Zernike polynomials and aberration balancing

Virendra N Mahajan

doi:10.1117/12.511384

3 November 2003 Zernike polynomials and aberration balancing

Virendra N Mahajan

Proceedings Volume 5173, Current Developments in Lens Design and Optical Engineering IV; 517302 (2003) https://doi.org/10.1117/12.511384
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

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.

Citation Download Citation

Virendra N Mahajan "Zernike polynomials and aberration balancing", Proc. SPIE 5173, Current Developments in Lens Design and Optical Engineering IV, 517302 (3 November 2003); https://doi.org/10.1117/12.511384

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