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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.