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

Journal of the Optical Society of America A
 Pub Date:
 February 2003
 DOI:
 10.1364/JOSAA.20.000209
 Bibcode:
 2003JOSAA..20..209C
 Keywords:

 eye;
 aberrations;
 vision defects;
 matrix algebra;
 Zernike polynomials