A map transformation is a willful geometrical distortion of an image. Examples are rotation, shearing, and local stretching of the coordinate system. We describe an optical setup that performs a map transformation by spatial filtering with two phase-only filters. The system is able to perform in x- and y-linear distortions (e.g., shears) as well as certain x- and y-nonlinear distortions. The distorting filters introduce no aberrations. The object may radiate coherently, incoherently, or partially coherently. Some experimental results are presented.
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Lohmann et al. (1983) studied this question.