Cylindrical and spherical gratings

Abstract
An approximate expression for the aberrations of a spheroidal grating in a near-Rowland-circle mounting is developed using Fermat’s theorem. Its validity is tested by use of an unexpanded, exact, geometric expression of Fermat’s condition. The special cases of a cylindrical and a spherical grating are compared and the cylindrical grating is shown to give superior resolution under some conditions.

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