Theory of spatial-frequency filtering by the human visual system. I. Performance limited by quantum noise

A theory and model of the visual system are presented to explain the detection of static sinusoidal gratings near the threshold. The model incorporates a set of independent decision centers and associated photoreceptive fields (PRFs). The decision criterion value at each decision center is proportional to the standard deviation of the excitation current transmitted from a PRF to its associated decision center caused by quantum fluctuations in the absorption of light. It is well known that the spatial-frequency-response (SFR) function and the spatial-impulse-response (SIR) function of a photodetector are a Fourier transform pair. A systematic examination of the SIR and SFR functions of PRF configurations consisting of rectangular regions of alternately excitatory and inhibitory response reveals that modulation sensitivity of the visual system is explained at scotopic and photopic illuminance by a set of PRFs composed of a single excitatory region and a central excitatory region bordered by inhibitory regions, respectively. The complete model is shown to yield a high degree of conformity between theoretical and experimental threshold modulation curves.