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 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.

RETINAL PROCESSING NEAR ABSOLUTE THRESHOLD: From Behavior to Mechanism

“…Multiplicative noise can explain the observation that the variance of the ganglion cell spike count is greater than the mean [28]. As with the behavioral data, multiplicative noise may help explain why the inferred quantum efficiency of ∼0.15 is lower than the absorptive quantum efficiency of ∼0.3 in cat [17,19,7]. If each photon produces more than one spike, however, multiplicative noise will play a lesser role in limiting sensitivity than Poisson fluctuations in photon absorption.…”

“…Barlow suggested that this discrepancy could originate because the behavioral quantum efficiency can trade for additive Poisson noise when fitting frequency of seeing data with Equation 2 [5]. This is illustrated in Figure 1C, which shows fits to the frequency of seeing data from Teich and colleagues [7] with a quantum efficiency of 0.11. Raising the quantum efficiency increased the threshold by a factor of ∼ 4.5 and the dark light by a factor of ∼ 3 when compared to fits with a quantum efficiency of 0.05 ( Figure 1B).…”

“…Figure 1D shows fits for the frequency of seeing data according to Equation 3. A combination of additive and multiplicative noise allows for a quantum efficiency of 0.2 and relatively low thresholds [20].…”

“…Both behavioral [5,6,7] and physiological [8,9,2] studies have identified conditions under which this requirement is not met and intrinsic noise limits sensitivity. The intrinsic noise has been associated with spontaneous activation of rhodopsin in the rod photoreceptors [5,8,9].…”

Detection Sensitivity and Temporal Resolution of Visual Signals near Absolute Threshold in the Salamander Retina

“…Finally, the sensitivity of human observers (Hecht et al, 1942;Sakitt, 1972) is limited by neural noise whose magnitude is approximately comparable with the measured rate of spontaneous activation of rhodopsin in rods. However, behavioral studies involved significant experimental uncertainty about the number of photons reaching the retina and do not provide a unique estimate of the intrinsic neural noise (Barlow, 1977;Teich et al, 1982;Donner, 1992). Furthermore, physiological estimates of the rate of rhodopsin activation in mammalian rods are themselves subject to considerable uncertainty (Baylor et al, 1984).…”