Discrete matrix model for synthesis of mutual intensity functions

We discuss a discrete matrix formulation of partially coherent light, in which the mutual intensity functions (autocorrelations) are represented by matrices. Based on this representation, we focus-on the problem of obtaining light of a desired mutual intensity from a light source of given mutual intensity, by employing a linear optical system. This problem is quadratic. By singular value decomposition of the mutual intensity matrix, we obtain an equivalent representation which reduces this quadratic problem to a linear one. We then propose the use of fractional Fourier domain filtering circuits to efficiently implement this optical system.