Quantum Concepts in Visual Intensity-Discrimination

Increment thresholds at low intensities considered as signal/noise discriminations

“…The interpretation put on this here is that the internal noise in the visual system becomes the limiting noise when the fluctuations from the background are reduced below a certain point. Mueller (1950) offers an entirely different explanation for it which does not require intrinsic retinal noise and must therefore be carefully considered. He criticizes the formula Alocli for the relation between increment threshold and background intensity on the grounds that it only takes account of the fluctuations of the background (I) and neglects the fluctuations of the stimulus light (I + Al).…”

“…Aguilar & Stiles (1954) found big deviations from the behaviour expected according to fluctuation theory, and their very clear discussion casts some doubts on its usefulness in understanding psychophysical data. Mueller (1950) considered various ways of incorporating quantum concepts in theories of intensity discrimination, and Tanner & Swets (1954) have given a very general treatment of thresholds as signal/noise discrimination problems, but neither piece of work shows close agreemeilt between theoretical predictions and experimental results in the case of differential thresholds. Gregory & Cane (1955) have shown how Weber's law might result from 'neural noise' in the visual pathway, but Weber's law is not a good approximation to the truth at low intensities.…”

Vision

“…While criticizing formulations of intensity discrimination using quantum concepts employing Poisson distributions, Mueller in two papers (83,84) takes a somewhat intermediate position. He agrees that quantum variability found in visual experiments may furnish a baseline upon which all visual mechanisms must be considered to operate but that it is not possible to explain all the data of vision on quantum concepts alone.…”

A simple analyser for nerve-impulse trains

“…The visual and auditory "observers" described above are very different from each other. Weber functions, for example, are not the same: The quantum detector follows the square-root law of de Vries and Rose (Mueller, 1950); the auditory mechanism obeys Weber's Law (Green, 1960). In both cases, however, we have the important result that a simple energy detector does not exhibit Bloch's Law.…”

“…Poisson fluctuations in the number of quanta comprising two flashes (standard and incremented) were analyzed some years ago in a paper by Mueller (1950) that merits more attention than it has received. Mueller's derivation of the approximate distribution of differences leads directly to a square-root reciprocity between increment luminance and duration: A/ • t y2 = k (Pieron's Law).…”