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Models are developed and evaluated that are able to describe the response of blowfly photoreceptor cells to natural time series of intensities. Evaluation of the models is performed using an information theoretical technique that evaluates the performance of the models in terms of a coherence function and a derived coherence rate (in bit/s). Performance is gauged against a maximum expected coherence rate determined from the repeatability of the response to the same stimulus. The best model performs close to this maximum performance, and consists of a cascade of two divisive feedback loops followed by a static nonlinearity. The first feedback loop is fast, effectively compressing fast and large transients in the stimulus. The second feedback loop also contains slow components, and is responsible for slow adaptation in the photoreceptor in response to large steps in intensity. Any remaining peaks that would drive the photoreceptor out of its dynamic range are handled by the final compressive nonlinearity.

Abstract. We present an analytical ideal observer model to predict discrimination thresholds for stimuli that are processed by arrays of noise-perturbed receptors that have smooth and overlapping tuning functions. We show that hyperacuity phenomena are natural properties of these systems. A comparison of thresholds for a number of discrimination tasks allows a psychophysically derived estimate of parameters of the receptor array involved. We note the consistency of this scheme with data from a number of visual subfields.

A model is presented for the early (retinal) stages of temporal processing of light inputs in the visual system. The model consists of a sequence of three adaptation processes, with two instantaneous nonlinearities in between. The three adaptation processes are, in order of processing of the light input: a divisive light adaptation, a subtractive light adaptation, and a contrast gain control. Divisive light adaptation is modeled by two gain controls. The first of these is a fast feedback loop with square-root behavior, the second a slow feedback loop with logarithm-like behavior. This can explain several aspects of the temporal behavior of photoreceptor outputs. Subtractive light adaptation is modeled by a high-pass filter equivalent to a fractional differentiation, and it can explain the attenuation of low frequencies observed in ganglion cell responses. Contrast gain control in the model is fast (Victor, 1987), and can explain the decreased detectability of test signals that are superimposed on dynamic backgrounds. We determine psychophysical detection thresholds for brief test pulses that are presented on flickering backgrounds, for a wide range of temporal modulation frequencies of these backgrounds. The model can explain the psychophysical data for the full range of modulation frequencies tested, as well as detection thresholds obtained for test pulses on backgrounds with increment and decrement steps in intensity.

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