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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 20, Iss. 2 — Feb. 1, 2003
  • pp: 209–217

Matrix method to find a new set of Zernike coefficients from an original set when the aperture radius is changed

Charles E. Campbell  »View Author Affiliations


JOSA A, Vol. 20, Issue 2, pp. 209-217 (2003)
http://dx.doi.org/10.1364/JOSAA.20.000209


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Abstract

A matrix method is developed that allows a new set of Zernike coefficients that describe a surface or wave front appropriate for a new aperture size to be found from an original set of Zernike coefficients that describe the same surface or wave front but use a different aperture size. The new set of coefficients, arranged as elements of a vector, is formed by multiplying the original set of coefficients, also arranged as elements of a vector, by a conversion matrix formed from powers of the ratio of the new to the original aperture and elements of a matrix that forms the weighting coefficients of the radial Zernike polynomial functions. In developing the method, a new matrix method for expressing Zernike polynomial functions is introduced and used. An algorithm is given for creating the conversion matrix along with computer code to implement the algorithm.

© 2003 Optical Society of America

OCIS Codes
(000.3870) General : Mathematics
(220.1010) Optical design and fabrication : Aberrations (global)
(330.4460) Vision, color, and visual optics : Ophthalmic optics and devices

History
Original Manuscript: June 18, 2002
Revised Manuscript: August 26, 2002
Manuscript Accepted: August 26, 2002
Published: February 1, 2003

Citation
Charles E. Campbell, "Matrix method to find a new set of Zernike coefficients from an original set when the aperture radius is changed," J. Opt. Soc. Am. A 20, 209-217 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-2-209

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