We develop a phase-space representation (termed phase-space imager) suitable for analysis and design of imaging systems that use large illumination apertures (partially coherent illumination). The representation, developed from the transmission cross-coefficient model, falls in the general Cohen class of distributions and elegantly captures the bilinear nature of image formation in partially coherent systems. It uses only the requisite number of dimensions and leads to an efficient algorithm for calculating images. Computed partially coherent images of a double slit and a two-dimensional sinusoidal spoke are presented.
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