Optical data-processing systems in which the vectorial nature of light has to be taken into account can be described adequately by a theory in which the point spread is a tensor. The well-known scalar theory and the Jones calculus are, as special cases, both incorporated into this theory. Some basic properties and restrictions that can be imposed upon the optical system will be introduced. A general reciprocity relation will be derived, and the restriction that the reciprocity relation imposes upon the optical system will be discussed. This discussion leads to the remarkable conclusion that a reciprocal optical system neither can be described exactly in terms of a scalar theory nor by a Jones matrix with constant coefficients.
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