Constructive Model of Object Image Formation in Partially Coherent Light

A constructive theory of the formation of images of one-dimensional binary objects in a partially coherent diffraction-limited projection system with an arbitrary ratio of the angular sizes of the light source and aperture diaphragm is developed. The solution of the two-dimensional problem for such objects can be reduced to a one-dimensional problem, i.e., to calculating the integral in the form of convolution of the object with a generalized aperture response whose spectrum has a tapered profile determined by system parameters. The convolution integral is further subjected to a nonlinear transformation whose level is defined by the ratio of the angular sizes of the source and aperture diaphragm. It is shown that the profile of images formed in partially coherent light is determined by the threshold characteristic of the system that ensures reliable detection of the binary object boundaries. An approximation of this characteristic is proposed. The theory admits a simple physical interpretation of phenomena that occur in partially coherent projection systems.