Model for the Spatial Contrast Sensitivity of the Eye

In the previous chapter, equations were given for the effect of noise on contrast sensitivity. In this chapter, these equations will be used for a model of the spatial contrast sensitivity of the eye. This model is based on the assumption that the contrast sensitivity is mainly determined by the internal noise generated in the visual system. For this model, additional assumptions have to be made about the optical properties of the eye and about the neural processing of the information. In this way, a quantitative description of the contrast sensitivity function will be obtained that also explains the dependence of contrast sensitivity on luminance and field size. The predictions by this model will be compared with a large number of published measurements of the contrast sensitivity. These measurements are usually made at medium and high luminance, which condition is called photopic vision (= daylight vision), but are sometimes also made at low luminance, which condition is called scotopic vision (= night vision). At photopic vision the cones act as photo-receptors, whereas at scotopic vision the rods act as photo-receptors. For practical reasons, the application of the model is restricted to photopic vision. In the model, use will be made of the modulation transfer function or MTF. This function describes the filtering of the modulation by an image forming system as a function of the spatial frequency. The use of an MTF has the advantage that according to the convolution theorem, the MTFs of different parts of an image forming system can simply be multiplied with each other to obtain the total effect on the image. See, for instance, Papoulis (1968, p. 74). The MTF is based on the application of Fourier analysis and can, therefore, only be applied to linear systems. However, as the model is based on threshold signals and the system may be assumed to be linear around the threshold, nonlinearity effects may be neglected. From a comparison of the model with measured data, it appears that this neglect is justified.