A theoretical expression is derived for the least distinguishable step in the number of pulses from an area whose image is focused on and measured by a single photoemissive detector. For large numbers of pulses this discrimination step is found to be equal to 6.8 times the rms fluctuation of the number of pulses at the given level. For the threshold step, the 6.8 factor must be replaced by 4.1. The maximum noise-to-signal ratio is computed for the cases of sample and path noise. A formula is found for the total number of discrimination steps in a macrocell whose photon number may vary between two given limits. Satisfactory agreement is found between computed and experimental values found by other researchers for the discrimination step of temperature, the discrimination step for the eye, the number of discrimination steps in a TV picture element and the number of equal lightness steps in a grey sample as given by the formula of the original Munsell system. A theory which assumes that in observing areas of even radiance, the eye adds up the signals from neighboring retinal detectors can explain some experimental data for the eye.
ELLEN HISDAL, "Discrimination Step," J. Opt. Soc. Am. 58, 985-991 (1968)