0042~6989/92 $5.00 + 0.00

Vision Res. Vol. 32, No. 8, pp. 1461-1470, 1992 Printed in Great Britain. All rights reserved

Copyright Q 1992Pergamon Press Ltd

Fourier Analysis of the Stimuli for PatternInduced Flicker Colors MARK F. TRITSCH* Received 20 August 1991; in revised form 3 February

1992

Pattern-induced flicker colors (PIFCs) were observed and color matched in rotating discs from which higher-harmonic Fourier components in the square-wave temporal luminance functions of a conventional black-and-white Benham disc had been removed. Since both reddish-brown and blue PIFCs were visible with purely sinusoidal stimuli they cannot result from differences in temporal stimulus shape or pattern and do not provide evidence for a temporal coding theory of color. Green PIFCs differed in that they did require the presence of ad~tional harmonics. In a second experiment the luminance means upon which the sinusoidal PIFC stimuli were imposed were varied. The results show that color is determined by the phase of the time-varying contrast between the two parts of the stimulus pattern. This points to a site proximal to the outer plexiform layer for the phase-sensitive interaction causing PIFCs. Pattern-induced flicker colors Fourier components Color matching Lateral interaction Contrast stimulus

INTRODUCTION Pattern-induced flicker colors (PIFCs) can best be demonstrated with Benham’s top, which is shown in a simplified form in Fig. l(a). When this disc rotates at 7 Hz, three colored rings are seen in place of the black arcs which intrude in to the white half of the disc. The ring nearest the center appears blue, the middle one green and the outer one reddish-brown when the disc rotates clockwise. Discs producing PIFCs are usually described in terms of the pulses of light and dark produced by the arcs and by the areas of the disc on each side of them when the disc rotates. In Fig. l(a) the temporal modulation functions corresponding to these pulses are shown on the right for the disc illustrated, with the convention that Pl (Program 1) refers to the function generated by the parts of the disc on each side of the arcs, and P2 (a, b, c) to that generated by the arcs themselves. It has been shown (v. Campenhausen, 1968a, b, 1970) that PIFCs are caused by a phase-sensitive mechanism of lateral interaction between the excitations generated by Pl and P2 in the retina. The color effects can be explained in principle by assuming different temporal and/or spatial, characteristics for such interactions in different spectrally selective pathways in the retina. The nature of the interaction itself has not been investigated, but Both and v. Campenhausen (1978) were able to fit data on detection of small PIFC stimulus phase shifts *Institut fiir Zoologie, Johannes Gutenberg UniversitHt, Postfach 3900, SaarstraDe 21, D-6500 Mainz, Fed. Rep. Germany. “R

ws--D

b

FIGURE 1. (a) Simplified Benham’s top; on the right, temporal modulation functions for Pl (between the arcs), P2a (inner ring), P2b (middle ring) and P2c (outer ring). (b) Disc with sinusoidal temporal m~ulation functions, derived as described in the text; on the right, Pl together with P2 for the inner and outer rings (respectively upper and lower diagrams). Scaling differs for (a) and (b).

1462

MARK

I.

with a model based on a multiplicative interaction. An alternative explanation for PIFCs favored by Fry (1945). Festinger, Allyn and White (1971) and Young (1977) is that the temporal shape or pattern of excitation produced in the retina by the stimulus in some way mimics a “Morse code” which, according to the “alternation of response theory” (Nelson & Bartley, 1964), signals color to the brain. Both Festinger et al. (1971) and Jarvis (1977) investigated the PIFCs resulting from a variety of different temporal stimulus shapes. indeed, PIFCs have been cited as the principal evidence for a temporal code for color (Troland, 1921; Kozak, Reitboek & Meno, 1989). In the model given by Both and v. Campenhausen (1978), only the fundamental sinusoidal Fourier components of the square-wave stimuli that were employed play a significant role in the phase-sensitive interaction determining color. This suggests that PIFCs may change without any accompanying change in the shape or pattern of temporal modulation in PI and P2, and that PIFCs may occur when Pl and P2 are of identical shape. SQUARE-WAVE I . .

I

. . . . . .:

/ )

I..............

2n

It should be noted that in sinusoidal stimuli not only Pl and P2 themselves but also any linear combination 01‘ them in any phase relation would be sinusoidai in shape. Now by applying Fourier analysis, the temporal modulation in square-wave PIFC stimuli can be described in terms of the amplitudes and phases of the (sinusoidal) Fourier components (Fig. 2). If harmonic-depleted PIFC stimuli could be derived from square-wave stimuli by elimination of all higher harmonics as in Fig i(b). thus reducing them to their fundamental component. no differences in shape or pattern of modulation would remain; there would only be differences in phase and amplitude of the remaining first harmonic sine waves. In the first experiment reported in this paper, rotating discs are compared in which the upper harmonics of square-wave Pl and P2 stimuli for PIFCs have one after another been removed until only the fundamentals remain. Quantitative results for such comparisons are obtained by using a color-mixing apparatus to match the color sensations produced by each kind of disc. When all the higher harmonics are removed from the Pl and P2 stimuli in Fig. l(a), the mean stimulus luminances (i.e. the d.c. Fourier components) remain in addition to the fundamentals, and that for PI is greater than that for P2. In the second experiment, the effect of changing these relative stimulus means of PI and P2 is examined. If only the pattern of modulation is responsible for causing PIFCs, then obviously this change should have no effect.

Phase

EXPERIMENT 1

INPUT.

Pl . . .

i

in*

t

P?L

l-l I

-

0

2n 7

I I

0

n

FFT Pl k

Amplitude

0

10001 06L 0 21 0 13 009

1 3 5 7

PIFCALL

l

t

FFT P2 Phase 0’ 0” 0’ 0”

STIMULUS

k 0 1 2 L 5

Amplitude I-0331 05s 028 OlL 011

330 30’ 330’ 30

OUTPUT:

FOURIER COMPONENTS PRESENT:

At

0

1~RITSCH

2n

COMPONENTS AEWE EXCLUDED:

THE 3RD HARMONIC

FIGURE 2. Fourier analysis (FFT) of square-wave input for PI and P2 (above) and reconstitution as PIFC stimulus (below). Amplitude and pha.seas described in the text. In the reconstituted PIFC stimuli, PI (dotted lines) and P2 (solid lines) are shown together for each ring.

Method

Discs with both square-wave and smoothly varying temporal modulation functions were printed on a computer-run dot-matrix printer using a special random-dot method, a detailed description of which is given in the Appendix to this paper. This permitted discs to be produced containing many desired combination of fundamental and higher harmonics for Pl and P2. In particular, series of discs could be made in which the first of the series had a conventional square-wave PI and P2 stimulus, while all the others were depleted versions of it. For these, various of the higher harmonics found in the Fourier transform of the stimulus were removed, and each disc contained only the components left over. with the modulation amplitudes and phases given by the transform of the original square-wave stimulus. In the following, the square-wave stimuli for Pl and P2 will sometimes be referred to as the “input functions” for the computer software which generated all the discs of a given series. The software for printing the discs had facilities for input of square-wave modulation functions with given pulse lengths [e.g. Pl, P2a, etc. in Fig. l(a)]. Fourier component selection. All discs printed had two P2 arcs, both of which generated the same temporal modulation function when the disc was rotated. However, because they differed in their phase relation to PI, the two arcs produced two differently colored rings. The

FOURIER

ANALYSIS

Surround

Colour mixing

.

square

20.15cm (8.l’x 6.1’)

5 mm (0.2’1 %I 353 cdlm2 or 41 cdlm2 LSO cd/m2

I

PIFC discs @18cm (7.3’) stripe width Smm 10.2’) max. luminance 376 cd/m2 min. luminance 5L cd/m2

FIGURE

3. Experimental

arrangement

for color-matching

of PIFCs.

graphs in the top part of Fig. 2 are of the square-wave input functions used for Pl and P2 in the discs that are shown in Fig. 3. The ordinate is the reflectance of the disc, the abscissa is the phase of temporal modulation for one complete rotation of the disc. Under the conditions of illumination available, the resulting maximum and minimum luminance were respectively 54 and 376 cd/m’, giving a maximum contrast of 0.75. Elements of the Fourier transforms of the input functions are shown below the graphs of the latter in Fig. 2. The mean (in brackets) and the amplitude and phase lag of the first four harmonic components with non-zero amplitude are listed. The calculation assumed that the input functions could only take the values + 1 or - 1, so the means given for Pl and P2 are respectively 0 and -0.33. Altogether the first 512 harmonics were calculated automatically by the program. k is the relative frequency of the harmonic (with 0 for the mean) so that for Pl every even harmonic and for P2 every third harmonic is missing (as is to be expected for trains of pulses of length 71/2 and n/3 respectively). The discs were printed using as PIFC-stimulus output functions, expressions of the form

.f(t) = All + i A,sin(kl

- 27c&)

k=I

wheref(t) is the temporal modulation function, k = 1,2, . ..) N and A, is the amplitude and $Q the phase of the kth harmonic. By setting an appropriate value for N, any desired number of higher harmonics could be eliminated from the stimulus to be produced. For example, when N = 512 was chosen, the original squarewave function appeared as output. When N was only 1, 2 or 3, then discs with the mean (A,,) and respectively

OF STIMULI

FOR

PIFCs

1463

the fundamental (N = l), the first two (N = 2) or the first three harmonics (N = 3) were printed. The lower half of Fig. 2 shows the stimulus output. Pl and P2 are shown together in their actual phase relation on the left for the inner ring and on the right for the outer ring, which appear respectively blue and reddishbrown in clockwise rotation. The top two diagrams show the square-wave functions resulting when all Fourier components are included (i.e. N = 512), as in the lefthand disc in Fig. 3. The bottom two diagrams show the case corresponding to the middle disc in Fig. 3, where N = 3, so that PI consists of the first and third harmonic and P2 of the first and second. The right-hand disc in Fig. 3 contains only the fundamental and is the same as the one in Fig. l(b). The stimulus means around which Pl and P2 are modulated in time remain unaffected by these operations. Materials. All observations were carried out in a brightly lit chamber using an apparatus in which up to three discs could be driven synchronously by the same motor. All surfaces in the chamber were white, and the ceiling fluorescent lights used for illumination (Osram L-25 Universalweiss with a correlated color temperature of ca 3775 K) were driven by d.c. current. The viewing field as seen by the observer is shown in Fig. 3. The discs were seen from a distance of 1.4 m against a 450 cd/m2 background. A comparison color mixing square was located about 40 cm above the discs. The length of a side of the square was the same as the width of stripes on the discs, and it was placed in a 353 cd/m2 white surround. The color mixing square consisted of a square opening into an enclosed cavity in which the exit surface of a light guide from the color mixer could be viewed. The cavity ensured that ambient illumination did not interfere with the comparison color viewed. The computer-driven color mixer, developed by Schramme (1989), used three tungsten-halogen lamps as light sources for colored glass combination filters (Schott SFK 6, 10 and 15) with transmission peaks at 420,523 and 655 nm. The intensity of the light emitted by each of the sources could be independently controlled by the observer using three motor-driven neutral density wedges. The design of the light guide allowed the light transmitted by the three filters to be combined into one homogenous exit surface. The settings used by the observer for the neutral wedges were registered by a microcomputer (Apple II) and automatically transformed into the CIE 193 1 X, Y, Z calorimetric system using the known spectral characteristics of the components of the optical system. Procedure. Three square-wave PIFC stimuli, producing the colors reddish-brown, blue and green, were chosen for the experiment: those for reddish-brown and blue are shown in Fig. 2; that for green consisted of the same Pl as in Fig. 2 but had the double-pulse P2 shown in Fig. 4. All discs were driven at a rotation frequency of 7 Hz. In initial observations, the three synchronized motors had been used to compare each of the squarewave discs with a large number of discs in which the harmonic content of the PIFC stimulus had been varied. On the basis of these purely qualitative observations,

1464

1. T‘RITSCH

MARK

FFT

0+t

FIGURE

the mean were included. For the green. double-pulse stimulus an additional case was examined. in which the first two harmonics of P2 were present but only the fundamental of PI. The PI and P2 stimulus functions used are shown in the box insets in Fig. 5. The color matching itself was carried out with the disc to be matched mounted on the middle one of the three motors. Altogether ten different PIFC stimuli were matched calorimetrically by two observers. Each setting was made three times and interleaved between different stimuli. The reddish-brown and the blue stimuli were on the same discs [as in Fig. l(b)] and were matched in the same session, but the green ones were on separate discs and were matched at another time. At the beginning of each session the observers were given 15 min to adapt

P2

k

Amplttude

0 1

I-025) OL22

Phase

13’

2

3

0 2251

225”

0 3396

328’

1

01591

0’

4. Fourier analysis (FFT) of double-pulse

square-wave

P2

input (solid line) for green PIFCs.

two levels of harmonic depletion were chosen, in addition to the square-wave stimuli, for the discs that were to be compared by color matching the PTFCs. For discs with the first level of depletion, only the harmonics for which k d 3 were included in addition to the mean. In the second kind of disc, only the fundamental and

50'

ULL 1

100

3

s

GREEN

IL, 1

3

1M)

s

RED

50 OBSERVER

H T I._LtL

a22

026

03

ox

036

012

046

1

3

’

’ GRtEN

s

Y

OL2.

100 1

026.

so 022

OBSERVER. M T 022

026

03

038

0%

OL2

OL6

illl 1

3

s

x

FIGURE 5. Colour match= produced by two observers for P1FC.s with square-wave and harmonic-depleted stimuli. plotted in CIE x, y chromaticity coordinates. Harmonic-depleted stimuli (shown in boxes) were derived from reddish-brown (a), blue (A) and green (0) square-wave stimuli. Box insets show Pl (dotted lines) and P2 (solid lines) for the color matches. W is the white point. Bar diagrams on the right show the relative vector lengths in CIE tristimulus space for square-wave stimuli (S) and for stimuli reduced to the first (1) the first two (2) or the first three (3) harmonics.

FOURIER ANALYSIS OF STIMULI FOR PIFCs

themselves to the lighting conditions; between each matching the controls of the color mixer were returned to zero. Results

Casual observation of the discs producing reddishbrown or blue PIFCs revealed that when the harmonic content of the square-wave stimuli was reduced to the fundamental, the colors observed differed only slightly from those seen with the original square-wave stimuli. The colors in sinusoidal stimuli appeared slightly lighter and less saturated. The color matches produced by two observers are shown plotted as averages in CIE chromati~ity coordinates in Fig. 5 and confirm the above observation. Standard errors were generally < 0.01 units on the x and y axes. For both reddish-brown (solid squares) and blue (solid triangles) PIFCs, the color patches produced when the stimuli are reduced to the first or the first three harmonics lie close in the ~hromaticity diagram to those that result with the square-wave stimuli. Associated with each data point in the diagram is a box with a graph showing the corresponding Pl (dotted line) and P2 (continuous line) stimulus functions. Although the color matches for the square-wave stimuli always lie furthest away from the white locus (W), confirming the casual impression that these PIFCs are slightly more saturated, the difference between them and the harmonic-depleted stimuli is small. For both reddish-brown and blue, the coordinates of all three color matches appear to lie close to a line from the white locus, indicating that only a change in saturation and not a hue shift occurs. The PIFCs matched also varied considerably in lightness. Although this information is not contained in the CIE chromaticity chart, the tristimulus values from which this chart is derived and which represent the settings made by the subjects do preserve it and can be represented in 3-D space. The bar diagrams on the right of Fig. 5 show the relative length (normed to 100) of each vector representing a PIFC match in tristimulus space, as a measure of the apparent darkness or lightness of the PIFC. Once again, the results of color matching confirm the casual observation that stimuli reduced to their fundamental have a lighter appearance. Thus harmonic depletion of the stimuli for reddishbrown and blue PIFCs had practically no effect. In complete contrast to this was the effect for green PIFCs. When such double-pulse, square-wave stimuli (see Fig. 4) were reduced to their fundamental, the green color disappeared entirely! Figure 5 also shows (solid circles) the chromaticity coordinates of the matches produced for these stimuli and the harmonic-depleted stimuli derived from them. For both observers, the stimulus including the first three harmonics was matched at a locus close to that of the square-wave stimulus, and the chromaticity coordinates for both sets of matches lay in a region of the chart normally corresponding to the color green. When the stimuli were reduced to their fundamental, however, the matches collapsed onto the line connecting the matches for the reddish-brow and

1465

the blue PIFCs. In the case of the observer NT., the color match produced when the fundamental alone was present in the stimulus lay close to the white locus. For observer M.T. this match lay half-way along the line connecting the white locus with the matches made for the reddish-brown stimuli. Indeed the stimulus was described by observer H.T. as colorless but by M.T. as faint pink; the 13” phase shift of the P2 fundamental relative to Pl (Fig. 4) was smaller than that for reddish-brown PIFCs but of the same sign (Fig. 2). An additional case was examined for the green PIFC (see Procedure), in which the first and second harmonic of the original double-pulse P2 stimulus was combined with the fundamental of Pl. This suthces to produce a very unsaturated green PIFC. Figure 5 shows for one observer (M.T.) the coordinates of the match produced for this stimulus (Pl and P2 are shown in the associated box inset). The match lies between that for the squarewave stimulus and that for the stimulus which has only the Pl and P2 fundamentals. The bar diagrams with the relative vector lengths in tristimulus space for the green PIFC stimuli show that in both observers, associated with the loss of green color when the stimulus was reduced to its fundamental, there was a very considerable increase in lightness; indeed, the matches for the sinusoidal stimulus are the lightest reported in the whole experiment. In conclusion, it can be said that reduction of the double-pulse P2 stimulus to the fundamental clearly eliminates the stimulus parameter responsible for the presence of the green color. Discussion

Using only sinusoidal stimulus functions it is possible to produce reddish-brown and blue PIFCs which are the same as those produced by the more usual square-wave stimuli of Benham’s top, apart from minor differences of saturation and lightness. For two reasons, it is not possible to dismiss this as a trivial demonstration of the low-pass filter properties of the eye. Firstly, the second and third harmonics of the stimulus evidently are transmitted by the neural elements of the eye, since they must be included in the stimulus in order to produce green PIFCs. Secondly, there is ample evidence from other mammalian species that neither the cones (Baron & Boynton, 1975), nor the horizontal cells (van de Grind & Griisser, 1981; Lankheet, van Wezel & van de Grind, 1991), nor the ganglion cells (Lee, Martin & Valberg, 1989a) severely attenuate luminance modulation below 20 Hz. The results of the experiments show that the difference between reddish-brown and blue PIFCs cannot be explained as resulting from a change in the temporal pattern or shape of modulation in the PIFC stimulus (Festinger et al., 1971). When the stimulus is reduced to its fundamental, both Pi and P2 are modulated sinusoidally and differ only in phase and mean. All additive and subtractive combinations of PI and P2 remain sinusoidal as well. This is also the case for the flow of excitation produced when PI and P2 pass through different, linear filters in the retina and then

1466

MARK l- TRITSCH

interact subtractively (Young, 1977). Since PIFCs cannot be explained in terms of differing shapes or patterns of temporal stimulation, they can no longer be regarded as constituting “the main arguments for a theory of temporal codes for transmission of color information in the visual system” (Kozak er ul., 1989). The sinusoidal stimuli producing reddish-brown and blue PIFCs differ only in one respect, namely the phase relation of P2 to Pl. In reddish-brown PIFCs, P2 has a phase lag on Pl, in blue PIFCs it has a phase advance. This corresponds to the theory of phase-dependent lateral interaction advanced by v. Campenhausen (1968a, 1970). A multiplicative interaction between PI and P2 was proposed by Both and v. Campenhausen (1978) as part of a cross-correlation model of PIFC generation to explain the results of experiments on detection of short time-delays in PIFC stimuli. Their model in fact predicts that purely sinusoidal stimuli should produce PIFCs. This is because the wei~ting of successive higher harmonics in the cross-correlation function decreases exponentiaily to such an extent that harmonics above the fundamental can be ignored and therefore cannot play a significant role in the generation of PIFCs. Polizotto and Peura’s (1975) more complex double cross-correlation model has similar consequences. The disappearance of the green PIFC when the stimulus is reduced to its fundamental suggests that this PIFC may result from a different process in the retina than the reddish-brown and blue PIFCs. One simple explanation might be a difference in the stimulus frequency at which different PIFCs occur. Indeed, it is well known (Pieron, 1923; Verriest & Seki, 1964) that square-wave PIFCs do change their color when stimulus frequency is greatly varied (e.g. by changing the rotation frequency of the disc). A simple test of this was performed by examining the colors produced by driving (a) the green, square-wave PIFC stimulus at 3.5 Hz, so that the frequency of the second harmonic was the same as that of the fundamental driven at 7 Hz; and (b) the reddish-brown and blue, sinusoidal PIFC stimuli at 14 Hz, the same as the frequency of the second harmonic of the green stimulus driven at 7 Hz. In the first case the PIFC disappeared, as do all PIFCs at such low frequencies, while in the second case the colors remained unchanged. This does not speak for a stimulus-frequency explanation for the disappearance of green PIFCs in the main experiment, but does not exclude it either. However, the unsaturated green seen when the first and second harmonic of P2 were combined with the fundamental of Pl (see Fig. 5) suggests that some kind of interaction may occur between the excitations caused by the fundamental and the higher harmonics of the stimulus. EXPERIMENT 2 If reddish-brown and blue PIFCs are the result of differences in the relative phase of Pl and P2, then changes in their relative means should have no effect on the color seen. Indeed explanations of PIFCs which are

al OUTER

DISC

RING

A 0 C :

P2 . . . . . . . .. . . .. p1 w_____ fjiff

FIGURE 6. (a} Temporal modulation functions PI and P2 for discs A-E used in Expt 2. The graph shows the reduction in the mean of PI relative to that of P2 in each successive disc. See text for details. (b) PI, P2 and difference function Diff = fP1 - P21 for the outer ring of disc B.

restricted to phase-dependent interactions between Pl and P2 generally have this corollary. The discovery that these PIFCs can be produced with sinusoidal stimuli opens up an easy way to test this assertion. Method

In this experiment only discs with sinusoidal modulation were used. These could be produced using the same random-dot method and software as that described for Expt 1. Within the limits imposed by the maximum and minimum reflectance of the discs, the mean, modulation amplitude and phase of both PI and P2 could be specified. Figure 6(a) shows how the temporal modulation function for Pi (dotted lines) was varied relative to P2 (solid line) on the 5 discs that were used in this experiment. Only the mean reflectance of PI relative to that of P2 was varied in the experiment; the discs were labeled from A to E in order of PI’s decreasing mean. The modulation amplitudes of Pl and P2 were kept constant at respectively 25 and 33 units of reflectance on the disc (white = 100, black = 0). The first two columns of Table 1 show the means of Pl and P2 in the same units TABLE I. Mean retIectances of Pl and P2 in discs A-E and phase (relative to PI) of Diff in the inner and outer rings of discs B and D Phase Mean Dim

Pl

P2

A B C D E

75 63 46 33 33

46 46 46 46 6.5

Diff inner ring

Diff outer ring

102” -102” -78”

78”

FOURIER

ANALYSIS

of reflectance. In discs A-D the mean of P2, i.e. the part of the disc which appeared colored, was kept constant; in disc E both means had to be shifted slightly upwards to avoid negative reflectance values. The phase shift of P2 relative to PI was 30” for the inner ring and - 30” for the outer ring. The colors seen in the rings when the discs rotated clockwise at 7 Hz were measured by the same matching procedure as in Expt 1. However, for reasons described in the results, two different surround luminances were used for the matching square surround. One was the same as for Expt 1 and could be used for color matches that had to be darker than the surround. The other was gray (41 cd/m*) and was used for matches that had to be lighter than the surround. Results

In discs A and B of Fig. 6(a) the mean of Pl was set so that Pl was at all points of its modulation brighter than P2. When these discs were observed, the inner ring appeared blue and the outer reddish-brown. The color appeared quite desaturated in disc A in comparison to disc B. Discs D and E, in which Pl was at all points of its modulation darker than P2, appeared altogether

OL-

yqpy-j 036

.Dt’ i/Li

A

‘.” ..........

Ohi

f02L

. 028

, OyFfVER; 032

"-7

~

OL

036

X

OLL-

B . .....”

ITi ,..I”

OL-

n

Y o?f-

OBSERVER.

M. T

FIGURE 7. Color matches produced by two observers for PIFCs on discs B and D, plotted in CIE x, y chromaticity coordinates. Box insets show the disc (B or D) and the Pl (dotted line) and P2 (solid line) stimuli; symbols show for which ring (m outer, A inner) each color match was made. W is the white point.

OF STIMULI

FOR

PIFCs

1467

Although at first glance the rings in these discs appeared merely very bright and colorless, on closer examination is could be seen that the inner ring in disc D was a bright but desaturated yellow. This color was even more desaturated in disc E. The rings on disc C, in which the temporal modulation functions for Pl and P2 cross back and forwards over each other, presented an irritating, flickering appearance; a faintly blue inner ring and a faintly brown outer ring were broken up by a rapid, white flicker. These observations were confirmed by the calorimetric settings of both observers for discs B and D, which are shown in Fig. 7. The chromaticity coordinates for the inner ring (solid triangles) showed a large shift right across the white locus from blur to yellow when the mean of Pl was shifted so that Pl was, at all points of its temporal modulation, darker instead of lighter than P2. At the same time this same shift in the mean of Pl causes the reddish-brown outer ring (solid squares) to lose its colored appearance altogether, with the resulting chromaticity coordinates lying on or near the white locus. The chromaticity coordinates in Fig. 7 do not reveal the changes in brightness which occurred. In order to achieve a satisfactory color match for disc D it was necessary to use a darker surround (41 cd/m*) for the matching square, in order to reduce the surround inhibition which otherwise limited the brightness of the square. For disc B the same surround was used as in Expt 1. Consequently, quantitative data cannot be provided for the large increase in the brightness of the rings experienced subjectively in disc D compared to disc B. Finally, it may be noted that in the discs of Fig. 6(a) the phase of Pl relative to P2 is just that of P2 relative to Pl with the opposite sign. If PIFCs are determined by the phase of lateral interaction between Pl and P2, one should expect that when a reddish-brown color is induced in the ring by the action of Pl on P2, a blue color should be induced by the action of P2 on Pl in the area around it (at least at the border with the ring), and vice-versa. Nothing of this sort occurs, however, on close examination, the area bordering on the ring appears to have a halo of the same color as the ring! In discs A and B this halo is bright, in discs D and E it is dark. different.

Discussion

The results of varying the relative means of Pl and P2 make it clear that previous explanations of PIFCs have missed out an important parameter. Theories based solely on the phase angle between Pl and P2 are unable to explain these results, since they predict that in discs A-E, in which the phase angle remains unchanged, the color should also remain the same. Instead, there is a dramatic reversal of the color of the rings as the average intensity of Pl is reduced; comparing discs B and D in Fig. 7, it can be seen that while the chromatic&y coordinates for the inner ring shift from blue to yellow, those for the outer ring shift in the opposite direction. This color reversal did not occur gradually as the mean of Pl was reduced from disc to disc. It happened

146X

MARK

F. TRITSCH

suddenly between discs B and D (disregarding disc C because of flicker). A further increase (disc A) or decrease (disc E) of the relative mean only resulted in a more desaturated PIFC. Both rings appeared dark in discs A and B, in which P2 was at all points of its modulation darker than Pl, and bright in discs D and E, where the reverse was the case. This suggests a mechanism responding to the contrast between PI and P2. Such a mechanism would be expected to respond particularly strongly to a stimulus in which the contrast continuously reverses sign, thus explaining the strong perception of fiicker in the rings of disc C, where the temporal modulation functions for Pl and P2 cross back-and-forward over one another [see Fig. 6(a)]. The PIFCs change (e.g. from blue to yellow, see Fig. 7) when the contrast between Pl and P2 is completely reversed, as between disc B, in which Pl is always brighter than P2, and disc D, in which PI is always darker than P2. This suggests that it is phase and contrast that are determining factors for PIFCs. This could be explained by involvement of the output of a contrast sensitive mechanism in PIFCs. Figure 6(b) shows for the inner ring of disc B the result of taking the difference between Pl and P2, which in one form or another is the likely stimulus for such a contrast mechanism. This difference is taken as Diff = ) PI - P21, since in a physiological process negative excitation would be meaningless. Table 1 gives in the last two columns the phase relation between Diff and PI, calculated according to tan $Dia =

API sin &, - AP2sin #r2 4, cos ~JPI- A,, cos 4~2

It can easily be seen that for each ring the contrast stimulus Diff undergoes a phase shift relative to Pl between disc B and D, corresponding to the observed color shift. This can also explain why the outer ring of disc B and the inner disc D both produced a color towards the upper right of the chromaticity diagram (reddish-brown and yellow), since both have an approximately similar phase relation of Diff to Pl. According to this explanation, the color of these PIFCs depends not on the phase of PI to P2, but rather on that of the contrast stimulus Diff to Pl. It should be noted, however, that the phase relation between Diff and P2 may also be a relevant parameter, as can be seen from a comparison of the phase positions of PI, P2 and Diff. The reduced saturation seen in disc A provides additional support for this explanation, since the contrast modulation is here superimposed on a higher mean contrast. Using the usual expression Diff,, - Diff,,, Diff,,, + Difft,+, for modulation of contrast results in a signal that is more weakly modulated for disc A than for disc B. This would be expected to diminish the strength of the resulting PIFCs.

CONCLUSIONS

Proposed anatomical sites for the lateral interactions that cause PIFCs include the horizontal cells (v. Campenhausen, 1968a), the receptive field of the color-opponent ganglion cells (Zrenner, 1983) and the amacrine cells (Adamczak, 1981). Since the results of Expt 2 suggest that one of the signals involved in the phase-sensitive generation of PIFCs is a contrast signal, it is clearly an attractive hypothesis to equate this signal with the excitation of the bipolar cells and place the site of subsequent phase-sensitive interaction in the inner plexiform layer. Opponent interactions have not been found in the activity recorded from primate horizontal cells (Dacheux & Raviola, 1990) so a contrast signal could not be generated earlier than the triadic synapse between cone, horizontal and bipolar cells. An alternative interpretation of the results of Expt 2 cannot be entirely excluded. This would allow the interaction leading to PIFCs to occur between PI and P2 before the contrast-sensitive mechanism. This has the corollary that, in order to explain the color shift that occurs when contrast reverses, the interaction must be assumed to have opposite phase preferences for the pathway responding to positive contrast to those for the pathway responding to negative contrast. If this were so, the results of Expt 2 could be reconciled with the hypothesis that PIFCs originate in the outer plexiform layer (v. Campenhausen, 1968a). The difference between reddish-brown and blue PIFCs, which require only the fundamental sinusoidal, and green PIFCs, for which the higher harmonics are required, may reflect the involvement of two different neuronal pathways. Schramme (1989) showed that reddish-brown and blue PIFCs, produced by squarewave stimuli similar to those used in Expt 1, did not lie along any of the confusion lines generally associated with single cone types in the CIE chromaticity chart. However, when they were plotted in opponent-color space (Ingling & Huong-Peng TSOU, 1977) they came to lie in the plane of excitation of cells with opposed inputs from short-wave cones and middle- and long-wave cones (S/M + L color opponent cells). This suggests that the interactions causing PIFCs involve such opponent cells. If the reddish-brown and blue PIFCs are generated in a pathway involving the S/M + L color opponent cells, the green PIFCs may be generated in one involving the M/L cells. The role of the higher harmonics in the green PIFC stimuius could be associated with the frequencydoubling effects which Boynton and Baron (1975) observed in the fovea1 local ERG with green sinusoidal flicker and attributed to (presumably non-linear) cone--cone interactions. These frequency-doubling effects are also observed in phasic ganglion cells (Gouras & Eggers, 1983; Lee, Martin & Valberg, f989b) which combine the output of M and L cones. In conclusion, while green PIFCs appear to offer a separate area of investigation, the simplest stimulus parameters for reddish-brown and blue PIFCs are the means, modulation amplitudes and relative phase of

FOURIER

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ANALYSIS OF STIMULI FOR PIFCs

sinusoidal Pl and P2. By varying these it may be possible to elucidate the nature of the interaction leading to PIFCs. It is not yet clear whether the rotating discs with sinusoidal patterns used in these experiments could simply be replaced by a stationary arrangement with a sinusoidally flickering center and a phase-shifted sinusoidally flickering surround. Attempts in this direction have so far not been successful. Both issues will be the subject of further reports.

Schramme, J. (1989). Farbmetrische Bestimmung musterinduzierter Flimmerfarben. Doctoral dissertation, Johannes Gutenberg University, Mainz, Fed. Rep. Germany. Troland, L. T. (1921). The enigma of color vision. American Journat of Physiological Optics, 2, 23-48.

Verriest, G. & Seki, R. (1964). Les chromaticitCs des couleurs subjectives suscit&es par la rotation du disque de Fechner-Benham. Revue d’optique,

43, 53-63.

Young, R. A. (1977). Some observations on temporal coding of color vision: Psychophysical results. Vision Research, 17, 957-965. Zrenner, E. (1983). Neurophysioiogicat aspects of color vision in primates. Berlin: Springer.

REFERENCES Acknowledgements-The

Adamczak, W. (1981). The amacrine cells as an important processing site of pattern-endued flicker colors. Vision Research, 21, 1639-1642.

Baron, W. S. & Boynton, R. M. (1975). Response of primate cones to sinusoidally flickering homochromatic stimuli. Journal qf Physiology, London, 246, 3 11-33 1. Both, R. & v. Campenhausen, C. (1978). Sensitivity of a sensory process to short time delays: A study in pattern induced flicker colors (PIFCs). Eiotogicat Cybernetics, 30, 63-74. Boynton, R. M. & Baron, W. S. (1975). Sinusoidal flicker characteristics of primate cones in response to heterochromatic stimuli. Journal of the Optical Society of America, 65, 1091-I 100. v. Campenhausen, C. (1968a). Uber die Farben der Benhamschen Scheibe. Zeitschrifr fiir vergteichende Physiotogie, 60, 351-374. v. Cam~nhausen, C. (1986b). uber den Ursprungsort von musterinduzierten Flimmerfarben im visuellen System des Menschen. Zeitschrift fiir vergleichende Physiotogie, 61, 355-360. v. Campenhausen, C. (1970). Musterinduzierte Flimmerfarben: Untersuchungen zur Psychophysik des Farbensehens. Verhandlungsbericht der Deutschen Zootogischen Gesettschaft, 64, 227-234.

Dacheux, R. F. & Raviola, E. (1990).Physiology of H I horizontal cells in the primate retina. Proceedings of the Royal Society o~London B, 239, 213.-230.

Festinger, L., Allyn, M. R. & White, C. W. (1971). The perception of color with achromatic stimulation. Vision Research, If, 591-612. Fry, G. A. (1933). Color phenomena from adjacent retinal areas for different temporal patterns of intermittent white light. American Journal qf

Psycho fogy, 45, 714-72 1.

Gouras, P. & Eggers, H. (1983). Responses of primate retinal ganglion cells to moving spectral contrast. Vision Research, 23, 1175-I 182.

van de Grind, W. & Griisser, O.-J. (1981). Frequency transfer properties of cat retina horizontal cells. Vision Research, 21, 1565-1572. Ingling, C. R. & Huong-Peng Tsuo, B. (1977). OrthogonaI combination of the three visual channels. Vision Research, 17, 1075-1082. Jarvis, J. R. (1977). On Fechner-Benham subjective colour. Vision Research,

author is grateful to Dr Jirgen Schramme for assistance in implementing the random-dot method of printing PIFC-discs as well as for many useful discussions on PIFCs, and also wishes to thank Professor C. v. Campenhausen for his thoughtprovoking critical reading of this paper.

APPENDIX Black and white rotating discs are used to investigate PIFCs because the stimulus must be modulated in both space and time (Both & Campenhausen, 1978; Kozak et at., 1989). CRT displays (e.g. computer monitors) are less suitable for several reasons; they are selfluminant, generating high contrast only at high average ~uminances relative to the surroundings, and they have temporal artefacts due to periodic frame renewal. Previously, the only rotating disc patterns in use have been ones which produced a square-wave luminance modulation. The following describes an easy method for varying luminance continuously on rotating discs, developed with the assistance of Dr Jiirgen Schramme. The method employs a conventional dot-matrix printer controlled by a personal computer. A satisfactory approximation to the continuously varying shade of gray required by the temporal luminance functions is obtained by varying the density of a random pattern of printed dots. A computer program converts the temporal luminance functions for the rings and the space between and on either side of them into dot density varying round the disc. Each disc is printed onto high-quality cartridge paper through a fresh sheet of non-smudge carbon film without using the printer ribbon. This ensures that ink density per dot remains constant from disc to disc. Improved contrast is obtained by printing each line of dots three times. The discs can also be printed onto transparent foil, allowing them to be used as modulators in the path of a light source.

17, 445-451.

Kozak, W. M., Reitboeck, Ii. J. & Meno, F. (1989). Subjective color sensations elicited by moving patterns: Effects of luminance. In Kulikowski, J. J., Dickinson, C. M. & Murray, I. J. (Eds), Seeing contour and cotour (pp. 294-310). Oxford: Pergamon Press. Lankheet, M. J. M., van Wezel, R. 3. A. &van de Grind, W. A. (1991). Light adaptation and frequency transfer properties of cat ho~zontal cells. Vision Research, 31, t 129-l 142. Lee., B. B., Martin, P. R. & Valberg, A. (1989a). Sensitivity of macaque retinal ganglion cells to chromatic and luminance flicker. Journal of Physiology, London, 414, 223-243.

Lee, B. B., Martin, P. R. & Valberg, A. (1989b). Nonlinear summation of M- and L-cone inputs to phasic retinal ganglion cells of the macaque. Journal of ~euro.~~ien~e, 9, 1433-1442. Nelson, T. M. & Bartley, S. H. (1964). The Talbot-Plateau Law and the brightness of restricted numbers of photic repetitions at CFF. Vision Research, 4, 403.-41

I.

Pitron, H. (1923). Le mkcanisme d’apparition des couleurs subjectives de Fechner-Benham. L’Ann& Psychotogique, 23, l-49. Polizzotto, L. & Peura, R. A. (1975). A mathemati~l approach to explain subjective color perception. Vision Research, 15, 613-616.

Since average luminance of the resulting printed gray shade is not a linear function of dot density, the actual relation is calibrated with sample discs using a Spectra Photo Research spotmeter. The samples are produced with the printer head pressure setting and the type of carbon film used for all discs. The calibration curve obtained is then incorporated into the software. The discs produced in this way display a high degree of reproducibility, in contrast to all attempts to achieve equivalent results using photographic techniques. These fail because the non-linearity of photographic film depends on a large number of not easily controlled factors. Te&hnic~l details

An 8088 computer with math co-processor sending output to a Star NL-10 printer can print one 7 in. disc in approx. 15 min. With this system, the 72 dots per in. “plotter” graphics mode produces a uniform dot density both horizontally and vertically, so that the entire disc can be represented as a 504 x 504 dot matrix. In 9-needle printers each graphics byte transmitted by the computer can define a column of 8 simultaneously printed dots. However, it is better to use only 6 of the

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MARK F. TRITSCH

needles in order to avoid problems from platen curvature, so that each byte represents 6 dots and the entire matrix is printed as 84 lines. each 6 dots deep. In order to generate the appropriate dot-density values, the computer program has to adjust the luminance values from the input functions using the calibration values obtained as described above. Since gray level is to be produced by the density of a random dot pattern, the lower the adjusted luminance value, the greater the probability has to be for printing the dot. This is accomplished by comparing the luminance value with the output of a random number generator which varies within the same range. If the former is smaller the dot is printed, i.e. the disc is “darker”. Apart from accepting input of the desired temporal luminance functions and performing various operations on them, the software has to construct the entire pattern of dots used as output fur the

printer. This is done using a template fur the disc. which tixes the width and position of the stripes and is defined in a tile produced by a separate templatede~nition utility. The disc is of course most appropriately described in terms of polar ccordinates, but the dot matrix into which the disc has to be embedded consists only of rows and columns of dots. Therefore the template-definition utility calculates the polar coordinates of each dot, tags a record of the dot with two variables derived from these coordinates and stores the results in a file which can be used for all discs with the same template. The two variables for each dot determine which temporal luminance function and which point (i.e. luminance value) on that function should be used for it. In principal, a similar method could also be used to vary the radial pattern of the disc, permitting control over both temporal and spatial characteristics of the stimulus produced by the rotating disc.