A formulation of light beam propagation through any complex optical system that can be described by an ABCD ray-transfer matrix will be given. Within the framework of complex ABCD-optical systems, the optical set-up itself is approximated, primarily by replacing all apertures with soft apertures having a Gaussian intensity transmission function, whereby a new matrix - now complex -can be added to the well-known suite of real-valued matrices, cf. Eq. 1.
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