Analytic formulas for the variance of an aberration of arbitrary order over a specified exit pupil with either uniform or untruncated Gaussian weighting are derived, and closed-form solutions are presented for the actual Strehl ratio of an untruncated Gaussian-beam system suffering from a primary aberration, except in the case of coma, for which an integral solution is given. These formulas are valid for an arbitrary magitude of the given primary aberration. It is shown that the aberration variance and Strehl ratio solutions for untruncated Gaussian-beam illumination depend on a reference-radius to beam-radius ratio, and judicious choice of this ratio allows one to apply the results of Strehl ratio calculations for uniformly illuminated systems to untruncated Gaussian-beam systems.
© 1985 Optical Society of America
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