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A method is presented that expands the scheme of physical optics propagation beyond the Fresnel approximation to include beams that are nonparaxial. The formalism retains most of the calculation advantages of the Fresnel approach; i.e., it is based on a single Fourier transform step. The kernel of the new transformation is no longer separable in Cartesian coordinates; thus the formalism can account for astigmatic coupling effects originating purely from diffraction. The validity limits of the proposed algorithm are explored. Analytical expressions, numerical simulation results, and experimental data are compared.
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Engelberg et al. (2004) studied this question.
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