Reciprocity between luminance and dot density in the perception of brightness

Thresholds were measured for detecting perturbations in a regular lattice of dots by modulating local dot density, local dot luminance, or some combination of the two. For high mean densities (dot spacing less than or equal to 15 min of arc), perturbations in local density increase the perceived brightnesses of the individually resolved elements in the more densely filled regions, and appear (at near threshold levels) as modulations of brightness rather than density. This illusory brightness modulation may be nulled by applying a real luminance modulation to make the lattice elements appear equally bright. Once this is done, thresholds for detecting any nonuniformity in the array are elevated compared to thresholds for detecting uncompensated density modulation. This result suggests that uncompensated density modulation is detected via the illusory brightness variations. This interpretation suggests that dot brightness is determined on the basis of the space average luminance of an area a substantial fraction of 1 deg in diameter. To test this hypothesis, thresholds were measured for detecting luminance modulation in a regular array of dots viewed against a comparatively dim background, where the modulation was applied to the dots themselves, to the background alone, or to both the dots and the background in either reinforcing or cancelling relative phase. For small, closely spaced dots, the threshold for modulation of luminance can be predicted on the basis of the amplitude of the Fourier component at the modulation frequency, regardless of whether it is carried by dots, the background, or both. The threshold is greatly elevated when modulation in the dots cancels the background modulation, so that there is contrast modulation of the dots, but no net energy at the fundamental frequency (zero amplitude of the Fourier component). For large, coarsely spaced dots, on the other hand, thresholds for conditions which contain energy at the fundamental modulation frequency are higher. The threshold increase is much greater when the modulation is applied to the dots than when it is applied to the background. This result suggests that the coarsely spaced dots are saturating the response of spatially opponent units. This hypothesis was confirmed by tests using backgrounds with the same luminance as the dots; threshold elevations selective for dots or background were abolished.