Detection efficiency of circular gratings and bandpass filtered points with randomized phase spectra

In the studies of spatial integration an increase in the spatial extent of the stimulus usually results in a decrease in the spatial frequency bandwidth of the stimulus. The authors investigated separately the effects of these two factors on contrast detectability.

Efficiencies were measured for a circular grating at 4 c/deg and for bandpass-filtered point stimuli having a constant center frequency at 4 c/deg and bandwidths of 0.25, 0.5, 1, and 2 octaves. The phase range of these two-dimensional stimuli was increased from zero to 90, 180, 270, and 360 degrees by replacing the original zero phase at each spatial frequency component by a random number with zero mean. This procedure left the spatial frequency bandwidth unaffected.

The increase in phase range and decrease in spatial frequency bandwidth caused a progressively larger proportion of the contrast energy of the point stimuli to spread into their surroundings. As a result, detection efficiency decreased with increasing bandwidth and phase range for all point stimuli. However, a change in the stimulus bandwidth affected efficiency only when it altered stimulus area. The area of the circular grating and its detection efficiency remained almost constant irrespective of the phase range. When efficiency was plotted in semi-logarithmic coordinates as a function of stimulus area expressed in terms of the spatial spread of contrast energy, the line of least squares explained 85% of the total variance.

The primary determinant of detection efficiency for stimuli with constant center spatial frequency is not stimulus bandwidth but stimulus area expressed in terms of the spatial spread of contrast energy.