Most of the measurements of vernier and stereo thresholds were made using the method of constant stimuli. In the vernier experiments, the observer reported whether the lower target appeared to be offset to the left or right of the upper target. In the stereo experiments, the observer reported whether the lower target appeared to be nearer or farther away than the upper target.
Vernier and stereo thresholds are plotted as a function of contrast in
Figure 3 for luminance and L-M modulated targets. Contrast is expressed logarithmically relative to detection thresholds. Thresholds are expressed logarithmically relative to 1 arcs. In all cases, the slopes are on the order of −0.5, in agreement with previous results on vernier thresholds (
Krauskopf & Farell, 1991) and on stereo thresholds (
Legge & Gu, 1989; but see
Westheimer & Pettet, 1990). One line of slope −0.56 fits both the chromatic and luminance data for vernier but the chromatic and luminance thresholds for stereo cannot be fit with a single line. The chromatic thresholds are approximately 0.5 log units higher than would be projected from the luminance thresholds. This effect is not as large as that shown in
Figures 4 and
5. In these experiments, the standard definition of isoluminance was used. In the subsequent experiments, isoluminance was defined as illustrated in
Figure 2 and the effects were, accordingly, larger.
Stereo and vernier thresholds are plotted for two observers as a function of elevation of the modulation out of the isoluminant plane in
Figure 4. Vernier thresholds are independent of elevation as expected of equally detectable stimuli if photons caught are used efficiently. Stereo thresholds are an order of magnitude higher for isoluminant stimuli than for luminance-modulated stimuli. For both observers, the stereo thresholds peak in the vicinity of the estimated elevation of the isoluminant plane.
Could the observers be using the information contained in the luminance component of the stimuli? Informal estimates of stereo thresholds as a function of elevation of targets out of the isoluminant plane were made assuming that only the luminance component of the tests were processed in evaluating target depth and that stereo thresholds are inversely proportional to the square root of target contrast (as shown in
Figure 3). Observed thresholds in the vicinity of isoluminance exceeded these estimates, suggesting that not all the available information is used. The finding that thresholds were higher than expected from the luminance component led us to perform the mixture experiment described later.
Berry (1948) reported that vernier thresholds increased with the size of the gap between the bottom and top targets, whereas stereo thresholds remained approximately constant, independent of the gap. We made similar measurements to see whether these functions might be different for chromatic and luminance targets. In
Figure 5, measurements of stereo and vernier thresholds for target modulated in luminance and isoluminantly are plotted as a function of the size of the gap between the top and bottom elements.
Vernier thresholds are essentially the same for targets modulated in luminance and along the L-M cardinal axis, confirming
Krauskopf and Farell (1991). Thresholds for vernier targets are 2 to 3 times larger with a gap of 20 arcmin than with a gap of 1 arcmin. The trends for stereo thresholds are quite different. Thresholds decrease with increasing gap by a factor of about 2 to 3, confirming
Westheimer and McKee (1979). The outstanding result is the marked elevation for the stereo thresholds for targets modulated isoluminantly compared to those modulated in luminance (a factor on the order of 10-fold), confirming the results plotted in
Figure 4.
The stimuli used in the mixture experiment are illustrated in
Figure 6. Stereo thresholds were measured by the standard staircase procedure for targets defined purely by luminance and for targets with the same luminance modulation to which was added a large chromatic component.
Median thresholds for three observers for the three conditions are presented in
Figure 7. If stereo disparity is processed by independent chromatic and luminance mechanisms, disparity thresholds should at least be as low for mixtures of chromatic- and luminance-modulated targets as they are for targets modulated only in luminance. This result would be expected whatever the postulated mechanism of summation: probability summation, energy summation, etc. But the performance of two of the observers is clearly poorer for the mixed stimuli and tends to be poorer for the third observer.
It should be noted that the luminance component was added in both phases with respect to the isoluminant component. This guarded against the possibility that the L-M component was not truly isoluminant, and thus might add constructively or destructively to the luminance modulation.
The observers found the stereo task more difficult to perform with stimuli modulated chromatically than with stimuli modulated in luminance, and the psychometric functions tended to be shallower for chromatically modulated stimuli. No such effects were noted in the vernier case.