Summation of Quantal Noise in Space and Time

Noise in visual neurons, or variability in psychophysical experiments, may be quantified in terms of photon fluctuations from an ‘equivalent’ steady illumination. The conversion requires assumptions on how photon signals are pooled in space and time, ie how to pass from the light flux to the numbers of photon events relevant to the Poisson statistics describing signal/noise. Real weighting profiles for the integration of photon events in space and time [the sensitivity distribution of the receptive field (RF) and the waveform of the impulse response (IR)] are commonly approximated by sharp-bordered apertures of ‘complete’, equal-weight summation of events. Such apertures based on signal equivalence cannot provide noise equivalence, however, because greater numbers of events summed with lower weights (as in reality) have lower variances than smaller numbers summed with full weight. Thus sharp-bordered apertures are necessarily smaller if defined for noise equivalence rather than for ...