness as the test field, as a function of test field luminance. The test field was presented to an eye light adapted to the log luminance given at the base of each curve. See text for explanation of the dashed curve. (Data from Onley and Boynton, 1962.)
the horizontal axis. The bipartite field was presented once every 6 set, and between presentations each eye viewed a 10” preadapting field The preadaptation field in the right ‘(matching eye) was always fixed at 0 log mL (i.e. about I log td). However, the preadap tation field in the other eye was not-each set of points connected by solid lines in Fig 5 was obtained with the preadaptation field whose intensity is indicated at the base of the function. Thus, each solid curve was obtained with a fixed state of adaptation in the test eye. (of course, the state of adaptation in the matching eye was also fixed) If these data agreed with Cralks finding that adap tation to a tixed level has the effect of reducing the intensity of all lights by a fIxed factor, then all the curves in the figure would be parallel. This seems to be approximately correct, although there is some tendency for the functions to come together at high test-field intensities. Also from Fig 5 a replication of one of Craik’s curves can be extracted-the one obtained with a 1 log td level of preadaptation in the matching eye. (However, since in Gnley and Boynton’s study the matching eye was always adapted to 1 log td none of their data provide a replication of Craik’s darkadapted condition that was replicated in Fig 4.) The x’s in Fig. 5 are the points that should fall along a Craik function, since they are the points for which the preadapting- and test-field luminances are the same. The Craik function formed by the x’s seems to be most similar in shape to the data in’ Fig. 4. This can be seen from the dotted line, which is the same as the sofid curve drawn through the data in Fig. 4, but shifted vertically by an appropriate amount The amount of vertical shift was calculated as follows. From Fig 4 it is seen that adapting to a light of 1 log td is equivalent to reducing its intensity by a factor of 10. Since preadapting to a fixed level has approximately the effect of reducing the intensity of all lights by the same factor, then preadapting to 1 log td in the matching eye would shift the
Y.R. 18/3--c
‘75
solid curve in Fig. 4 vertically by 1 log unit This is the dotted curve plotted in Fig. 5. The ha~bf~ch~g constant I,, can also be estimated from the x’s in the same way as before. The value obtained is about 4.0 fog td which agrees well with the other estimates. Thus, despite differences in procedure, Gnley and Boynton’s results agree fairly well with those of Craik and those we obtained_ In summary, the Craik function (e.g. Fig. 4) shows the effects of adaptation on the brightness of lights, over the whole range of intensities that the visual system normally encounters. For any intensity light along the horizontaf axis, the difference between the diagonal line of slope 1, and the Craik function gives a measure of the total change in apparent brightness that the light undergoes, from when it is first presented to the dark-adapted eye, until the eye has become completely adapted to it. The reduction in the brightness of lights for intensities up to 3.5 log td (the linear part of the Craik function) is primarily the result of adaptation processes other than the depletion effect. However, these other adaptation processes seem to behave in a simple fashion-they reduce the brightness of lights as if muitipl~ng their intensities by a factor between 0 and 1. For adaptedlight intensities above 3.5 log td, photopigment depletion becomes important and may be the primary reason the Craik function flattens out.
The abiity to discriminate lights on the basis of intensity differences is greatly dependent upon the current state of adaptation, as is apparent brightness The effects of adaptation on intensity discrimination are examined in some detail in the following paper (Geisler, 1978). In this paper, I want to briefly consider whether the depletion effect can account for some of the effects of light adaptation on increment threshold. A similar sort of analysis was presented by Alpem. Rushton and Torii (1970) for the increment threshold function they obtained. In order to analyze the role of photopigment depletion, it is conve~~t to consider the two increment-threshold functions that play the analogous role for intensity discrimination that Craik’s function does for brightness. These two increment-threshold functions (taken from Geisler, 1978) are shown in Fig. 6. The triangles are thresholds for detecting a SO-msec increment field against a 500-msec background fieid flashed in the relatively dark-adapted eye. The increment field fell in the fovea, and its onset was simultaneous with the background field The squares are thresholds for detecting the same 50-msec increment field against a continuously presented background to which the eye was allowed to adapt each time its intensity was changed (In other words, the squares are just a classical ~~~~t-~re~old function.) The difference between these two increment-threshold functions measures the effects of adaptation on intensity discrimination over the whole range of intensities that the eye normally encounters. For example, the functions show that adapting to a background of 4 log td lowers threshold by a factor of around 100. Consider the changes in threshold that would be obtained if the only adaptation mechanism
216
WUQH
t
L
-I
S. GEISLER
I
I
I
I
4
f
I
0
I
2
3
4
5
6
~00
1
BAOKGR~UND (TF~~LANDS)
Fig. 6. Increment threshold as a function of background intensity. The background field was either continuous (squares) or flashed for 500 msec in the relatively dark-adapted eye (triangles). See text for explanation of the theoretical curve. (Data from Geisler. 1978.)
were the depletion
effect. To begin with, note
that
when there is negligible photopigment ‘depletion, increment thresholds are described by the continuously accelerating function in Fig. 6, which can be represented symbolically as follows, tog AI = f(fog 1).
(13) (Actually, the continuously accelerating function is roughly parabolic in log-log coordinates) The effect of depleting all but proportion p of the available photopigment in the receptors is equivalent to reducing a light of intensity I to p-1. Therefore, after adapting to a background light (long enough for photochemical equiPbrium to be reached), the depletion effect predicts that increment thresholds should be described by, log hl = f[logO, . r)] - log p
(14)
where p is given by equation (8 The predictions of equation (14) for IO = 4.3 log td are shown by the dashed line in Fig. 6. As expected_ the depletion e%ct cannot account for the large decreases in threshold observed. Howevw, it does predict that light-adapted thresholds approach Weber’s law at high background intensities (i.e. above 4.3log td) It is easy to show that this prediction holds almost independently of the function f. thus photopigment depiction may be responsible for the Weber’s law behavior observed for cone thresholds, at background intensities above around 4.5 log td. The prediction that Weber’s law holds at high background intensities only follows for pulsed increment fields If the eye is allowed to adapt to the background plus increment field, the proportion of pigment bleached increases above that produced by the background alone. Under these conditions the increment-threshold function should begin aazelerating positively at high background intensities This can be
seen most easily by considering the Craik function. In particular, Figs 3 and 4 show that because of the depletion effect, steady lights above 3.5 log td differ very little in brightness. Therefore, intensity discrimination of intense, steady fields should be relatively poor. The analyses above lead to the conciusion that photopigment depletion improves detection of transient changes in intensity, but binders the intensity discrimination of steady fields Fortunately, under most real-life conditions photopigment depletion should work to improve caption, since eye, head, and body movements produce ~n~uous movement of the retinal image. Thus, there are transient changes in intensity associated with all the lines and edges within the visual field. Presumably, only the discriminations of steady lights separated by large visual angles, and judgments of absolute brightness are hindered by photopigmenr depletion. Weber’s law and pattern
constancy
The lower curve in Fig 6 shaws that if the eye is allowed
to adapt to background fields before thresholds are measured, then the thmholds are approximately described by Web&s
law,
tensities Web&
at all but the iowest background in-
law is also known to hold under 8 wide variety of other conditions (e.g. see Brown and Mueller, 1965). However, the square-root law provides a better description of the thresholds obtained for small, shortduration increment fields, at low to intermediate background intensities (Barlow, 1958). As we have sem, there seem to be at least two adap ration moChanisms, the depMion e&t and some other mechanism, working to ma&t&n Weber’s law over a wide range of intensities It is rmsouable, therefore, to ask if there is anything to be g&ned by having a visual system that obeys Wei&3 law as opposed to, say, the square-root law. Although 1 know of no one who has written about this question, it seems likely that many visual SCientiStS
The effects of photopigment
depletion on brightness and threshold
have considered it. since the visual systems of many animals obey Weber’s law over a substantial fraction of their sensitivity ranges The question is discussed below under the assumption that there arc othq like myself, who have
not considered the issue before. Wavelength aside, the retinal image is a two-dimensional pattern of intcnsitia Under an appropriate d&r&ion. the intensity differences (i.e. the lines and edges) that make up the pattern can be divided into two sets-those that are above threshold and those that are not According to
Webe& law, an intensity differcace is visible when the ratio of the intensities in the two regions is greater than 1 + K or less than l/(1 -I- K), where K is the Weber fraction. (Note that the Weber fraction associated with each line or edge depends upon its particular size and shape.) Now, the important point is that in the real wor& under conditions of relatively uniform illuminance (e.& sunlight). intensity differences are the result of differences in reflectance. Thus, an edge or line will be visible when the ratio of the reflectances of the two regions satisfies the above inequalities. Therdore, roughly speaking, Weber’s law implies that the set of lines and edges visible at one overall illumination level will remain visible at all illumination levels, and those invisible at one illumination lever will remain invisible at all illumination levels-in other words, the set of visible and the set of invisible intensity differences
remains constant It seems reasonable to call this property “pattern constancy”, since although the overall brightness of the visual field may change, the pattern of visible lines and edges remains constant. It is interesting to consider the implications of pattern constancy for the learning process If Weber’s law did not approximately hold, then the set of visibte luminance differences would be in constant Aux. For example, if the
square-root law held over a wide range of conditions then objects visible in mid-day sunlight might disappear long before sunset or disappear when a cloud passes over. It seems likely that learning under these conditions would be slow, would require more memory, and would require more sophisticated generalization mechanisms. If one were going to build a robot that could perform the same tasks at different illumination levels, it would seem reasonable to put a Weber’s law device in its eye. Then, the pattern of visual information sent to its brain from a given scene would change relatively little with overall illumination level. (Note that the above argument is still approximately valid if we suppose that the environment is divided up into a number of regions each of which is uniformly iliuminated.) IV.
SIMULTANEOUSBRIGHTNESSCONTRASI
Analysis of the role of the depletion effect in simultaneous brightness contrast leads, at first, to a paradoxical conclusion which is t&n resolved by considering the role of eye rno~~~ Recall that at photochemical equilibrium, a steady iight of intensity I will bleach all but proportion l,,/(l,+, + I) of the available photopigment, and therefore this steady light is equivalent, in terms of quantum absorptions per second, to a light of intensity I’ = 1. f&I + I,X presented to an eye with a full complement of unbleached photop~~L M~tipi~g the top and bottom of the right-hand side of this equation by l/1 shows that I’ asymptotically approaches I0 as I increases. It was argued earlier that this may be the reason that the brightnesses of steady lights reach an asymptotic value at high intensities For the very same reason, one might expect that the lateral effects produced by a surround should reach an asymptotic level at high surround intensities, For example, if a
2 log td surround
217
is increased by one log unit, then the quantum absorptions per second increase almost a full log unit But, if a 5 log td surround is increased by a log unit the quantum absorptions per second only increase by 0.06 log units. Therefore, the inhibitory effect produced by a 6 log td surround should not be much greater than that produced by a 5 log td surrolmd. The experiment carried out by Heinemaun (1961) is one of very few that employed stimuli intense enough to test this hypothesis Heinemann measured simultaneous brightness contrast with a binocularmatching procedure in which the stimulus presented to the right eye was comprised of a 30’ center field, and an annular, non-overlapping surround field whose outer diameter was l”36’. The left eye viewed a comparison field of the same diameter as the center field in the right eye. On each trial of the experiment, the surround and comparison fields were set to some intensity and the subject adjusted the intensity of the center field until its apparent brightness matched that of the comparison field The data obtained in this study agree quite well with those obtained earlier, in Heinemann’s more well-known study (Heinernann, 1955). There is no evidence in Heinemann’s data that the lateral effects produced by the surround reach an asymptotic level at high surround intensities Increasing the surround from 0.5 log units below to 0,5 log units above the center intensity has as much effect on center brightness when center intensities are low as when they are high. In fact, replotting Heinemann’s data in terms of relative quantum absorptions per second reveals that at high intensities, increasing the quantum absorptions per second in the surround by a few hundredths of a log unit reduces an almost equally intense Center from its uninhibited brightness to being blacker than an uni~um~at~ comparison field If this analysis is correct, it implies that lateral inhibitory effects get tremendously powerful at high intensities No current models of lateral inhibition can predict such huge effects. There is, however, good reason to believe that this analysis is not completely correct. It is likely that with the small fields that Heinemann used, d&ulty in maintaining fixation reduced $e amount of bleaching in the surround and increased the amount of bleaching in the center, or vice versa, depending on which field was more intense. This is a reasonable argument since photopigment regenerates so slowly-the time constant of regeneration is about 2 min (Rushton and Henry, 1968). Even relatively slow-drifting eye movements would produce ConsiderabIe smearing with respect to the amount of pigment bleached Suppose, for example, that due to eye movements the amount of bleached pigment in the center and surround is always the same. Then a log-unit difference between the surround and center intensity would always result in a log-unit difference in quantum absorptions per second If this is the case, then we predict that the depletion effect preserves rather than reduces brightness contrast effects, since as the brightness contrast data show (Heinemann, 1972). it is, roughly speaking, the ratio of intensities in the center and surround that determine the magnitude of the contrast e&c& Therefore, if it is assumed that due to eye movements the proportion of pigment bleached is fairly uniform
178
Wrlso~ S.
across the center and surround. then we avoid the paradoxical conclusion that lateral inhibitory effects get tremendously powerful at high intensities. REFERENCES
Alpem M. and Pugh E. N. (1974) The density and photosensitivity of human rbodopsin in the living retina. 3. Physioi.. tend. 237. 31-370. Alpem M., Rushton W. A. H. and Torii S. (1970) Signals from cones J. Physioi.. Land. 207. 463475. Barlow H. B. (1958) Temporal and spatial summation in human vision at different background intensities. J. Php siol.. Land. 141, 337-350. Barlow H. B. (1964) Dark adaptation: a new hypothesis. Vision Res. 4, 47-58. Boynton R. M. and Whitren D. N. (1970) Visual adaptation in monkey cones: recordings of late receptor potentials. Science 170. 1423-1426. Brindley G. S. (1955) A photochemical reaction in the human retina. Proc. Phys. Sot. 688. 862-870. Brown J. L. and Mueller C. G. (1965) Brightness discrimination and brightness contrast. In Vision wd I/isual Perception (Edited by Graham C. H.). Wiley. New York. Campbell F. W. and Rushton W. A. H. (1955) Measurement of the scotopic pigment in the living human eye. J. Physiol., Lond. 130. 131-347. Comsweet T. (1962) Changes in the appearance of stimuli of very high luminance. Psychol. Rev. 69, 257-273. Craik K. J. W. (1940) The effect of adaptation on subjective brightness. Prof. R. Sot. B 128, 232-247. Crawford B. H. (1947) Visual adaptation in relation to brief conditioning stimuli. Proc. R. Sot. B 134. 283-302. Enoch J. M. and Stiles W. S. (1961) The’colour change of monochromatic light with retinal angle of incidence. Optica Acta 8, 329-358.
Geisler W. S. (1978) Adaptation. afterimages, and cone saturation. i&on Rrs. This issue, pp. 279-289. Hecht S. (1934) The nature of the photoreceptor process In Handbook of GeneruI Experimenral Psycho&y (Edited by Murchison C.) pp. 704-828, Clark University Press, Worcester. Mass.
GEISLER
Hecht S. (1937) Rods, cones and the chemical basis of vision. Physiol. Rev. 17, 239-290. Heinemann E. G. (19%) Simultaneous brighmess induction as a function of inducing- and test-field luminances. J. e.~p. Psychol. 50, 89-96. Heinemann E. G. (1361) The relation of apparent brighrness to the threshold for differences in luminance. J. exp. Psychol. 61, 389-399.
Heinemann E. G. (1972) Simultaneous brightness induction. In Handbook of Sensory Physiology--Visual Psychophysics (Edited by Jameson D. and Hurvich L. M.), Vol. 7/4. Springer, Berlin. Hollins M. and Alpem M. (1973) Dark adaptation and visual pigment regeneration in human cones J. gen. PhySIX 62, 430-447. King-Smith P. E. (1973) The optical density of erythroiabe determined by retinal densitometry using the self-screening method. j. Physiol., Land. 230. 53%549. Le Grand Y. f1957) Liaht. Colour and Vision. Chaoman & Hall. London. ’ Onley J. W. and Boynton R. M. (1962) Visual responses to dually-bait stimuli of unequal luminance. J. opr. Sot. Am. 52, 934-940, Rushton W. A. H. (1961) Rhodopsin measurement and dark adaptation in a subject deficient in cone vision. J. Phvsiol.. Lond. 156. 193-205. Rushton W. A. H. (1963a) The density of chlorolabe in the fovea1 cones of the protanope. J. Physiol.. tond. 168, 360-373.
Rushton W. A. H. f1963b) Cone pigment kinetics in the protanope. J. Physiol., Land. 168, 374-388. Rushton W. A. H. (1964) Flash photolysis in human cones. Photochem
Photobiol.
3, X1-577.
Rushton W. A. H. (1965) Cone pigment kinetics in the deuteranope. J. Physiol., Land. 176, 38-45. Rushton W. A. H. and Henry G. H. (1968) Bleaching and regeneration of cone pigments in man. l&ion Res. 8. 617632. Weale R. A. (1962) Photo-chemical changes in the darkadapting human retina. Vision Res. 2. 25-33.
Preu
1978. tinted
m Great Britain
THE EFFECTS OF PHOTOPIG~ENT DEPLETION ON BRIGHTNESS AND THRESHOLD’ WILSONS. G~tstnn Depoirtmeat of Psychology. University of Texas. Austin. TX 78712, U.S.A. (Received 10 January 1977; in reuisedform 6 June 1977) Abstract-Viewing an intense light depletes the store of regenerated photopigment within the receptors, thereby reducing the proportion of quanta in a subsequent stimulus that can be absorbed by the regenerated photopigment. This effect of photopigment depletion is often thought to play an insignifL cant roie in the adaptation process. Although this appears to be true in the scotopic system, Rushton’s densitome~y measurements of the bleaching and regeneration of cone pigments are used here to show that in the photopic system photopigment depletion plays a substantial role in determining (a) darkadaptation ihresholds, (b) the brightness of steady lights, (c) increment thresholds obtained against continuous backgrounds, and (d) simultaneous brightness contrast at high test- and inducing-field intensities. The effects of photopigment depletion on brightness were examined using a modified version of Craik’s (1940) experiment.
it is a well-known fact that viewing an intense light depletes the store of regenerated photopigment within the receptors and that it takes many minutes in darkness before all the photopigment regenerates. Bleaching must, therefore, reduce the quantum-catching ability of the receptors In particular, if a pro~~on p of the photopigment is in the regenerated state, then (assuming self-screening effects are negligible) the rate of quantum absorptions is the proportion p of what it would have been if all the pigment were regenerated. This reduction in quantum-catching ability due to bleaching will be referred to here as the depletion effect. He&t (1934,1937) attempted to explain essentially all of visual adaptation on the basis of photopigment retinal-densitometry Unfortunately, depletion. measurements have shown that it plays a negligible role in rod vision (Campbell and Rushton, 1955; Weale, 1962; Rushton, 1961). On the other hand, photopigment depletion may account for some important aspects of cone vision. In particular, there is some evidence that the depletion effect can account for the changes in hue of intense lights (Brindley, 1955; Comsweet, 19623, for the fact that cone saturation is not observed with intense continuous backgrounds (Alpem, Rushton and Torii. 1970), and for some effects of light adaptation on the cone late-receptor potential in the macaque monkey (Boynton and Whitten, 1970) In this paper, the results of Rushton’s densitometry measurements (Rushton. 1963b. 1964, 1965; Rushton and Henry, 1968) are used to analyze, for the photopie system the effects of p~otopi~~t depletion on
(a) dark-adaptation thresholds, (b) the brightness of continuous lights, (c) increment thresholds obtained against continuous backgrounds, and (d) simultaneous brightness contrast at high test- and inducing-geld intensities I. DARK-AOAFTAl?ON
THRESHOLDS
To what extent can the cone thresholds obtained during dark adaptation be accounted for by the depletion effect? Consider the data in Fig 1, taken from Rushton (1964). The solid circles (scale on the left) are photopic &rk-a~p~tion ~~01~ obtained after bleaching away 99% of all cone pigment with an intense white light of 2min duration. The open circles (scale on the right) show the proportion, q. of bleached cone pigment present during the course of dark adaptation, for the same bleaching light The correspondence of the solid and open circles in Fig 1 demonstrates the well-~0~ linear relation-
‘This paper is based, in large part, upon a doctoral dissertation, “Visual Adaptation and Inhibition”, submitted to the Department of Psychology at Indiana University in August, 1975 (University Microfilms No. 76-2816, 137). I thank Dr. Sherman L. Guth and Dr. Richard M, Shiffrin for advice and criticisms while this research was being carried out 269
TIME (HIN) Fig 1. Analysis of the relationship between cone darkadaptation thresholds (solid circles) and the proportion of bl&ed cone pigment (open circles). gee text for exphmation of theoretical curvea (Data from Rushton, 1964.)
270
WILSW.
ship between log relative threshold and the proportion of pigment bleached.
,og$=zq
(1)
S. GEISLER
for the effects of photop~~ent depletion. The refationship between relative threshold in quantum absorptions and relative threshold in intensity is given by the equation
0
where, in this case, z is about 3.0. Although equation (if is used in the analysis below, it should be noted that it cannot hold in the limit as y approaches 1.0 since threshold must approach infinity-not a constant. Furthermore, there is even some debate as to whether equation (i) provides the best empirical description of the cone thresholds obtained over the ranges of photopigmenr bleaching covered in Fig. 1. Hollins and Alpem (1973) show that both equation (I) and the equation. log
A$=rq 0
log(l - 4).
provide a reasonable fit to their replication of Rushton’s experiment. [In order to obtain a good fit with equation (2). x must be made smaller than is needed with equation (I).] The predictions of the two equations differ primarily for bleaches above 80% and there is enough variability in the data to prevent rejection of either equation. Unfortunately, one of the potentially important implications of the analysis that fofiows depends upon the a~umption that equation (1) hoids for levels of bleaching in the range of so-90%. Neither equation (1) nor (2) is a relationship that one would expect to obtain if the only effect of bleaching were to reduce that q~t~~atchin~ ability of the receptors. This is illustrated by the dashed curve (lowest curve in Fig. 1). which is the photopic dark-adaptation curve that would have been obtained if only the depletion effect were operating. It was obtained by assuming that self-screening effects are negligible and, therefore, that threshold is inversely proportional to the proportion of unbleached pigment2 Clearly, simple photopigment depletion does not provide an adequate account of the data; thus there must be at least one other adaptation mechanism responsible for the observed thresholds. The dotted curve in Fig. 1 is the dark-adaptation curve that would be obtained if there were only this other adap tation mechanism(s). It was derived simply by plotting relative thresholds in terms of effective quantum absorptions rather than in terms of intensity, since this transformation corrects the observed thresholds
’ For the following reasons it is assumed throughout this paper that self-screening effects are negligible, First, the actual maximum optical densities (&,.,f of the cone pigments are not known; estimates vary from less than 0.2 up to 1.0 (Brindley, 1955; Enoch and Stiles. 1961; Rushton, 1963a; King-Smith, 1973).Second. in the experiments described here, the stimuli were composed of white light from a tungsten source. We have carried out calculations showing that the errors introduced by ignoring seff-screening effects are much less for white light than for monochromatic light of wavelength Amax. In fact, the calcuiations show that even if the maximum optical densities of the cones are as high as 1.0, the conclusions arrived at in this paper would remain essentially unchanged.
Taking the logarithms of both sides of this equation shows that the dotted curve in Fig. 1 is the difference between the solid and dashed curves. The equation that describes the dotted curve as a function of the proportion of pigment bleached can easily be derived by combining equations (I) and (3); thus, log
.s!.=rq i- log(I
420
-qi,
However, since equation (1) cannot hold at high levels of bleaching neither can equation (4). For this reason the dotted curve in Fig. 1 is not extended back before the point in time when the first threshotd (solid circfe) was obtained. To summarize Fig. 1, the dashed curve gives the threshold elevations due to the depletion effect. The dotted curve gives the threshold elevations produced by the other m~hanism. Finally, these two mechanisms combine to produce the sold curve that approximately describes the obtained thresholds. From this rather simple analysis there appear to be three important implications The f&t and third impiications are essentialfy independent of whether it is equation (1) or (2) that best describes the relationship between threshold and the proportion of pigment bleached. The second implication depends critically upon which equation is correct: 1. The depletion effect apparently does play an important role in determining cone ok-a~p~tion thresholds-it raises threshold from the dotted curve up to the solid curve. This means that the dark-adap tation function in need of explanation is not the solid curve. but the dotted curve (or the similar curve that would be obtained if equation (2) should prove to be correct). 2. The dotted function flattens out at high levels
of bleaching (i.e. within the first minute of dark-a&p tation). Thus, the threshold-elevating effect of the underlying adaptation mechanism seems to increase steadily until about 75% of the pigment is bleached, but further increases produce no additional increases in threshold This suggests that the underlying a&p tation mechanism (perhaps Barlow’s (1964) dark light) is saturating. As can be seen from Fig. 1. the v&lity of this conclusion depends totally upon the data obtained within the first JSsec after beans If equation (21, instead of equation (i), should prove to be correct for bleaches in the range of SO-90% then the derived dotted function would not flatten out. 3. It is incorrect to use photopic dark-adaptation curves like the soiid curve in Fig. 1 to calculate the equivalent backgrounds that are needed to test certain current explanations of dark adaptation. such as Barlow’s (1964) dark-light hypothesis. Rather, equivalent backgrounds should be calculated using darkadaptation curves, like the dotted curve in Fig. I. that
The effects of photopigment
depletion on brightness and threshold
271
have heen corrected for the effects of photopigment depletion. The particular case of estimating equivalent hackgrounds in order to test Barlow’s dark-light hypothesis is bri&y considered Mow.
conditions) that differ by a factor of nearly P. even though the dark-fight hypothesis is correct (On the other hand if g, and gr are both linear functions or are both squareroot functions then equations (5) and (6) are equivalent for testing the dark-light hypothesis, aithough they stiD
Let I, and f1 be photopic dark-adaptation curves obtained under two conditions, for example, test fields of two different diameters. and let g, and g2 be the incrementthreshold iunctions obtained with this same pair of testfields T&e equivalent backgrounds, It and iI, for these
would not produce the same estimates of the equivabmt backgrounds.)
two conditions would normahy be given by the following equations,
Barlow’s (1964) dark-light hypothesis is usually taken to be supported if I, = I2 for aU values of t. The above method for testing the hypothesis assumes that dark Light is the only adaptation mechanism goveming the sensitivity of the eye during dark adaptation. However. since the depletion effect plays a substantial role in cone dark adaptation, the dark-light hypothesis should be
tested with dark-adaptation curves that have been corrected for the effects of photopigment depletion (e.g. the dotted curve in Fig. 1) Therefore, the equivalent backgrounds should be calculated from the following equations, 1, = G;‘C(F/P,).f&)l 12 = 9;’ CWP,);fl(r)l
(6)
where p is the proportion of pigment bleached at time t. and P, and p2 are the proportions of pigment not bleached by II and IL. Cafculating equivakmt backgrounds with equation (5) instead of (6) should. under some circumstances, lead to apparent failures of Barlow’s hypothesis even when it is correct. For example, it is easy to show that if g, is a square-root function (square-root faw). and g2 is finear
(Weber’s law) then using equation (5) instead of (6) would result in estimated equivalent backgrounds (for the two
0)
0 RIGHT
LEFT
EYE
EYE
II. APPAREM’
BRiCHTiWSS
Subjectively, adaptation effects on brightness are even more dramatic than the threshold effects. Thus, when an intense tight is first presented to the &rkadapted eye it appears extremely bright, but it decreases greatly in brightness within a few minutes. What role does photopigment depletion play in the production of these brightness changes? In order to answer this question we need some relevant data.
A natural starting point in the study of these brightness changes is to compare the brightness of lights presented to the dark-adapted eye with their brightness after they have been viewed for a long time. This important experiment was carried out by Craik (1940). Craik used the successive, bmocularmatching procedure shown in Fig. 2a. I-ie first had subjects view a large field (45” in dia) continuously with the right eye until adaptation to it was complete; during this time the left eye was kept dark adapted. The stimulus-presentation sequence consisted of tuming off the adapting light and immediately pulsing the matching field (also 4.5” in dia) for I second. in the dark-adapted left eye. After this, the adapting field was also flashed on and off for 1 sec.and then turned back on until the next trial. Trials were spaced far enough apart to ensure that the left eye remained retatively dark adapted. The intensity of the light pulsed to the dark-adapted eye was adjusted until it
T 45’
1
j
I
I
I
i *I
u
SEC+
Fig. 2. Stimulus displays and stimulus presentation sequences for brightness matching experiments: (a) Craik (194Oh(b) the experiment described in the text.
WILSON S. GEISLER
313
had the same apparent brightness as the adapted light. (It should be noted that light adaptation produced color differences between the adapted and matching fields which, of course, increased the difficuity that subjects had in deciding when the two fields matched.) Craik’s results, for the condition just described, are shown in the lower curve (solid circles) in Fig. 3. Now, if there were no adaptation effects on brightness then an adapted light and a pulsed matching light of the same intensity would have the same brightness, and Craik’s data would fall along the diagonal line of slope 1 drawn in the figure. What Craik found was that for low to moderate intensities of the adapted light, the intensity of the matching light pulsed to the dark-adapted eye, increased linearly on this loglog plot. But, at high intensities the function breaks sharply indicating that little increase in brightness of the adapted light occurs with further increases in its intensity. The range of intensities over which brightness remains constant in Craik’s data corresponds roughly to the range of normal daylight intensities obtained out-of-doors. According to LeGrand (1957), the retinal illu~ation produced by a light colored object viewed in daylight will vary roughly from 3.5 to 5 log td-5 log td if viewed in direct sunlight. The difference between the diagonal line and Craik’s curve in Fig. 3 is a measure of the change in brightness due to adaptation. For exampfe, we see that a&pting to a light of 3.5 log td is approx~tely eq’uivalent to reducing its intensity by a factor of 100. Craik also reported similar conditions in which the pulsed, matching field was presented not to a darkadapted eye, but to a partially light-adapted eye. This was accomplished by filling the gap between successive presentations of the matching field with an adapting. background field whose intensity was fixed for all levels of the adapted field presented to the other eye. The open circles in Fig. 3 were obtained with a preadaptation field of 1.1 log td. The obvious feature of these data, and the other conditions not shown, is that they fali along a curve of approximately the same shape as that obtained with a dark-adapted eye,
rz
’
3-
i
/”
-I
0
I
2
LOG ADAPTEO
3
4
5
WfOLANDS)
Fig. 3. Intensit) of a light pulsed in a relatively darkadapted eye (solid circles) and in an eye adapted to I.1 log td (open circles) that matches the brighmess of a tight to which the other eye has become adapted, as a function of adapted-light intensity. See text for explanation of theoretical curves. (Data from Craik, 1940.)
but now the entire curve is shifted vertically. This is an important result that we will return to later. Craik’s experiment is very important. but it has never been fully replicated or extended. (Some of the data obtained by Onley and Boynton (1962) do provide a partial replication of one of Craik’s conditions in which the matching eye was preadapted to a fixed level. This experiment will be described later.] Furthermore, C&k mentioned in his paper that he had some problems in his experiment with stray light, with intensity control, and with variations in pupil size. For these reasons, we decided to replicate the base condition (the lower curve in Fig. 3). However, in order that this experiment might be more comparable to the increment-threshold experiments described in a subsequent paper (Geisler, 1977). a slightly different stimulus con~guration and procedure were used. Instead of using a successive. brightness-matching technique with large 45” fields, smaller adjacent fields were simultaneously presented for comparison. Method
The stimulus con~guratio~ shown at the top of Fig. tb was seen by the subject in Maxwellian view. It was comprised of two semicircles, one presented to the left eye and the other to the right eye, and a pattern of 5 dim red fixation lights presented to both eyes to help maintain binocular fusion. Together, the semicircles subtended a visual angle of 5’. and were composed of white light (color temp. 3ooO”Kj. Subjects were instructed to fixate the center fixation light. The image of the filament at the pupil was less than 1.7 mm in dia. The stimulus presentation sequence, which was computer-controlled. is shown in the bottom half of Fig. 2b. After dark-adapting for IOmin, the right-eye field was turned on and the subject adapted to it for 2 min. lhis was followed by presentation of a series of trials that consisted of turning off the continuous right-eye field for 0.5 see, pulsing the left- and rig&eye fields on and off together for 0.5 see, and then, 0.5 set later, turning the right-eye field back on until the next trial. The stimulus fields were turned on and off by electromagnetic shutters whose rise and decay times were less than I msec. The interval between trials was IOsec. It was hoped that this was enough time between presentations for the left eye to remain relatively dark-adapted. (Results of threshold studies (e.g. Crawford, 1947) suggest that at least for the intensities of the left-eye field reached in this study, this is approximately true.) Subjects controlled the intensity of the field pulsed to the dark-adapted left eye, and adjusted it to have the same brightness as the field simuItaneously pulsed in the right eye. The computer recorded the subject’s final setting, and then the subject began adapting to the next right-eye field intensity. In ail experimental sessions. the field in the right eye started at the lowest intensity and worked upward to the highest, (As in Craik’s experiment, slight color differences developed between the lights presented to the adapted and dark-adapted eyes.)
Figure 4 shows the results for two subjects. Each data point is the average of at least three brightness matches. Despite the differences in procedure and stimuli, these results are very similar to Craik’s (compare Figs.. 3 and 4). The slope of the linear portion of the curve is 0.70, as compared with Craik’s slope of 0.65, and both curves begin to flatten out for adapted-field intensities above 3.0 to 3.5 log td.
The effects of photopigment depletion on brightness and threshold
-I
0
I
2
3
273
5
4
LOG ADAPTED (BINDS) eye that matches the brightness of intensity. The closed and open .symbols are, respectively, the data for subjects S.J. and W.G. (the author). See text for explanation of theoretical curves Fig. 4. Intensity of a light pulsed in a relatively dark-adapted
a light to which the other eye has become adapted, as a function of adapted-light
To what extent can the large changes in apparent brightness shown in Figs 3 and 4 be accounted for by photopigment depletion? To begin with, suppose that the depletion effect is the only adaptation process in operation. If this were the case, a matching field of intensity I’, and an adapted field of intensity I, would have the same brightness if the quantum absorptions per set for each field were the same; that is, 1’
mr.4, P
where p’ and p are the proportions of pigment present in the hrvo eyes. In or&r to make predictions we need, of course, to estimate the values of p’ and p. These estimates can be obtained from the results of Rushton’s densitometry measurements In particular, Rushton and his colleagues (e.g. R&&n and Henry, 1968) have shown that the steady-state proportion of unbleached photo-
3 This equation is based upon measurements of the density of all cone pigments together. However, blue cone pig-
ment (choke) apparently is so scarce that the measurements p&nariIy rctlat the kinetics of the red (crythrolabc) and green (chlorolabc) cone pigments Rushton (1963b. 1965) has shown that these two pigments regenerate at the same rate, and furthermore, that with the white (tungsten) tight he used for bleaching, they aiso bicach at the same rate. Rushton’s measurements should apply to the bleadring and regeneration of cone pigments in all of the experiments described or presented. here, sina in atl cases the stimuli were dso comprised of white light from a tungsten source.
pigment
is given by, P
10 ==+
where lo, which is the intensity of a steady white light (from a ~n~ten soura) needed to bleach half the photopigment in cones, is about 4.3 log td.j Rushton’s results also imply that negligible amounts of pigment are bleached by the matching field at any of the intensities shown in Fig. 3; therefore, we can set P’ = 1.0. Finally, using equation (8) to replace p in equation (7) gives,
The &shed line in Fig. 4 shows the predictions of equation (9). Again, as was the case for dark-adap tation thresholds, it is seen that most of the observed changes in brightness are due to some adaptation process other than the depletion of photopigment. However, an interesting aspect of the depletion effect is its prediction that the brightness-matching function should break over sharply in the neighborhood of 3.5 to 4.5 log td. Is this, in facf the reason that the data show a similar flattening out for adapted lights above 3.5 log tds? One way to test this hypothesis is to partial out the depletion effect, as before, by plotting the data in terms of effective quantum absorp tions However, it is more instructive to assume instead that without the depletion effect the data would have continued along the straight line that describes the data at low intensities Then the depletion effect can be added back in, to see how we11 the resultant function agrees with the data.
271
WILSONS.
First. note that the data in Fig. 1 are approximately linear on a log-log plot for intensities below 3.5 log td In other words, the data are de&bed by a function of the form,
log I’ = a.log I + 6.
(10)
The “depletion effect alone” curve shows that photopigment depletion plays essentially no role at these lower intensities; therefore, equation (10) is totally the result of other adaptation processes. Suppose equation (10) also describes the effect of these other adap tation processes at higher intensities. In other words, suppose that the data would be described by equation (10) at all intensities if there were no photopigment depletion. This is shown by the dotted line in Fig. 4. which was obtained by setting a = 0.70 and 6 = -0.70 in equation (10). Now, as mentioned earlier, depleting all but proportion p of the available photopigment is equivalent to reducing a light of intensity I to p.1. Therefore, the predicted relationship between a light pulsed in the dark-adapted eye and a light to which the other eye had become completely adapted is given by. log I’ = a. log(p.1)+ 6,
(11)
where p is given by equation (8). The dotted/dashed line in Fig. 4 is a plot of this function. The same analysis was carried out for Craik’s data, and the predicted functions are shown in Fig. 3. The depletion effect does correctly predict the shape of the curve, but the asymptotic brightness of the adapted lights is “over-predicted” by about l/3 log unit. There are two possible reasons for this. One possibility is that the effect of the other adaptation process alone is not described by equation (10) at high adapted-light intensities. If the dotted function in Fig. 4 were to decelerate somewhat at high intensities, then the combined processes would more accurately account for the results. The other possibility is that the half-bleaching constant, I,. is really smaller than 4.3 log td. If it is assumed that equation (11) is correct. then I, can be estimated from the data by forcing equation (11) to predict the correct asymptotic brightness. Doing this gives an average value for I0 of about 3.8 log td which is l/2 log unit lower than Rushton and Henry’s (1968) estimate. This value may be reasonable since Rushton and Henry estimated I,, under the assumption ‘that the optical densities of the cone pigments are negligible at the wavelength of the measuring light (56Onm). When Rushton (1963b. 1965) assumed that the optical densities of the cone pigments were substantial (in the range of 0.35-0.2), he then estimated I0 to be 4.1
4 Rushton (1963b) notes that these values of f ,,, together with his finding that the time constant of regeneration (to) is between 120-14Osec. implies that the maximum (effective) photosensitivity of the cone pigments is quite high, around 7 x 10-‘6cm’/quantum for chloroiabe. Rushton. and later Alpern and Pugh (1974). argue that this value is reasonable even though it is about 2.5 times greater than that obtained for rhodopsin in uiuo. which in turn is about 2-4 times greater than the estimates obtained for cattle rhodopsin in vitro. Their explanation is based upon two factors--orientation of the pigment molecules and optical funneling by the inner segments.
GEISLER
and 3.8 log td. respectively.’ Unfortunately, the actual optical densities of the cone pigments is still a controversial issue (see footnote 1). Regardless of which explanation is correct. the analysis presented here shows that for daylight intensity levels. the depletion effect may play an important role in visual perception-it may be the primary reason that brightness remains constant for all steadystate retinal illumination levels above 1 log td. Most of the brightness changes that occur during light adaptation are the result of a mechanism other than photopigment depletion. An important property of this other adaptation mechanism is revealed by the experimental conditions in which Craik lightadapted the matching eye to a fixed level. As mentioned earlier, the effect of this manipulation is to shift vertically by some amount the curve obtained with a dark-adapted matching eye (see Fig. 3). As Craik realized, he would have obtained essentially the same results if he simply ran the dark-adapted condition (solid circles) with an appropriate neutral density filter over the subject’s left (matching) eye. In other words, it appears that the effect of pre-adapting to a fixed level is to reduce visual response to all lights as if multiplying their intensities by a factor between
0 and I. Craik’s data (and that of Onley and Boynton (1962) described below) show that this characterization of the adaptation effect is onl! approximately correct; however, it is accurate enou& to sene as a rough rule-of-thumb. In particular. it allows us to write a simple formula that approximately describes all the data. Let I represent the intensity of a white light presented to the left eye and let I’ be the intensity of a white light presented to the right eye. The two will approximately match in brightness when. I.n.11 ,’
-
-
f
-.
p’ u’
.
(12)
where p' and p are the proportions of pigment present in the left and right eyes, respectively. and u’ and u are the corresponding factors (both between 0 and 1.0) resulting from the other adaptation mechanism. Rushton and Henry’s (1968) results can be used to calculate p' and p under a wide variety of conditions. (However, as demonstrated above, the predictions of equation (12) will be best when the half-bleaching constant, lo, is approximately 3.8 log td) Unfortunately, there are no general formulae like those described by Rushton and Henry for calculating IA’and u under all conditions. However, for fixedintensity adapting fields u (or u’) can be obtained from Fig. 4. In particular, if we let J be the intensity of the preadapting field in the right (left) eye, then -log u (-log u')is the difference between the solid, diagonal line and the dotted line at 1ogJ. The results of a brightness-matching study carried out by Onley and Boynton (1962) are in general agreement with the analysis presented above. The data for their subject J.O. are shown in Fig. 5. (These data have been replotted to facilitate comparison with Figs. 3 and 4.) The vertical axis shows that intensity of one half of a 5” bipartite field, pulsed for 300 msec to the right eye, that has the same apparent brightness as the other half which was presented simultaneously to the left eye, and whose intensity is given along
The effects of photopigment
depletion on brightness and threshold
JO 3-
-I
0
~1 2 3 tOG TEST (mL)
4
Fig. 5. Luminance of the matching field. presented to an eye adapted to 1 mL. that has the same apparent brightness as the test field, as a function of test field luminance. The test field was presented to an eye light adapted to the log luminance given at the base of each curve. See text for explanation of the dashed curve. (Data from Onley and Boynton, 1962.)
the horizontal axis. The bipartite field was presented once every 6 set, and between presentations each eye viewed a 10” preadapting field The preadaptation field in the right ‘(matching eye) was always fixed at 0 log mL (i.e. about I log td). However, the preadap tation field in the other eye was not-each set of points connected by solid lines in Fig 5 was obtained with the preadaptation field whose intensity is indicated at the base of the function. Thus, each solid curve was obtained with a fixed state of adaptation in the test eye. (of course, the state of adaptation in the matching eye was also fixed) If these data agreed with Cralks finding that adap tation to a tixed level has the effect of reducing the intensity of all lights by a fIxed factor, then all the curves in the figure would be parallel. This seems to be approximately correct, although there is some tendency for the functions to come together at high test-field intensities. Also from Fig 5 a replication of one of Craik’s curves can be extracted-the one obtained with a 1 log td level of preadaptation in the matching eye. (However, since in Gnley and Boynton’s study the matching eye was always adapted to 1 log td none of their data provide a replication of Craik’s darkadapted condition that was replicated in Fig 4.) The x’s in Fig. 5 are the points that should fall along a Craik function, since they are the points for which the preadapting- and test-field luminances are the same. The Craik function formed by the x’s seems to be most similar in shape to the data in’ Fig. 4. This can be seen from the dotted line, which is the same as the sofid curve drawn through the data in Fig. 4, but shifted vertically by an appropriate amount The amount of vertical shift was calculated as follows. From Fig 4 it is seen that adapting to a light of 1 log td is equivalent to reducing its intensity by a factor of 10. Since preadapting to a fixed level has approximately the effect of reducing the intensity of all lights by the same factor, then preadapting to 1 log td in the matching eye would shift the
Y.R. 18/3--c
‘75
solid curve in Fig. 4 vertically by 1 log unit This is the dotted curve plotted in Fig. 5. The ha~bf~ch~g constant I,, can also be estimated from the x’s in the same way as before. The value obtained is about 4.0 fog td which agrees well with the other estimates. Thus, despite differences in procedure, Gnley and Boynton’s results agree fairly well with those of Craik and those we obtained_ In summary, the Craik function (e.g. Fig. 4) shows the effects of adaptation on the brightness of lights, over the whole range of intensities that the visual system normally encounters. For any intensity light along the horizontaf axis, the difference between the diagonal line of slope 1, and the Craik function gives a measure of the total change in apparent brightness that the light undergoes, from when it is first presented to the dark-adapted eye, until the eye has become completely adapted to it. The reduction in the brightness of lights for intensities up to 3.5 log td (the linear part of the Craik function) is primarily the result of adaptation processes other than the depletion effect. However, these other adaptation processes seem to behave in a simple fashion-they reduce the brightness of lights as if muitipl~ng their intensities by a factor between 0 and 1. For adaptedlight intensities above 3.5 log td, photopigment depletion becomes important and may be the primary reason the Craik function flattens out.
The abiity to discriminate lights on the basis of intensity differences is greatly dependent upon the current state of adaptation, as is apparent brightness The effects of adaptation on intensity discrimination are examined in some detail in the following paper (Geisler, 1978). In this paper, I want to briefly consider whether the depletion effect can account for some of the effects of light adaptation on increment threshold. A similar sort of analysis was presented by Alpem. Rushton and Torii (1970) for the increment threshold function they obtained. In order to analyze the role of photopigment depletion, it is conve~~t to consider the two increment-threshold functions that play the analogous role for intensity discrimination that Craik’s function does for brightness. These two increment-threshold functions (taken from Geisler, 1978) are shown in Fig. 6. The triangles are thresholds for detecting a SO-msec increment field against a 500-msec background fieid flashed in the relatively dark-adapted eye. The increment field fell in the fovea, and its onset was simultaneous with the background field The squares are thresholds for detecting the same 50-msec increment field against a continuously presented background to which the eye was allowed to adapt each time its intensity was changed (In other words, the squares are just a classical ~~~~t-~re~old function.) The difference between these two increment-threshold functions measures the effects of adaptation on intensity discrimination over the whole range of intensities that the eye normally encounters. For example, the functions show that adapting to a background of 4 log td lowers threshold by a factor of around 100. Consider the changes in threshold that would be obtained if the only adaptation mechanism
216
WUQH
t
L
-I
S. GEISLER
I
I
I
I
4
f
I
0
I
2
3
4
5
6
~00
1
BAOKGR~UND (TF~~LANDS)
Fig. 6. Increment threshold as a function of background intensity. The background field was either continuous (squares) or flashed for 500 msec in the relatively dark-adapted eye (triangles). See text for explanation of the theoretical curve. (Data from Geisler. 1978.)
were the depletion
effect. To begin with, note
that
when there is negligible photopigment ‘depletion, increment thresholds are described by the continuously accelerating function in Fig. 6, which can be represented symbolically as follows, tog AI = f(fog 1).
(13) (Actually, the continuously accelerating function is roughly parabolic in log-log coordinates) The effect of depleting all but proportion p of the available photopigment in the receptors is equivalent to reducing a light of intensity I to p-1. Therefore, after adapting to a background light (long enough for photochemical equiPbrium to be reached), the depletion effect predicts that increment thresholds should be described by, log hl = f[logO, . r)] - log p
(14)
where p is given by equation (8 The predictions of equation (14) for IO = 4.3 log td are shown by the dashed line in Fig. 6. As expected_ the depletion e%ct cannot account for the large decreases in threshold observed. Howevw, it does predict that light-adapted thresholds approach Weber’s law at high background intensities (i.e. above 4.3log td) It is easy to show that this prediction holds almost independently of the function f. thus photopigment depiction may be responsible for the Weber’s law behavior observed for cone thresholds, at background intensities above around 4.5 log td. The prediction that Weber’s law holds at high background intensities only follows for pulsed increment fields If the eye is allowed to adapt to the background plus increment field, the proportion of pigment bleached increases above that produced by the background alone. Under these conditions the increment-threshold function should begin aazelerating positively at high background intensities This can be
seen most easily by considering the Craik function. In particular, Figs 3 and 4 show that because of the depletion effect, steady lights above 3.5 log td differ very little in brightness. Therefore, intensity discrimination of intense, steady fields should be relatively poor. The analyses above lead to the conciusion that photopigment depletion improves detection of transient changes in intensity, but binders the intensity discrimination of steady fields Fortunately, under most real-life conditions photopigment depletion should work to improve caption, since eye, head, and body movements produce ~n~uous movement of the retinal image. Thus, there are transient changes in intensity associated with all the lines and edges within the visual field. Presumably, only the discriminations of steady lights separated by large visual angles, and judgments of absolute brightness are hindered by photopigmenr depletion. Weber’s law and pattern
constancy
The lower curve in Fig 6 shaws that if the eye is allowed
to adapt to background fields before thresholds are measured, then the thmholds are approximately described by Web&s
law,
tensities Web&
at all but the iowest background in-
law is also known to hold under 8 wide variety of other conditions (e.g. see Brown and Mueller, 1965). However, the square-root law provides a better description of the thresholds obtained for small, shortduration increment fields, at low to intermediate background intensities (Barlow, 1958). As we have sem, there seem to be at least two adap ration moChanisms, the depMion e&t and some other mechanism, working to ma&t&n Weber’s law over a wide range of intensities It is rmsouable, therefore, to ask if there is anything to be g&ned by having a visual system that obeys Wei&3 law as opposed to, say, the square-root law. Although 1 know of no one who has written about this question, it seems likely that many visual SCientiStS
The effects of photopigment
depletion on brightness and threshold
have considered it. since the visual systems of many animals obey Weber’s law over a substantial fraction of their sensitivity ranges The question is discussed below under the assumption that there arc othq like myself, who have
not considered the issue before. Wavelength aside, the retinal image is a two-dimensional pattern of intcnsitia Under an appropriate d&r&ion. the intensity differences (i.e. the lines and edges) that make up the pattern can be divided into two sets-those that are above threshold and those that are not According to
Webe& law, an intensity differcace is visible when the ratio of the intensities in the two regions is greater than 1 + K or less than l/(1 -I- K), where K is the Weber fraction. (Note that the Weber fraction associated with each line or edge depends upon its particular size and shape.) Now, the important point is that in the real wor& under conditions of relatively uniform illuminance (e.& sunlight). intensity differences are the result of differences in reflectance. Thus, an edge or line will be visible when the ratio of the reflectances of the two regions satisfies the above inequalities. Therdore, roughly speaking, Weber’s law implies that the set of lines and edges visible at one overall illumination level will remain visible at all illumination levels, and those invisible at one illumination lever will remain invisible at all illumination levels-in other words, the set of visible and the set of invisible intensity differences
remains constant It seems reasonable to call this property “pattern constancy”, since although the overall brightness of the visual field may change, the pattern of visible lines and edges remains constant. It is interesting to consider the implications of pattern constancy for the learning process If Weber’s law did not approximately hold, then the set of visibte luminance differences would be in constant Aux. For example, if the
square-root law held over a wide range of conditions then objects visible in mid-day sunlight might disappear long before sunset or disappear when a cloud passes over. It seems likely that learning under these conditions would be slow, would require more memory, and would require more sophisticated generalization mechanisms. If one were going to build a robot that could perform the same tasks at different illumination levels, it would seem reasonable to put a Weber’s law device in its eye. Then, the pattern of visual information sent to its brain from a given scene would change relatively little with overall illumination level. (Note that the above argument is still approximately valid if we suppose that the environment is divided up into a number of regions each of which is uniformly iliuminated.) IV.
SIMULTANEOUSBRIGHTNESSCONTRASI
Analysis of the role of the depletion effect in simultaneous brightness contrast leads, at first, to a paradoxical conclusion which is t&n resolved by considering the role of eye rno~~~ Recall that at photochemical equilibrium, a steady iight of intensity I will bleach all but proportion l,,/(l,+, + I) of the available photopigment, and therefore this steady light is equivalent, in terms of quantum absorptions per second, to a light of intensity I’ = 1. f&I + I,X presented to an eye with a full complement of unbleached photop~~L M~tipi~g the top and bottom of the right-hand side of this equation by l/1 shows that I’ asymptotically approaches I0 as I increases. It was argued earlier that this may be the reason that the brightnesses of steady lights reach an asymptotic value at high intensities For the very same reason, one might expect that the lateral effects produced by a surround should reach an asymptotic level at high surround intensities, For example, if a
2 log td surround
217
is increased by one log unit, then the quantum absorptions per second increase almost a full log unit But, if a 5 log td surround is increased by a log unit the quantum absorptions per second only increase by 0.06 log units. Therefore, the inhibitory effect produced by a 6 log td surround should not be much greater than that produced by a 5 log td surrolmd. The experiment carried out by Heinemaun (1961) is one of very few that employed stimuli intense enough to test this hypothesis Heinemann measured simultaneous brightness contrast with a binocularmatching procedure in which the stimulus presented to the right eye was comprised of a 30’ center field, and an annular, non-overlapping surround field whose outer diameter was l”36’. The left eye viewed a comparison field of the same diameter as the center field in the right eye. On each trial of the experiment, the surround and comparison fields were set to some intensity and the subject adjusted the intensity of the center field until its apparent brightness matched that of the comparison field The data obtained in this study agree quite well with those obtained earlier, in Heinemann’s more well-known study (Heinernann, 1955). There is no evidence in Heinemann’s data that the lateral effects produced by the surround reach an asymptotic level at high surround intensities Increasing the surround from 0.5 log units below to 0,5 log units above the center intensity has as much effect on center brightness when center intensities are low as when they are high. In fact, replotting Heinemann’s data in terms of relative quantum absorptions per second reveals that at high intensities, increasing the quantum absorptions per second in the surround by a few hundredths of a log unit reduces an almost equally intense Center from its uninhibited brightness to being blacker than an uni~um~at~ comparison field If this analysis is correct, it implies that lateral inhibitory effects get tremendously powerful at high intensities No current models of lateral inhibition can predict such huge effects. There is, however, good reason to believe that this analysis is not completely correct. It is likely that with the small fields that Heinemann used, d&ulty in maintaining fixation reduced $e amount of bleaching in the surround and increased the amount of bleaching in the center, or vice versa, depending on which field was more intense. This is a reasonable argument since photopigment regenerates so slowly-the time constant of regeneration is about 2 min (Rushton and Henry, 1968). Even relatively slow-drifting eye movements would produce ConsiderabIe smearing with respect to the amount of pigment bleached Suppose, for example, that due to eye movements the amount of bleached pigment in the center and surround is always the same. Then a log-unit difference between the surround and center intensity would always result in a log-unit difference in quantum absorptions per second If this is the case, then we predict that the depletion effect preserves rather than reduces brightness contrast effects, since as the brightness contrast data show (Heinemann, 1972). it is, roughly speaking, the ratio of intensities in the center and surround that determine the magnitude of the contrast e&c& Therefore, if it is assumed that due to eye movements the proportion of pigment bleached is fairly uniform
178
Wrlso~ S.
across the center and surround. then we avoid the paradoxical conclusion that lateral inhibitory effects get tremendously powerful at high intensities. REFERENCES
Alpem M. and Pugh E. N. (1974) The density and photosensitivity of human rbodopsin in the living retina. 3. Physioi.. tend. 237. 31-370. Alpem M., Rushton W. A. H. and Torii S. (1970) Signals from cones J. Physioi.. Land. 207. 463475. Barlow H. B. (1958) Temporal and spatial summation in human vision at different background intensities. J. Php siol.. Land. 141, 337-350. Barlow H. B. (1964) Dark adaptation: a new hypothesis. Vision Res. 4, 47-58. Boynton R. M. and Whitren D. N. (1970) Visual adaptation in monkey cones: recordings of late receptor potentials. Science 170. 1423-1426. Brindley G. S. (1955) A photochemical reaction in the human retina. Proc. Phys. Sot. 688. 862-870. Brown J. L. and Mueller C. G. (1965) Brightness discrimination and brightness contrast. In Vision wd I/isual Perception (Edited by Graham C. H.). Wiley. New York. Campbell F. W. and Rushton W. A. H. (1955) Measurement of the scotopic pigment in the living human eye. J. Physiol., Lond. 130. 131-347. Comsweet T. (1962) Changes in the appearance of stimuli of very high luminance. Psychol. Rev. 69, 257-273. Craik K. J. W. (1940) The effect of adaptation on subjective brightness. Prof. R. Sot. B 128, 232-247. Crawford B. H. (1947) Visual adaptation in relation to brief conditioning stimuli. Proc. R. Sot. B 134. 283-302. Enoch J. M. and Stiles W. S. (1961) The’colour change of monochromatic light with retinal angle of incidence. Optica Acta 8, 329-358.
Geisler W. S. (1978) Adaptation. afterimages, and cone saturation. i&on Rrs. This issue, pp. 279-289. Hecht S. (1934) The nature of the photoreceptor process In Handbook of GeneruI Experimenral Psycho&y (Edited by Murchison C.) pp. 704-828, Clark University Press, Worcester. Mass.
GEISLER
Hecht S. (1937) Rods, cones and the chemical basis of vision. Physiol. Rev. 17, 239-290. Heinemann E. G. (19%) Simultaneous brighmess induction as a function of inducing- and test-field luminances. J. e.~p. Psychol. 50, 89-96. Heinemann E. G. (1361) The relation of apparent brighrness to the threshold for differences in luminance. J. exp. Psychol. 61, 389-399.
Heinemann E. G. (1972) Simultaneous brightness induction. In Handbook of Sensory Physiology--Visual Psychophysics (Edited by Jameson D. and Hurvich L. M.), Vol. 7/4. Springer, Berlin. Hollins M. and Alpem M. (1973) Dark adaptation and visual pigment regeneration in human cones J. gen. PhySIX 62, 430-447. King-Smith P. E. (1973) The optical density of erythroiabe determined by retinal densitometry using the self-screening method. j. Physiol., Land. 230. 53%549. Le Grand Y. f1957) Liaht. Colour and Vision. Chaoman & Hall. London. ’ Onley J. W. and Boynton R. M. (1962) Visual responses to dually-bait stimuli of unequal luminance. J. opr. Sot. Am. 52, 934-940, Rushton W. A. H. (1961) Rhodopsin measurement and dark adaptation in a subject deficient in cone vision. J. Phvsiol.. Lond. 156. 193-205. Rushton W. A. H. (1963a) The density of chlorolabe in the fovea1 cones of the protanope. J. Physiol.. tond. 168, 360-373.
Rushton W. A. H. f1963b) Cone pigment kinetics in the protanope. J. Physiol., Land. 168, 374-388. Rushton W. A. H. (1964) Flash photolysis in human cones. Photochem
Photobiol.
3, X1-577.
Rushton W. A. H. (1965) Cone pigment kinetics in the deuteranope. J. Physiol., Land. 176, 38-45. Rushton W. A. H. and Henry G. H. (1968) Bleaching and regeneration of cone pigments in man. l&ion Res. 8. 617632. Weale R. A. (1962) Photo-chemical changes in the darkadapting human retina. Vision Res. 2. 25-33.
