It is clear from
Figure 1that at higher test spatial frequencies, masking functions were band-pass in character but severely asymmetric (peak at ∼1 octave below the test). In an attempt to rule out the possibility that the asymmetry could be in some way due to the high contrast of the masks, masking functions was remeasured at 2 cyc/deg, with mask contrasts of 0.125, 0.0625, and 0.03125 (Michelson). The results are presented in
Figure 2and make it clear that the amount of masking scaled (became less) almost perfectly with decreasing mask contrast. However, maximum threshold elevation still occurred when the mask was positioned ∼1 octave below the test spatial frequency, irrespective of the contrast of the jittering mask pattern.
Another possibility was that the shape of the masking functions (i.e., the peak off-test frequency) may reflect underlying sensitivity to the masks themselves. For example, if all mask patterns were presented at say a contrast of 0.25, the mask spatial frequency to which observers were most sensitive would be of higher effective contrast to the visual system than the mask spatial frequency to which observers were least sensitive. Therefore, the greatest degree of masking would occur at the mask frequency to which observers were most sensitive. To investigate, we measured detection thresholds for each mask using a two-interval, forced-choice procedure. A jittering grating appeared in one of the two intervals, and the observer’s task was to judge in which interval it had appeared. Thresholds were estimated by using an adaptive staircase technique in a manner analogous to that described in the Methods section. Modulation sensitivity functions (the reciprocal of modulation depth at threshold) for the masks are shown in
Figure 3a . The shape of the modulation sensitivity functions suggests that the shape of the masking functions, especially at a test frequency of 2 cyc/deg, may indeed have reflected underlying sensitivity to the masks. Modulation sensitivity functions are band-pass in nature, peaking at ∼1 cyc/deg (corresponding to the mask positioned 1 octave below the 2 cyc/deg test pattern). Moreover, sensitivity was generally greater at frequencies below 2 cyc/deg than at frequencies above, in accordance with the general asymmetry in the masking functions at 2 cyc/deg.
If the shapes of the masking functions do reflect differential sensitivity to the masks, then if the masks are presented at equal multiples of detection threshold, each mask should be of approximately equivalent contrast (detectability) to the visual system (assuming that the slopes of the contrast response functions are identical across spatial frequency). In this case, the asymmetry in the masking functions should disappear, and a “conventional” masking function should be observed where maximum masking occurs when the test and mask share the same frequency and decreases as the test-mask spatial frequency difference increases. To test this possibility, masking was measured at a test spatial frequency of 2 cyc/deg, with each mask presented at an equal multiple of detection threshold. The mask pattern to which sensitivity was lowest was set to 0.25 Michelson contrast, and the contrasts of the masks at other spatial frequencies were adjusted so that they were at the same multiple above threshold. Maximum masking effects did not occur when the test and mask shared the same spatial frequency but rather remained maximum when the mask was positioned at 1 octave below the test frequency
(Fig. 3b) .
As an additional control, we used a contrast-matching task in which observers made a subjective judgment about which of two patterns (a standard and a match) had the greater contrast. The standard pattern was a 2-cyc/deg jittering grating, and the match pattern was a jittering grating that was 0.25, 0.5, 1, 2, 4, 8, or 16 cyc/deg (corresponding to each mask spatial frequency). A two-interval, forced-choice procedure was used in which the standard grating appeared in one interval, and the match grating appeared in the other (the grating that came first was randomized across trials with a probability of 0.5). The modulation depth of the standard grating was fixed at 0.25 and the modulation depth of the match grating varied. The observer’s task was to judge which interval contained the grating with the highest contrast. The modulation depth at which the match grating was judged to have the same perceived contrast as the standard grating (the point of subjective equality) was estimated using an adaptive staircase technique in a manner analogous to that described in the Methods section.
Figure 4ashows that the modulation depth at which the match grating was judged to have the same perceived contrast as the 0.25 contrast standard grating hovered at ∼0.25 for match gratings that had low spatial frequencies (≤ ∼4 cyc/deg). For higher spatial frequency match gratings, the modulation depth of the match grating that had the same perceived contrast as the standard grating rose rapidly (especially for observer CVH).
Masking was then measured at a test spatial frequency of 2 cyc/deg with each mask presented at the modulation depth at which it had the same perceived contrast as the 2-cyc/deg standard grating. Once more, maximum threshold elevation did not occur when the test and mask shared the same spatial frequency but when the mask was 1 octave below the test frequency
(Fig. 4b) .
The masking functions produced by presenting the masks at equal multiples of threshold
(Fig. 3b)exhibited less threshold elevation (masking) than those produced when masks were matched for perceived contrast
(Fig. 4b) , because in
Figure 3bthe masks were of a much lower physical contrast than those in
Figure 4b , thus resulting in less masking at each mask frequency. This result suggests that, although matching contrast by taking equal multiples of threshold is a commonly used method, it may not be the most appropriate technique for perceptually equating stimuli of different spatial frequencies. However, most important, in both cases maximum masking occurred when the mask was ∼1 octave below the test frequency, and the masking functions do not differ markedly in terms of shape.