Modelling contrast sensitivity as a function of retinal illuminance and grating area

We extended the contrast detection model of human vision [Rovamo, Luntinen & Näsänen (1993b) Vision Research, 33, 2773-2788] to low light levels by taking into account the effect of light-dependent quantal noise. The extended model comprises (i) low-pass filtering due to the optical modulation transfer function of the eye, (ii) addition of light-dependent noise at the event of quantal absorption, (iii) high-pass filtering of neural origin (lateral inhibition), (iv) addition of internal neural noise, and (v) detection by a local matched filter whose efficiency decreases with increasing grating area. To test the model we measured foveal contrast sensitivity as a function of retinal illuminance and grating area at spatial frequencies of 0.125-32 c/deg. In agreement with the model, monocular contrast sensitivity at all grating areas increased in proportion to I when retinal illuminance (I) was smaller than critical illuminance. Thereafter the increase saturated and contrast sensitivity became independent of retinal illuminance. Similarly, at all levels of retinal illuminance contrast sensitivity increased in proportion to A when grating area (A) was smaller than critical area. Thereafter the increase saturated and contrast sensitivity became independent of area. Critical level of retinal illuminance increased in proportion to the spatial frequency squared. Critical area marking the saturation of spatial integration was constant at low spatial frequencies but decreased in inverse proportion to spatial frequency squared at medium and high spatial frequencies. The maximum contrast sensitivity obtainable by spatial integration in bright light increased at low spatial frequencies in proportion to spatial frequency, was constant at medium spatial frequencies, and decreased in inverse proportion to spatial frequency cubed at high spatial frequencies. The increase was due to the neural modulation transfer function of the visual pathways whereas the decrease was due to the optical modulation transfer function of the eye. The model explained 91-99% of the total variance of our contrast sensitivity data at various spatial frequencies.