A rating-scale psychophysical method was employed to obtain receiver operating characteristics for detection and for discrimination of luminance increments. These curves were used to estimate the parameters of a normal probability-density function which was assumed to describe the relevant internal effects of the test flash. The over-all results strongly indicate that the mean of this distribution is a positively accelerated function of luminance of the test flash, and suggest that the standard deviation is a nonmonotonic function of luminance. It is argued that quantum fluctuations and criterion fluctuations cannot account for these findings, whereas channel uncertainty may be at the root of some of them.
JACOB NACHMIAS and ELIZABETH C. KOCHER, "Visual Detection and Discrimination of Luminance Increments," J. Opt. Soc. Am. 60, 382-389 (1970)