Noise recorded in visual neurons, or variability
in psychophysical experiments, may be quantified in terms
of quantal fluctuations from an “equivalent”
steady illumination. The conversion requires assumptions
concerning how photon signals are pooled in space and time,
i.e. how to pass from light fluxes to numbers
of photon events relevant to the Poisson statistics describing
signal/noise. It is usual to approximate 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]) by sharp-bordered apertures of “complete,”
equal-weight summation of events. Apertures based on signal-equivalence
cannot provide noise-equivalence, however, because
greater numbers of events summed with smaller 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- than for signal-equivalence.
We here consider the difference for some commonly encountered
RF and IR profiles. Summation areas, expressed
as numbers of photoreceptors (cones or rods) contributing
with equal weight, are denoted NS
for signal and NN
for noise; sharply delimited summation times are
correspondingly denoted tS
and tN. We show that
the relation in space is NN
= 0.5NS for the Gaussian distribution (e.g.
for the RF center mechanism of retinal ganglion cells).
For a photoreceptor in an electrically coupled network
the difference is even larger, e.g., for rods in the toad
retina NN = 0.2NS
(NS = 13.7 rods and NN
= 2.8 rods). In time, the relation is tN ≈ 0.7tS for realistic
quantal response waveforms of photoreceptors. The surround
input in a difference-of-Gaussians RF may either decrease
or increase total noise, depending on the degree of correlation
of center and surround noise. We introduce a third useful
definition of sharp-bordered summation apertures: one that
provides the same signal-to-noise ratio (SNR) for large-long
stimuli as the real integration profiles. The SNR-equivalent
summation area is N*
= NS 2/NN and summation time t* = tS2/tN.
