Abstract
This paper presents a physiological math model which predicts the liminal contrast required to detect a target as a function of target size, background brightness and exposure time. The model is based on the premise that target detection occurs when the difference in response of cells across a target/background brightness contour is greater than some threshold. This premise is supported by recent physiological and psycho-physical measurements.
A logical “wiring diagram” for the retina is conceived which resembles the actual anatomy of the retina. The photo-receptor cells, bipolar cells and ganglion cells in the model are given simple mathematical response functions. The target detection requirement for a minimum threshold response difference across a contour is used to develop a mathematical expression of threshold target brightness as a function of background brightness. There are two major parameters in the expression for threshold target brightness: 1) Photo-receptor sensitivity to incident luminance, 2) The threshold response difference required for target detection. The expression for threshold target brightness fits the experimental data well.
The model is expanded to explain the variation of the sensitivity and threshold parameters with target size and exposure time. The resulting model is self-consistent and closely agrees with the experimental data for background luminance levels of less than one foot lambert and exposure times less than .1 sec.
The results presented in this paper indicate that a coupling of psycho-physical measurements with physiological and anatomical findings leads to both a greater understanding of the physiological processes involved and a more powerful formulation of the psycho-physical results.
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