ramp luminance profile were compared to sine-wave thresholds in normal and amblyopic ... For the amblyopic eyes, detection of the ramp also occurred,.
Spatial processing of complex stimuli in the amblyopic visual system Anastas F. Pass and Dennis M. Levi Thresholds for detection and discrimination of the polarity (phase) of repetitive gratings with a ramp luminance profile were compared to sine-wave thresholds in normal and amblyopic observers. In the high-frequency range (4 cy/deg), normal observers detected ramp-wave gratings when the contrast of the fundamental spatial frequency was close to its independent threshold and discriminated the polarity (phase) of the ramp when the second harmonic reached its independent threshold. For the amblyopic eyes, detection of the ramp also occurred, when the contrast of the fundamental frequency was near its independent threshold. In contrast, discrimination of the polarity (phase) of the ramp required contrast levels 2 to 10 times greater than needed to detect the second harmonic. The reduced ability of the amblyopic eye to discriminate the polarity of the ramp represents an abnormality in phase processing and appears to be roughly proportional to the reduced optotype acuity of the amblyopic eyes. (INVEST OPHTHALMOL VIS SCI 23:780-786, 1982.)
Key words: amblyopia, psychophysics, detection, phase discrimination, Fourier analysis
T
he spatial frequency response of the visual system can provide a useful way of characterizing spatial vision. More importantly, to the extent that the visual system approximates a linear system, its response to sine-wave gratings may be valuable in predicting the response to more complex stimuli. 1 ' 2 Campbell and Robson1 first applied linear systems analysis to the detection and discrimination of complex gratings. Their results showed that over a wide range of spatial frequencies (above about 1.0 cy/deg), the contrast threshold of a complex grating is determined by the amplitude of the fundamental Fourier component of its waveform and that complex gratings can be distinguished from sine-wave gratings when the contrast of the relevant higher harmonics reach their independent From the College of Optometry, University of Houston, Central Campus, Houston, Tex. Supported by a research grant from the National Eye Institute R01 EYO 1728. Submitted for publication Nov. 2, 1981. Reprint requests: Dennis M. Levi, College of Optometry, University of Houston, Central Campus, Calhoun Blvd., Houston, Tex. 77004.
780
thresholds. These results were of particular importance because they provided strong evidence that the visual system responds independently to each spatial frequency component of the stimulus (i.e., a multiple spatial-frequency channel model). Since any spatial pattern can be considered as the sum of a series of sinusoidal components, within limits, the response to a complex pattern may be predicted by considering the responses to the separate components. However, to completely specify a complex visual stimulus, information about the relative phase of the frequency components is also essential. Recently, investigations of the spatial frequency response of amblyopic eyes3' 4 have shown that in addition to the reduced acuity, amblyopes show reduced sensitivity to spatial contrast over a wide range of spatial frequencies below the acuity limit; however, spatial frequency-selective mechanisms derived by adaptation or masking experiments appear to show the same degree of specificity in amblyopic eyes as in normal eyes. 5 " 7 On the other hand, several aspects of the vision of amblyopes are not simply explained on the
0146-0404/82/120780+07$00.70/0 © 1982 Assoc. for Res. in Vis. and Ophthal., Inc.
Volume 23 Number 6
Detection and discrimination of phase amblyopia
781
1.00-n Hi
a
D
a.
.25LU
I I I I I I
0-1
I DC
I 12
I 16
I 20
I I I
I
24
I 28
HARMONIC Fig. 1. Top, Example of the ramp-wave gratings. Bottom, Power spectrum of the stimulus. Left inset, Luminance profile of the ramp; center inset, power spectrum of a ramp that has been digitally filtered to limit the harmonic make-up to the fundamental and second harmonic; right inset, luminance profile of such a digitally filtered ramp. Note that the phase of the resultant waveform is apparent.
basis of reduced contrast sensitivity and suggest that in addition to the reduced sensitivity to spatial contrast at threshold, spatial processing may be abnormal. For example, the visual acuity of the amblyopic eye measured with optotypes is often poorer than would be predicted from grating resolution.8 Moreover, it has been reported that some amblyopes show spatial distortions for suprathreshold stimuli.8"11 Hess et al.10 suggested that these sup rath reshold distortions might represent an abnormality in phase processing in the visual system of amblyopes. Recently, they have reported12 that amblyopes show an abnormality for distinguishing the relative phase of a compound grating composed of a sine wave and its third harmonic. Thus it is possible that thresholds for sine-wave gratings do not provide a complete prediction for the vision of amblyopes under more complex conditions. Therefore, in the present study thresholds were determined in normal observers and observers with amblyopia for de-
tection of simple and complex gratings. Thresholds were also determined for discrimination of the relative phase of the complex gratings and the results have been considered in terms of the sensitivity of the visual system to the individual Fourier components. Specifically, we asked whether thresholds for detection of a complex grating (a ramp wave) could be predicted from the threshold for its most visible Fourier component (the fundamental frequency) and whether discrimination of the phase of the complex grating could be predicted on the basis of the threshold of the next most visible component (the second harmonic). Methods The stimuli (sine-wave and ramp-wave gratings) were generated on a Tektronix 608 monitor (P4 Phosphor) by conventional techniques. The mean luminance of the screen was 40 cd/m 2 and the display was masked by an equiluminance surround to produce a circular field that subtended 7.25° at
Invest. Ophthalmol. Vis. Sci. December 1982
782 Pass and Levi
the 75 cm viewing distance. Fig. 1 (top) shows an example of the ramp grating. It is evident from the amplitude spectrum (Fig. 1, bottom) that a ramp can be described by a series of harmonics. For a given contrast, c, of the ramp waveform, the contrast of the individual harmonics can be described as m, m/2, m/3, etc., for the fundamental, second harmonic, and third harmonic, where m = 2C/TT. The Fourier series for the relative phase of the components of the ramp grating is given by the following equation: L(x) = L o (1 + msin 2TT fx + ^ sin 2n 2 fx + ^
sin 2TT 3 fx + . . . sin 2TT nfx. . . .)
-I n
Reversing the polarity of a ramp is accomplished by changing the sign of the coefficient, m, which is equivalent to a 180° phase shift of each harmonic (the ramp shown in Fig. 1 has a negative value of m). The insets in Fig. 1 show the luminance profile of a ramp (left), the amplitude spectrum of a ramp that is digitally filtered to limit the harmonic make-up to the fundamental and second harmonic (middle), and the luminance profile for such a digitally filtered ramp (right). It may be noted that with only the presence of a fundamental and second harmonic, the phase of the resultant waveform is recognizable. (It should be noted that the stimuli used in these experiments were not filtered). The data were gathered with a procedure similar to that described by Nachmias and Weber13 and Furchner et al.2 The procedure was a two-bytwo temporal forced-choice paradigm, which yields simultaneous information about detection and discrimination. Each trial consisted of two 500 msec observation intervals marked by tones. In each trial, either a left or a right ramp was presented during one of the two intervals; both the direction of the ramp (right or left) and the intervals were randomly selected. After each trial, the observer made two judgments: (1) the interval that contained the stimulus, and (2) the direction of the ramp. Since a left and right ramp are identical in all respects but phase, correct discrimination of the direction of the ramp is equivalent to the discrimination of the phase of the ramp. Feedback was provided after each trial as to the interval in which the stimulus was presented and the direction (or phase) of the ramp. Data were collected in blocks of 40 trials. The contrast of the stimulus was varied between blocks
of trials to generate psychometric functions relating probability of correct detection and correct discrimination to stimulus contrast. Thresholds for detection and discrimination were obtained by interpolation to the contrast that yielded a 75% probability of correct responses. Thresholds for sine-wave gratings were obtained with the same procedure; however, for sine-wave stimuli, the observer signaled only the interval that contained the stimulus. Six to nine contrast levels were chosen to determine the psychometric functions, based on a prior estimate of threshold (using a method of limits procedure). The standard errors of the thresholds, determined by probit analysis of the data, were approximately 5% of the mean for the normal eyes and for both nonamblyopic and amblyopic eyes of the amblyopic observers. The presentation of the stimuli, acquisition of responses, and feedback were controlled by computer. Each of the subjects was given extensive practice prior to data acquisition. Subjects. Two adults with normal visual acuity and four representative adult amblyopes due to strabismus and/or anisometropia served as observers. All subjects had clear media and normal fundi and were appropriately corrected for refractive error during the experiments. The visual characteristics of each of the observers are summarized in Table I. Results Detection thresholds: ramps and sine-wave gratings. The specific question of interest is whether the detectability of the ramp-wave grating is determined by the detectability of the most visible Fourier component. Table I shows the ratio of the contrast of the sine wave at the independent detection threshold to the contrast of the most visible Fourier component of the ramp (which was the fundamental in each case) at detection threshold for each amblyopic observer and for the two normal observers at 0.5 and 4.0 cy/deg. A ratio of 1.0 would be obtained if detection of the ramp occurred when the contrast of the most visible component was at its independent threshold. A value greater than 1.0 would indicate that the ramp was detectable when the contrast of the most visible component was less than the independent threshold for that component. A value somewhat larger than 1.0 would be expected if allowance were
Volume 23 Number fi
Detection and discrimination of phase amblyopia 783
Table I. Visual characteristics of the observers, and their detection ratios
Observer
Binocular status
Eye
Acuity
Refractive status
A. P. D. L. M. M.
OD OD OD OS
20/15 20/15 20/15 20/40
Piano Piano +0.50 + 2.75-1.25 x 75
Normal Normal No strabismus
J- v.
OD OS
20/20 20/80
+ 0.75-0.25 x 70 +4.50-0.50 x 23
8^ constant O.S. esotropia
D. S.
OD
20/36
+4.50-1.00 x 90
No strabismus
R. G.
OS OD OS
20/15 20/15 20/46
+ 1.00 -4.50-1.25 x 90 -5.00-1.00 x 90
6^ constant O.S. exotropia
Ratio Independent sine-wave threshold Contrast ofFx of ramp at threshold* Fixation Central Central Central Unsteady central Central 1° Nasal and superior Unsteady central Central Central ¥i° Temporal
0.50 cy/deg ramp 4.0 cyldeg ramp 1.73 2.38 1.53 1.59
1.17 1.09 1.31 0.68
2.25 1.60
0.99 1.25
1.83
0.70
2.11 1.85 1.50
1.07 0.81 0.86
*The fundamental frequency (Fi) of the ramp was always the most visible component. The 95% confidence intervals for the ratios are approximately ± 15%.
made for probability summation; however, most models of probability summation would set an upper limit of about 1.26.2 Therefore values greater than 1.26 would indicate facilitation of the detection of the most visible component. In the high spatial frequency range, detection of the ramp-wave gratings could be reasonably well predicted from the sine-wave thresholds for both normal and amblyopic observers. At 4.0 cy/deg normal eyes detected the ramp grating when the most visible component reached its independent contrast threshold. For normal observers D. L. and A. P., the ratios were 1.09 and 1.16, respectively, and the mean of the ratios of the nonamblyopic eyes of the amblyopic observers was 1.05. At 4.0 cy/deg detection of the ramp grating with the amblyopic eyes also occurred with a contrast level close to that of the threshold of the most visible component, although three of the four amblyopic eyes tested required slightly higher contrast to detect the ramp than would be predicted from their sine-wave thresholds (average ratio of 0.87 for all amblyopic eyes). However, the detection ratios of the nonamblyopic and amblyopic eyes were not significantly different (p > 0.05, Wilcoxon-Mann-Whitney nonparametric test for small samples). On the
other hand, at low spatial frequencies for both normal and amblyopic eyes, detection of the ramp gratings occurred at a contrast well below the independent threshold level of the most visible component.* Similar results at low spatial frequencies have been previously reported in normal observers.1' 2 Since neither detection nor discrimination ratios at 0.50 cy/deg differed significantly between amblyopic and nonamblyopic eyes, they are not discussed further here. Phase discrimination. To completely specify a complex stimulus, phase as well as amplitude information is needed. With the ramp-wave gratings used in this study, the phase is the relative angular relationship between the first and higher harmonics. Therefore the thresholds for discrimination of the relative phase of the ramp were compared with the contrast at which the second harmonic of the ramp-wave reached its independent threshold. *Thefindingof facilitation at low spatial frequencies does not imply that there are not multiple spatial frequencyselective channels at low spatial frequencies. These results would be expected if: (1) the bandwidth of the channels were broad enough to encompass the fundamental and second harmonic, and (2) the detectability of these components was approximately equal (due to the low frequency fall off in the contrast sensitivity function).
Invest. Ophthalmol. Vis. Sci. December 1982
784 Pass and Levi
AP
.25
MM .25
JV .25
V
1.25-
< 0=
1.0
.5-
.5
1.0
1.0
GC
2.0
2.0
Z O O
5.0
5.0
5.0
10.0
10.0
10.0
i .son
20.0
20.0-
20.0-1
50.0
50.0-
50.0
GC O C0 Q
CO
•5-I 1.0
1
2.0
.25-
0 A
B
I *M m
NAE DS RG MM JV
Fig. 2. Contrast of the second harmonic of the ramp at the discrimination threshold (A) and the independent contrast threshold for the second harmonic (B). Open bars, Nonamblyopic eyes; shaded bars, amblyopic eyes. Note that the ordinate shows contrast increasing downward and is logarithmic. The far-right panel shows the phase discrimination ratios for the amblyopic eyes of each observer (shaded bars). Open bar, Mean ratio for the nonamblyopic eyes (NAE).
Fig. 2 shows the data for normal observer A. P. and for two amblyopic observers (M. M. and J. V.). The figure shows (in histogram form) the contrast of the second harmonic of the ramp at the discrimination threshold (A) and the contrast threshold of the second harmonic measured independently (B). The contrast of the second harmonic of the ramp at the discrimination threshold (A) was derived from the contrast threshold for discrimination of the phase of the ramp grating, since the contrast relationship of the second harmonic to the contrast of the ramp grating is 2C/2T7\ The point of interest is whether the contrast level for discrimination of the phase of the ramp grating occurs when the second harmonic reaches its independent threshold, as would be predicted by the model of Campbell and Robson.1 Thus a ratio of B/A (referred to here as the discrimination ratio) of 1.0 indicates that discrimination of phase occurs when the second harmonic of the ramp reaches its independent contrast threshold. At 4.0 cy/deg, for normal observer A. P. the discrimination ratio was 1.18, indicating that discrimination of phase occurred when the second harmonic reached its independent threshold. The data for the nonamblyopic eyes (open bars) were quite similar to those of the normal observers. Discrimination of the phase by the nonamblyopic eyes
occurred when the second harmonic reached its independent threshold with ratios close to 1. In contradistinction, the data for the amblyopic eyes (shaded bars) demonstrated a markedly reduced ability to discriminate the phase of the ramp at this spatial frequency. For J. V., with the most marked amblyopia 20/80), the ratio was 0.09, while for D. S., with the mildest amblyopia, (20/36) it was 0.48. The right panel of Fig. 2 shows the discrimination ratio for each of the amblyopic eyes (shaded bars). The open bar shows the mean discrimination ratio for the nonamblyopic eyes. Thus in the high-frequency range, for both normal eyes and the nonamblyopic eyes of amblyopic observers, thresholds for both detection and discrimination of the phase of a complex stimulus can be predicted from the Fourier components of the stimulus. The amblyopic eyes, however, display ratios for discrimination that are considerably less than 1.0 and that are significantly lower than those of the nonamblyopic eyes (p < 0.005, Wilcoxon-Mann-Whitney nonparametric test for small samples.) The loss in the ability to discriminate phase at 4.0 cy/deg appears to be roughly proportional to the loss in the ability to discriminate optotypes, with the correlation coefficient between optotype acuity (minimum angle of resolution) and the discrimination ratio equal to —0.84.
Volume 23 Number 6
Detection and discrimination of phase amblyopia 785
The present results show that in the high spatial-frequency range for observers with normal vision and for nonamblyopic eyes of amblyopic observers, detection and discrimination of the phase of a ramp can be predicted by considering the observer's sensitivity to the individual sine-wave components. However, amblyopes appear to have great difficulty in discriminating the phase of the ramp gratings with their amblyopic eyes. These results cannot be attributed to eccentric fixation, since two of the four observers had central fixation and the display was large enough to encompass the fovea in the other two observers. To further investigate the effects of nonfoveal fixation, a supplemental experiment was performed in which normal observer A. P. viewed the stimuli in an annulus, with the central 2° of the field covered by a translucent mask. A central fixation target was provided. The main effect of the mask was to elevate the contrast thresholds; however, unlike the discrimination ratios of the amblyopic eyes, that of the normal observer with the central mask was 1.05. There appear to be two plausible explanations for the present results: (1) there may be a masking spatial interaction of the fundamental on the detectability of the second harmonic, or (2) as Hess et al.10'12 suggested,there may be a specific phase anomaly. To test between these two alternatives, detection of the second harmonic in the presence of the fundamental was measured by asking the observers to distinguish between sine and ramp waveforms. Briefly, in this experiment each trial consisted of a 500 msec presentation of either a 4.0 cy/deg sine wave, a right ramp, or a left ramp at one of four to six contrast levels (at each level the contrast of the fundamental component of the ramp wave and sine wave were equated). The observer's task was to identify the waveform. Feedback was provided after each trial. Each stimulus was presented 40 times at each contrast level, with the order of stimuli and contrasts randomized. The results for the nonamblyopic eye and amblyopic eye of one observer (J. V.) are shown in Fig. 3. With the nonamblyopic eye, when the contrast of the
% CONTRAST
OF F2
0.25
0.5
1.0
2.5
0.5
1
2
5
% CONTRAST
5.0
10
OF F1
Fig. 3. Probability of correct identification of the waveform (I) and correct phase discrimination (?) for the nonamblyopic (squares) and amblyopic (circles) eyes for observer J. V. The lower abcissa shows the contrast of the fundamental; the upper abcissa shows the contrast of the second harmonic. The arrows show the independent contrast threshold of the nonamblyopic (open arrow) and amblyopic eyes (filled arrow) for an 8.0 cy/deg sine wave.
second harmonic of the ramp is near threshold (open arrow), the observer can reliably (p ^ 75%) distinguish between a sine wave and a ramp wave and can also reliably discriminate the phase. With the amblyopic eye, when the contrast of the second harmonic of the ramp is at threshold (filled arrow) the observer could reliably (p 5: 75%) distinguish between a sine wave and ramp wave; however, phase discrimination is at chance and does not reach the 75% correct level until the contrast of the second harmonic is about 1 log unit above threshold. Thus for the amblyopic eyes there was a range of contrasts over which the observers could distinguish between the sine wave and ramp wave but could not discriminate the phase of the ramp. These results provide strong evidence in favor of the second alter-
Invest. Ophthalmol. Vis. Sci. December 1982
786 Pass and Levi
native, i.e., that amblyopes exhibit a specific phase processing anomaly. Discussion The application of the linear systems approach to anomalies of vision may be useful not only in characterizing vision for spatial frequencies lower than the resolution limit but also in predicting thresholds for complex stimuli. In the present study, this was demonstrated in normal and nonamblyopic eyes. At 4.0 cy/deg the detection threshold for complex stimuli (ramps) roughly coincided with the fundamental Fourier component reaching its independent threshold. Discrimination of the phase occurred when the second harmonic reached its independent threshold. In the amblyopic eyes, the detection thresholds for ramp waves showed only minor departures from those predicted from the sine-wave thresholds. In contradistinction, amblyopic eyes show marked abnormalities in the discrimination of the phase of complex stimuli. This abnormality in discrimination of the relative phase of complex stimuli is present for both strabismic and anisometropic amblyopes and has also been recently reported for compound gratings composed of a sine wave and its third harmonic.12 It is of particular interest that strabismic and anisometropic amblyopes show similar losses in phase discrimination, since they show markedly different losses in vernier discrimination.8 The present results suggest that for normal observers and for nonamblyopic eyes of amblyopic observers, detection thresholds for high spatial-frequency sine-wave gratings may, to a rough approximation, allow reasonably accurate predictions regarding both detection and discrimination of more complex patterns. In amblyopic eyes, thresholds for sine-wave gratings provide a useful means of characterizing one aspect of the amblyopic loss and may also allow rough predictions regarding the detection of complex stimuli. However, the usefulness of the Fourier approach in amblyopic eyes is severely limited by the abnormality in phase discrimination. For example, while the ramp detection
thresholds for J. V. are reasonably well predicted by his sine-wave thresholds, phase discrimination is poorer by about a factor of 10 than would be predicted by his threshold data. Thus the visual handicap of amblyopes, under everyday conditions, may be much greater than suggested by measures of simple contrast sensitivity. We thank Drs. Ronald Harwerth, Bruno Breitmeyer, Stanley Klein, and Ruth Manny for their interest and helpful suggestions, and Dr. James Walters for help with the power spectrum and digital filtering of the stimuli.
REFERENCES 1. Campbell FW and Robson JG: Application of Fourier analysis to the visibility of gratings. J Physiol 197:551, 1968. 2. Furchner CS, Thomas JP, and Campbell FW: Detection and discrimination of simple and complex patterns at low spatial frequencies. Vision Res 17:827, 1977. 3. Levi DM and Harwerth RS: Spatio-temporal interactions in anisometropic and strabismic amblyopia. INVEST OPHTHALMOL VIS SCI 16:90, 1977.
4. Hess RF and Howell ER: The threshold contrast sensitivity function in strabismic amblyopia: evidence for a two-type classification. Vision Res 17:49, 1977. 5. Levi DS, Harwerth RS, and Venverloh J: Spatial and temporal masking in amblyopia. INVEST OPHTHALMOL VIS SCI 19(ARVO Suppl.):9, 1980. 6. Hess RF: A preliminary investigation of neural function and dysfunction in amblyopia. I. Sizeselective channels. Vision Res 20:749, 1980. 7. Rentschler I, Hilz R, and Brettel H: Spatial tuning properties in human amblyopia cannot explain the loss of optotype acuity. Behav Brain Res 1:433, 1980. 8. Levi DM and Klein S: Differences in vernier grating discrimination between strabismic and anisometropic amblyopes.
INVEST OPHTHALMOL VIS SCI
23:398, 1982. 9. Pugh M: Visual distortion in amblyopia. Br J Ophthalmol 42:449, 1958. 10. Hess RF, Campbell FW, and Greenhalgh T: On the nature of the neural abnormality in human amblyopia; neural aberrations and neural sensitivity loss. Pflugers Arch 377:201, 1978. 11. Bedell HE and Flom MC: Monocular spatial distortion in strabismic amblyopia. INVEST OPHTHALMOL
VIS SCI 20:263, 1981. 12. Hess RF, Lawden MC, and Campbell FW: Amblyopes exhibit a phase discrimination abnormality. INVEST OPHTHALMOL VIS SCI 20(ARVO Suppl.):126,
1981. 13. Nachmias J and Weber A: Discrimination of simple and complex gratings. Vision Res 15:217, 1975.
