Mathematical expressions derived for the primary aberrations of a thin, flat Fresnel lens (grooved on both surfaces, in general) as functions of the constructional parameters are convenient for the analytic design of optical systems containing one or more Fresnel lenses. In general. such systems have five primary monochromatic aberrations of the Seidel type plus a sixth that is identically zero for ordinary lenses. The new aberration (called line coma to distinguish it from ordinary circular coma) bears the same relation to sagittal and tangential coma that Petzval curvature bears to sagittal and tangential astigmatism. Moreover line coma is independent of stop position, whereas Petzval curvature varies with stop position unless the line coma is corrected. The primary chromatic aberrations and the aberration contributions of Fresnel aspherics are the same as for ordinary lenses. Specific applications of the theory are discussed.
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