Abstract
Based on the special affine Fourier transformation (SAFT), which is an extension of the fractional Fourier transformation, the small deviations from the perfect optical operations on wave functions are treated in a unified way. As simple and instructive examples, the almost-Fourier and almost-Fresnel transformations are constructed explicitly. The present investigation shows transformations which include the small imperfections of optical instruments can be developed within the framework of linear theory.
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