A Model of Human Contrast Sensitivity as a Function of Retinal Illuminance

Abstract

We present a mathematical model for signal transformation by the receptor-horizontal-bipolar cell triad, which gives a good prediction of the spatial-contrast modulation transfer of the visual system at different levels of retinal illuminance. We assume that rod-driven and cone-driven bipolar output signals, s_r and s_c, depend on the mean rates of photoisomerisations in rods and cones, y_r and y_c, and their derivatives, y_r' and y_c', as expressed by the equations s_r=c_ry_r'/(d _ry_r+d_cy_c), and s_c=c_cy_c'/(d_ry_r+d_cy_c), where c_r, c_c, d_r, d_c are constant coefficients. The total output signal is S=s_r+s_c. During scotopic vision s_r >> s_c and spatial frequency characteristics are determined by the rod system. When illumination increases and rods saturate, contrast sensitivity is determined by the cone system. A formula for calculation of the spatial-contrast modulation transfer function is derived with mean illumination as a parameter. The predictions of the model are in good agreement with experimental data measured at various levels of retinal illumination.