plots contrast sensitivity for both eyes of the three observers under the three optical conditions. The red and blue symbols represent sensitivity with normal, well-focused optics for pupil diameters of 6 and 4mm, respectively. The green symbols represent sensitivity with improved optics. As you can see, contrast sensitivity was higher with improved optics than with normal, well-focused optics in both eyes of all three observers. We subjected the data to a 3-way, repeated-measures ANOVA with factors optical condition, spatial frequency, and eye. There was a statistically significant effect of optical condition: Highest sensitivity was observed with improved optics and lowest with normal optics and 6mm pupil [F(2,4) = 24.711, p = 0.006; missing data at 40 and 28cpd for observer GYY were assigned sensitivities of 1]. The improvements were in some cases quite large. The contrast sensitivity of observer BV increased nearly 7-fold at 28cpd in his left eye from the normal, 6mm condition to the improved condition. The increase was more than 4-fold for HRF at 28cpd, right eye and nearly 4-fold for GYY at 20cpd, left eye. The improvement in sensitivity from the normal, 4mm condition to the improved optics condition was also statistically significant [F(2,2) = 22.863, p = 0.041]. These results show that our procedure for producing sharper-than-normal retinal images was quite effective.
Figure 2 Contrast sensitivity and stereo resolution for different optical conditions. Each row plots the data from one observer. a) Contrast sensitivity. The left and middle columns show sensitivity for the left and right eyes, respectively. Each panel plots the (more ...)
Stereo resolution with corrugations
shows the stereo resolution thresholds—the highest discriminable corrugation frequency as a function of dot density—for the three observers under the three optical conditions. The left column shows the whole functions; the right column shows exploded views of the data at high dot densities.
The Nyquist sampling frequency is the highest corrugation frequency that can be conveyed by the random-dot stimulus:
is dot density. The diagonal dashed lines in the figure represent this frequency. When dot density was low, the highest discriminable frequency for all three optical conditions was near the sampling limit. (Some thresholds slightly exceeded the Nyquist frequency because the random dot arrangement yielded regions in which local density was higher than overall density.) We conclude that stereo resolution is determined under those conditions strictly by the number of samples in the stimulus. However, when dot density was higher, resolution leveled off at a particular frequency, so something other than sample number is limiting performance there. Our primary interest is in understanding the determinants of that asymptotic frequency.
The different symbols in represent the data from the three optical conditions: Red for the normal, well-focused condition with 6mm pupil, blue for the normal, well-focused condition with 4mm pupil, and green for the improved optical condition. As you can see, performance leveled off at the same spatial frequency for all three optical conditions. We subjected the data at the two highest dot densities to a repeated-measures ANOVA and there was no reliable effect of optical condition [F(2,2) = 2.74, p = 0.178]. Examining the individual observer data reveals no systematic differences with the possible exception of observer GYY who had a slightly lower asymptotic frequency in the 6mm condition than in the other two (10.5% lower with 6mm pupil than with improved optics). Furthermore, there was no systematic relationship between the quality of individual observers’ optics and their stereo performance. With normal, well-focused optics, HRF had the best image quality (quantified by HORMS), and BV had the poorest (HRF = 0.19μm; BV = 0.7μm). Yet BV had the best stereo resolution (his asymptotic frequency was 5.3cpd in the 6mm condition) and HRF had the poorest (in the same condition, her asymptote was 2.8cpd). Collectively, these results suggest rather remarkably that improving the optics has no effect on stereo resolution. We know that degrading the optics from normal reduces stereo resolution(Westheimer & McKee, 1980
; Banks et al., 2004
), but it seems that the resolution of stereopsis is not limited by the blur in normal, well-focused eyes.
Two-line stereo resolution
We tested the generality of our observations by assessing stereo resolution another way. The data points on the right side of represent the results from the two-line, depth-discrimination experiment. The red and blue symbols again represent the data with normal, well-focused optics and 6 and 4mm pupils, respectively. Green symbols represent data with improved optics. There was no systematic relation between performance and optical quality. For improved optics with 4 and 6mm pupil, stereo resolution for observer BV was respectively 18.7arcsec (95% confidence interval: −4.2, +7.6), 11.3 (−4.6, +6.9), and 14.6 (−4.1, +5.0) arsec; for HRF, acuity was 32.8arcsec (−9.2, +11.4), 27.3 (−5.6, +6.8), and 59.9 (−15.7, +34.1). Thus, the differences across optical condition were not statistically reliable. There was also no consistent relationship between the optical quality of individual observers and their performance in the task. For example, HRF’s 6mm optical quality was significantly better than BV’s, but her disparity threshold was poorer than his: 32.8 vs 18.7arcsec. Again we conclude that stereo resolution is not limited by the blur associated with normal, well-focused optics.
Figure 3 Two-line stereo resolution for different optical conditions and contrasts. The smallest discriminable disparity is plotted as a function of the contrast of the line stimuli. As before, blue and red symbols represent the data with normal, well-focused (more ...)
Stereo resolution with low-contrast stimuli
Improving optical quality increases retinal-image contrast. Perhaps the failure to observe an improvement in stereo resolution was due to saturating non-linearity early in visual processing (MacLeod et al., 1992
; Chen et al., 1993
) such that the high-contrast dots and lines were effectively clipped and therefore the contrast increase was not retained for processing at later neural stages. If this were the case, improving optical quality should yield better resolution with lower-contrast stimuli. We examined this possibility in two ways.
First, we re-tested observer BV in the corrugation task with low-contrast stimuli. The background was gray with a retinal illuminance of 561Td. Contrast, defined as (Ldot – Lbkgrnd)/Lbkgrnd, ranged from 0.125–1. Dot density was fixed at 232 dots/deg2. The results are plotted in . Reducing contrast had no reliable effect on the highest discriminable corrugation frequency at contrasts from 0.25–1. At a contrast of 0.125, there was a clear reduction in stereo resolution in the 6mm condition, but this is because the dots became generally invisible. Thus, this particular finding is due to dot visibility rather than the precision of stereo processing.
Figure 4 Stereo corrugation resolution for different optical conditions and contrasts. The highest discriminable corrugation frequency is plotted as a function of the contrast of the random-dot patterns. As before, blue and red symbols represent the data with (more ...)
Second, we redid the two-line experiment with lower-contrast stimuli. Observers BV and HRF participated. The background was gray with a retinal illuminance of 446Td and contrast was varied from 0.125–1. The results are shown on the left side of . There was again no systematic effect of optical condition at any contrast provided that the lines were visible. BV’s disparity threshold was not measurable at 0.125 in the 6mm condition because he could not see the lines.
We conclude that the failure to observe an improvement in stereo resolution with improved optics is not a byproduct of clipping due to a saturating non-linearity. Human stereopsis simply does not seem to benefit from better retinal-image quality than that associated with natural viewing.