Multiplication noise in the human visual system at threshold: 1 Quantum fluctuations and minimum detectable energy

Abstract

We have carried out a series of frequency-of-seeing experiments similar to those performed by Hecht, Shlaer, and Pirenne [ J. Gen. Physiol. 25, 819– 840 ( 1942)], using an Ar⁺ laser operated at 514.5 nm as the source of light. In certain blocks of trials, our subjects were encouraged to report as seen those trials in which the stimulus might have been present. It was determined that sensitivity and reliability were traded against each other over a broad range: for our four subjects, the detection of 147 photons at the cornea with 60% frequency of seeing entailed, on the average, a 1% false-positive rate (FPR), whereas the detection of 34 photons at the cornea with 60% frequency of seeing was accompanied by a 33% FPR. A new neural-counting model has been developed in the framework of signal-detection theory. It combines Poisson stimulus fluctuations with additive and multiplicative neural noise, both of which are known to be present in the visual system at threshold. The resulting probability-of-detection curves, derived from the Neyman Type-A counting distribution, are in good accord with our experimental frequency-of-seeing data for sensible values of the model parameters. We deduce that, on the average, our four subjects are able to detect a single photon at the retina with 60% frequency of seeing, at the expense of a 55% FPR. In Part 2 of this set of papers [ P. R. Prucnal and M. C. Teich, Biol. Cybern. 43, 87– 96 ( 1982)], we use the normalizing transform, together with probit analysis, to provide improved estimates of threshold parameters, whereas in Part 3 [ M. C. Teich, P. R. Prucnal, G. Vannucci, M. E. Breton, and W. J. McGill, submitted to Biol. Cybern.], we consider the effects of non-Poisson quantum fluctuations.