Retinal loss sets a fundamental limit to the variance of visual signals originating from single-photon stimulation

Abstract

Purpose : The uncertainty arising from Poisson statistics of light has until recently precluded the possibility to stimulate the visual system with precise number of photons. Recent studies utilizing a single-photon gun (SPG) postulate that it is possible to produce sub-Poisson signal statistics in retinal rods¹ and in human psychophysics². However, the key prerequisite for these results has remained untested, namely that the loss of single-photon signals in the retina strictly constrains the extent at which biological signal statistics can deviate from Poisson statistics. Now we test the impact of single-photon loss on the variability of visual signals from rods to human psychophysics at the sensitivity limit of vision.

Methods : We stimulated toad (Bufo marinus) retinal rods axially using a state-of-the-art SPG and measured their light-sensitive current using suction pipette technique. We measured the minimum loss of single-photon signals in rods. Finally, we estimated the minimum loss of single-photon signals across the relevant pathway in the primate retina (rod bipolar pathway) to analyze the minimum number of trials required for distinguishing the biological signal distributions originating from a Poisson source or a SPG.

Results : We estimate that the minimum cumulative single-photon loss in rods is 86% (source loss: ~75%, rod loss ~43%), requiring a minimum of ~3 000 trials in optimal conditions for a statistically significant difference between the response distributions arising from a Poisson source or a SPG. The cumulative single-photon loss in human psychophysics experiments even with a lossless SPG was estimated to be ~99.5%, requiring a minimum of > 4 000 000 trials (several months of experiment) and a perfect memory for distinguishability in response distributions between Poisson and SPG stimulation.

Conclusions : We show that due to the loss of single-photon signals it is impossible to distinguish the response distributions originating from Poisson or SPG sources in retinal outputs or at the level of perception on a biologically relevant timescale. Our results require a fundamental re-evaluation of the previous results relying on SPG stimulation and set tight constraints to which extent visual signal statistics can deviate from Poisson statistics at the sensitivity limit.
¹Phan et al. (2014). Phys. Rev. Lett. 112, 213601.
²Tinsley et al. (2016). Nature Communications 7, 12172.

This is a 2020 ARVO Annual Meeting abstract.