Generalized grating ray-tracing equations

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Abstract
A vector method has been developed for tracing rays through gratings formed by (i) the intersection of a surface with parallel planes, (ii) the intersection of a surface with concentric cylinders, and (iii) holographic means. The equations are in a form that prevent indeterminancy due to unusual ray-surface intersection points, and arbitrary orientation of the ruling direction is permitted. A special provision permits the inclusion of ruling errors into the ray trace, if required.

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