THEORY OF CONCAVE GRATINGS BASED ON A RECURSIVE DEFINITION OF FACET POSITIONS

A general theory for concave gratings is presented that is based on a recursion formula for the facet positions and that differs from previo us theories that are based on a power-series expansion of the light pa th function. Ln the recursion formula approach the facet positions are determined from a numerical solution for the roots of two constraint functions. Facet positions are determined in sequence, starting from t he grating pole. One constraint function may be chosen to give a stigm atic point. A variety of grating designs are discussed, including a de sign that cannot be generated with the power-series approach. (C) 1996 Optical Society of America