Quantum efficiency and false positive rate

Abstract

1. This paper presents an analysis of the efficiency of performance at the absolute threshold of human vision. The data are from the same series as the previous papers (Hallett, 1969b, c) and consist of frequency-of-seeing curves, thresholds, false positive rates and equivalent background measurements, accumulated as small samples over a number of days.2. Quantum efficiency is defined here as the ratio of the thresholds of an ideal and a real detector performing the same task with the same sampling error. This avoids the problem as to whether the frequency-of-seeing curve of the real detector is exactly a Poisson sum or not.3. The long-term quantum efficiency can be low (about 0.04) as a result of drifts in the mean threshold.4. The average short-term quantum efficiency is in the region of 0.1, which is roughly the physiological limit set by Rushton's (1956b) measurements of rhodopsin density in the living rods. If this is correct, then the absorption of a quantum, and not the bleaching of a rhodopsin molecule, is sufficient for the generation of a neural event.5. Application of a simple signal/noise theory to the data gives solutions close to those suggested by Barlow (1956) and shows that false positives almost invariably arise from errors subsequent to the signal/noise decision process.