Matrix method to find a new set of Zernike coefficients from an original set when the aperture radius is changed
- 1 February 2003
- journal article
- Published by Optica Publishing Group in Journal of the Optical Society of America A
- Vol. 20 (2) , 209-217
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.Keywords
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