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Phase and detection of compound gratings
LETTER TO THE EDITORS
PHASE AND DETECTION OF COMPOUND GRATINGS* (Rrcrirrd 16 ,Uarcll 1979) Abstract-The detection thresholdsof two gratings differing onIy in the phase of one of their sine harmonic constituents have been measured. A difference is found only when the gratings have a fundamental frequency below 1cideg. In this case the grating whose waveform has the greater contrast gradient is the more readily seen. This supports the hypothesis that low frequency structure in the visual world is analysed by contrast gradients.
INTRODUCTION
Graham and Nachmias (197 1) showed that phase has no effect on the detection threshold of gratings which consist of the sum of two sine gratings. This result has since then been confirmed by many others, most recently by Graham, Robson and Nachmias (1978). These studies have principally been concerned with high frequency gratings above 1 c/deg and they provide evidence for the existence of independent, spatial frequency selective channels in this range. Little attention has been given to the effects of phase at low spatial frequencies. Hoekstra, van der Groot, ven den Brink and Bilsen (1974) suggested that thresholds depend on tuminence gradients. at spatial frequencies below 0.5 c/deg. Campbell, Johnstone and ROSS (1978) have suggested that the coarse structure of the visual world is analysed over regions 0.5” wide by a gradient-sensitive mechanism. They showed that halving the width of the ramp of a trapezoidal grating of low fixed frequency halves its threshold. This continues for successive halvings until a minimum but finite ramp width is reached at which threshold of the trapezoid equals that for a square gratings. Thresholds of other low frequency waveforms were predictable from luminance gradients. Thresholds of low frequency compound gratings should therefore be considerably affected by phase, since waveform is a function of phase. There are infinitely many compound gratings identical in power spectrum but different in the phase of their harmonic. We restricted ourselves to the harmonic series which generates a square wave and found by trial anderror a suitable five component compound: all harmonics up to the 9th. either with all components in square waveform phase (0’) (Figs fa and b) or all in phase except the 5th which is out of phase by 180” (Figs 2a and b). The slope of the square phase waveform is S/3. or 4.5 dB greater than the slope of * This research was supported by a grant from the Australian Research Grants Committee. and a grant from the National Health and Medical Research Council. 189
the out of phase 5th waveform at the mean luminance crossover. This difference should be large enough to detect by a forced-choice procedure without too much difficulty. Simpler waveforms (e.g. I&and 3rd harmonics) gave much smaller differences. METHODS
on a TV monitor screen. The subject viewed the 1I” screen From distance of 64 cm. Eye movements were not restricted. Fundamental frequency was 0.2 c/deg. The screen was initially blank and of luminance 12 cd/m*. The subject pressed a button and the luminance immediately increased to 45 cd/m2 for 3.6 sec. Then the teletype bell sounded and the screen either remained unmodulated at 45 cd mz for 3.6 set or at the same mean luminance, displayed one of the two compound gratings. The grating started with low contrast, increasing linearly to a preset contrast vafue over I.Zsec and remaining there for l.Osec before decreasing and finally returning to the original blank screen display. The subject pressed one of two buttons to indicate that he had or had not seen a grating. He could then repeat the procedure. Each run consisted of 50 presentations,. the computer setting the contrast of the gratings randomly at one of three values. As a check on the validity of this procedure the compound grating was replaced with a simple sine grating. Using the method of adjustment one subject produced a contrast sensitivity function similar to those described by Campbeil and Robson (1968) and Campbell er al. (1979). In particular, the low frequency part of the curve was not flattened. but fell off with a slope of one, showing that the rise time of the grating contrast was not so fast as to change thresholds in the way described by Robson (1966). Gratings
were displayed
RESULTS
Four subjects took part. In each case the square phase grating was the more readily detected. The difference between the two thresholds varied from 4.5 dB
190
Letter to the Editors DISCLSSIOS 99 -
The
simple
accounts
90
s
so -
;
70.
2
40-
:
40. 50-
3
30.
Y 2
ao-
of
Campbell
Ed al.
of low frequency
(1978)
structures
in the visible world in terms of the contrast within 0.5’ regions of the visual field: if the contrast within any 0.5” region exceeds 0.002 (even if there are no independently visible Fourier components of frequency greater than about 3 c,/deg) then detection threshold is exceeded. This theor! predicts that the threshold for the 0’ phase gratin9 should be lower than that for the 180’ phase grating. This should be so even though the amplitude of the 180” grating is 1.3 times that of the O- grating. Our findings confirm this prediction.
-
0
theory
for the visibility
-_-.
Departments
10 -
0
PHASE
ANGLE
O”
l
PHASE
ANGLE
180’
ojPsycholog~
and Physiology L~r7i~~~it~
‘vedla/lt/.s bt’rsrtwf
of If.c,srrrjr
JOHN Ross J. R.
JOHNSTONE
.Ausfra/ia
6009 Ak~rruiitr
l-
-33
-a0
ATTENUATION
-17 IN
DECIBELS
Fig. 3. Mean frequency of seeing curves for four subjects. Contrast
REFERESCES
-24
is expressed as dB below 0.8.
(BJ) to 3.0 dB (JRJ). The non-square waveform phase detection curves were very similar in all cases: the differences between subjects is almost entirely in their square phase thresholds. Figure 3 shows the means of the four subjects with a probit scale. The mean difference in threshold for the two gratings is 3 + 1 dB. For two subjects (JH and JRJ) the measurements were repeated for a fundamental frequency of 3 and I c,dcg respectively. There was no difference in thresholds for the two gratings differing in phase; a result to be expected from the measurements of Graham and Nachmias (197 I).
Campbell F. K.. Johnstone J. R. and Ross J. (1978) An explanation for the visibility of low frequency gratings. Submitted. Campbell F. W. and Robson J. G. (1968) Application of Fourier analysis to the visibility of gratings. J. Physiol. 197. 5SI-556.
Graham N. and Nachmias J. (1971). Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channel models. iision Rrs. Il. 251-259. Graham N.. Robson J. G. and Nachmias summation in fovea and periphery.
J. (1978) Grating Vision Res. 18.
8 I j-825. Hoekstra J.. van der Groot D. P. J., van den Brink G. and Bilsen F. A. (1974) The influence of the number of cycles upon the visual contrast threshold for spatial sine-wave patterns. Vision RPS. 14. 365-368. Robson J. G. (1966) Spatial and temporal contrast-sensitivity functions of the visual system. J. opr. Sot. Am. 56. I141-I 142.
Fig. la. Waveform produced by adding the 1st. 3rd. 5th. 7th and 9th harmonics of the series which generates a square wave.
Fig. lb. Grating corresponding
to the waveform shown in Fig. la (not to scale).
191
Fig. ?a. As in Fig. I but with the 5th harmonic 180’ out of phase.
Fig. Zb. Grating corresponding
to the waveform shown in Fig. Za (not to scale).
192
PHASE AND DETECTION OF COMPOUND GRATINGS* (Rrcrirrd 16 ,Uarcll 1979) Abstract-The detection thresholdsof two gratings differing onIy in the phase of one of their sine harmonic constituents have been measured. A difference is found only when the gratings have a fundamental frequency below 1cideg. In this case the grating whose waveform has the greater contrast gradient is the more readily seen. This supports the hypothesis that low frequency structure in the visual world is analysed by contrast gradients.
INTRODUCTION
Graham and Nachmias (197 1) showed that phase has no effect on the detection threshold of gratings which consist of the sum of two sine gratings. This result has since then been confirmed by many others, most recently by Graham, Robson and Nachmias (1978). These studies have principally been concerned with high frequency gratings above 1 c/deg and they provide evidence for the existence of independent, spatial frequency selective channels in this range. Little attention has been given to the effects of phase at low spatial frequencies. Hoekstra, van der Groot, ven den Brink and Bilsen (1974) suggested that thresholds depend on tuminence gradients. at spatial frequencies below 0.5 c/deg. Campbell, Johnstone and ROSS (1978) have suggested that the coarse structure of the visual world is analysed over regions 0.5” wide by a gradient-sensitive mechanism. They showed that halving the width of the ramp of a trapezoidal grating of low fixed frequency halves its threshold. This continues for successive halvings until a minimum but finite ramp width is reached at which threshold of the trapezoid equals that for a square gratings. Thresholds of other low frequency waveforms were predictable from luminance gradients. Thresholds of low frequency compound gratings should therefore be considerably affected by phase, since waveform is a function of phase. There are infinitely many compound gratings identical in power spectrum but different in the phase of their harmonic. We restricted ourselves to the harmonic series which generates a square wave and found by trial anderror a suitable five component compound: all harmonics up to the 9th. either with all components in square waveform phase (0’) (Figs fa and b) or all in phase except the 5th which is out of phase by 180” (Figs 2a and b). The slope of the square phase waveform is S/3. or 4.5 dB greater than the slope of * This research was supported by a grant from the Australian Research Grants Committee. and a grant from the National Health and Medical Research Council. 189
the out of phase 5th waveform at the mean luminance crossover. This difference should be large enough to detect by a forced-choice procedure without too much difficulty. Simpler waveforms (e.g. I&and 3rd harmonics) gave much smaller differences. METHODS
on a TV monitor screen. The subject viewed the 1I” screen From distance of 64 cm. Eye movements were not restricted. Fundamental frequency was 0.2 c/deg. The screen was initially blank and of luminance 12 cd/m*. The subject pressed a button and the luminance immediately increased to 45 cd/m2 for 3.6 sec. Then the teletype bell sounded and the screen either remained unmodulated at 45 cd mz for 3.6 set or at the same mean luminance, displayed one of the two compound gratings. The grating started with low contrast, increasing linearly to a preset contrast vafue over I.Zsec and remaining there for l.Osec before decreasing and finally returning to the original blank screen display. The subject pressed one of two buttons to indicate that he had or had not seen a grating. He could then repeat the procedure. Each run consisted of 50 presentations,. the computer setting the contrast of the gratings randomly at one of three values. As a check on the validity of this procedure the compound grating was replaced with a simple sine grating. Using the method of adjustment one subject produced a contrast sensitivity function similar to those described by Campbeil and Robson (1968) and Campbell er al. (1979). In particular, the low frequency part of the curve was not flattened. but fell off with a slope of one, showing that the rise time of the grating contrast was not so fast as to change thresholds in the way described by Robson (1966). Gratings
were displayed
RESULTS
Four subjects took part. In each case the square phase grating was the more readily detected. The difference between the two thresholds varied from 4.5 dB
190
Letter to the Editors DISCLSSIOS 99 -
The
simple
accounts
90
s
so -
;
70.
2
40-
:
40. 50-
3
30.
Y 2
ao-
of
Campbell
Ed al.
of low frequency
(1978)
structures
in the visible world in terms of the contrast within 0.5’ regions of the visual field: if the contrast within any 0.5” region exceeds 0.002 (even if there are no independently visible Fourier components of frequency greater than about 3 c,/deg) then detection threshold is exceeded. This theor! predicts that the threshold for the 0’ phase gratin9 should be lower than that for the 180’ phase grating. This should be so even though the amplitude of the 180” grating is 1.3 times that of the O- grating. Our findings confirm this prediction.
-
0
theory
for the visibility
-_-.
Departments
10 -
0
PHASE
ANGLE
O”
l
PHASE
ANGLE
180’
ojPsycholog~
and Physiology L~r7i~~~it~
‘vedla/lt/.s bt’rsrtwf
of If.c,srrrjr
JOHN Ross J. R.
JOHNSTONE
.Ausfra/ia
6009 Ak~rruiitr
l-
-33
-a0
ATTENUATION
-17 IN
DECIBELS
Fig. 3. Mean frequency of seeing curves for four subjects. Contrast
REFERESCES
-24
is expressed as dB below 0.8.
(BJ) to 3.0 dB (JRJ). The non-square waveform phase detection curves were very similar in all cases: the differences between subjects is almost entirely in their square phase thresholds. Figure 3 shows the means of the four subjects with a probit scale. The mean difference in threshold for the two gratings is 3 + 1 dB. For two subjects (JH and JRJ) the measurements were repeated for a fundamental frequency of 3 and I c,dcg respectively. There was no difference in thresholds for the two gratings differing in phase; a result to be expected from the measurements of Graham and Nachmias (197 I).
Campbell F. K.. Johnstone J. R. and Ross J. (1978) An explanation for the visibility of low frequency gratings. Submitted. Campbell F. W. and Robson J. G. (1968) Application of Fourier analysis to the visibility of gratings. J. Physiol. 197. 5SI-556.
Graham N. and Nachmias J. (1971). Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channel models. iision Rrs. Il. 251-259. Graham N.. Robson J. G. and Nachmias summation in fovea and periphery.
J. (1978) Grating Vision Res. 18.
8 I j-825. Hoekstra J.. van der Groot D. P. J., van den Brink G. and Bilsen F. A. (1974) The influence of the number of cycles upon the visual contrast threshold for spatial sine-wave patterns. Vision RPS. 14. 365-368. Robson J. G. (1966) Spatial and temporal contrast-sensitivity functions of the visual system. J. opr. Sot. Am. 56. I141-I 142.
Fig. la. Waveform produced by adding the 1st. 3rd. 5th. 7th and 9th harmonics of the series which generates a square wave.
Fig. lb. Grating corresponding
to the waveform shown in Fig. la (not to scale).
191
Fig. ?a. As in Fig. I but with the 5th harmonic 180’ out of phase.
Fig. Zb. Grating corresponding
to the waveform shown in Fig. Za (not to scale).
192