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Radially symmetric pupil plane phase retardation functions are derived that extend focal depth and alleviate third-order spherical aberration (SA) effects. The radial symmetry of these functions means that they can be more conveniently manufactured by use of traditional techniques such as diamond machining than previously reported filters with rectangular symmetry. The method employs minimization of the variation of Strehl ratio with defocus, W20, and SA, W40. The performance of the derived phase filters is illustrated by comparison with standard optical systems and with previously reported phase filters.

Phase pupil functions for reduction of defocus and spherical aberrations