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Proceedings Paper

Zernike polynomials and aberration balancing
Author(s): Virendra N Mahajan
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Paper Abstract

For small aberrations, the Strehl ratio of an imaging system depends on the aberration variance. If the aberration function is expanded in terms of a complete set of polynomials that are orthogonal over the system aperture, then the variance is given by the sum of the square of the aberration coefficients. One such set is that of Zernike polynomials, which are orthogonal over a circular pupil. Its advantage lies in the fact that Zernike polynomials can be identified with the classical aberrations that are balanced to yield minimum variance, and thus a maximum Strehl ratio. We discuss classical aberrations, balanced aberrations, and Zernike polynomials for systems with circular pupils. How these polynomials change for an annular or a Gaussian pupil are also discussed.

Paper Details

Date Published: 3 November 2003
PDF: 17 pages
Proc. SPIE 5173, Current Developments in Lens Design and Optical Engineering IV, 517302 (3 November 2003); doi: 10.1117/12.511384
Show Author Affiliations
Virendra N Mahajan, The Aerospace Corp. (United States)

Published in SPIE Proceedings Vol. 5173:
Current Developments in Lens Design and Optical Engineering IV
Pantazis Z. Mouroulis; Warren J. Smith; R. Barry Johnson, Editor(s)

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