A ray representing a vector wave is traced through an optical system. The electric field perpendicular to the (ray) direction of propagation is represented by a Jones vector. At each surface the results of a thin-film calculation are used to form a "surface" Jones matrix. For a given ray, a product of surface Jones matrices forms an "instrumental" ray matrix. Coordinate frames and sign conventions are emphasized.
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Eugène Waluschka (1989) studied this question.
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