Optimum balanced wave-front aberrations for radially symmetric amplitude distributions: Generalizations of Zernike polynomials
- 1 June 1980
- journal article
- Published by Optica Publishing Group in Journal of the Optical Society of America
- Vol. 70 (6) , 739-742
- https://doi.org/10.1364/josa.70.000739
Abstract
The Zernike aberration theory for constant amplitude circular apertures is extended to annular apertures having a Gaussian-like radial taper. Explicit expressions are obtained for the optimum balanced wave-front aberrations in terms of shifted Jacobi polynomials. Properties of the polynomials (e.g., Rodrigues formula, recurrence relations, derivatives, etc.) are investigated.Keywords
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