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Compute Zernike polynomials and coefficients of a Zernike fit with mutually consistent functions.

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Zernike polynomials are orthogonal on the unit circle and are commonly used in optics for phase aberrations.

  Use zernike_fcn3.m to generate Zernike polynomials. Input includes a vector of the desired polynomials; these do not have to be consecutive. Possible polynomial orderings include:
  'noll' = Bob Noll's original ordering
  'fringe' = Univ. of Arizona Zernike set
  'original'= original order of zernfun.m
  'default' = the 'fringe' (UofA) set + more terms
zernike_fcn3.m does consistency checking, selects the appropriate m & n values for a particular ordering and then calls zernfun.m to generate the polynomials.

  Use zernike_coeffs3.m to fit Zernike polynomial to an input function. Since zernike_coeffs3.m calls zernike_fcn3.m, these files are automatically consistent with each other, unlike some previous functions.


Zernike Polynomials and Zernike Polynomial Coefficients For A Given Wavefront Using Matrix Inversion In Matlab inspired this file.

MATLAB release MATLAB 7.10 (R2010a)
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Comments and Ratings (3)
28 Dec 2016 Zeng Zhen

25 Aug 2015 David Marx

I think the ordering for Noll ordered Zernike polynomials in Zernike_fcn3 is incorrect. All the even order terms have the sin and cos terms reversed compared to Noll's paper and also compared to the Zemax manual.

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23 Dec 2010 Robin Martin


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