Modelling the increase of contrast sensitivity with grating area and exposure time.

We extended the contrast detection model of human vision to temporal integration by taking into account the effect of exposure duration on contrast sensitivity for stationary gratings. The extended model thus comprised: (i) low-pass filtering due to the optical modulation transfer function of the eye; (ii) high-pass filtering (lateral inhibition) due to the neural modulation transfer function of the visual pathways; (iii) addition of internal neural noise; and (iv) detection by a local matched filter whose efficiency for gratings decreased with increasing area and exposure duration. To test the model we measured binocular contrast sensitivity in foveal photopic vision as a function of exposure duration and area for sinusoidal gratings with equiluminous surround at spatial frequencies of 0.25-16 c/deg. In agreement with the model, contrast sensitivity at all grating areas first increased in proportion to square root of t when exposure duration (t) was shorter than critical duration. Thereafter the increase saturated and contrast sensitivity became independent of exposure time. Critical exposure duration was found to be independent of grating area but increased with spatial frequency. Similarly, at all exposure durations contrast sensitivity first increased in proportion to square root of A when grating area (A) was smaller than critical area. Thereafter the increase saturated and contrast sensitivity became independent of area. Critical area was found to be independent of exposure duration but decreased with increasing spatial frequency. The extended model explained 95-97% of the total variance of our contrast sensitivity data at the spatial frequencies studied. Our results also mean that spatial and temporal integration processes are mutually independent and thus area and time are separable variables in the detection of stationary gratings.