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Zernike decomposition

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Zernike decomposition

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10 Dec 2007 (Updated )

Decomposition of a 2-D function by set of Zernike functions

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Description

This code was written to deal with "Zernike polynomials" code graciously donated by Paul Fricker via file exchange.
Here you will find a practical example of a function decomposition by
Zernike basis.
The function is F below, feel free to modify
Unlike Paul's example found in 'zernfun2.m' here the domain is the true unit circle, without NaN's filling it up to the unit square.
You will have to download Paul's functions to run this code.

Acknowledgements

Zernike Polynomials inspired this file.

MATLAB release MATLAB 7.5 (R2007b)
Other requirements Code ID#7687 by Paul Fricker
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Comments and Ratings (8)
07 Apr 2014 Alexander

Thank you for sharing, Alex. Good means for quick and robust illustration of Zernike decomposition.

09 Nov 2012 Francesco

I'm using this code to decompose a wave aberration function. I'm experiencing a problem with the decomposition. Why if I try to expand a function like
F = A*r^4
where A is constant, I get 2 non-negative coefficients: not only the coefficient corresponding to spherical aberrations but also that one who correspond to Field Curvature ?!?!
thanks

16 Jul 2010 Eric

This is an extraordinarily slow way of fitting Zernike coefficients. See "Wavefront fitting with discrete orthogonal polynomials in a unit radius circle" by Malacara, et al, in Optical Engineering, Vol 29, No 6, pages 672-675 for a much more efficient, least-squares approach. You can speed the decomposition up significantly by using linear algebra functions rather than interp2() and dblquad().

13 Nov 2009 Alex Kararg

Any idea if there is a Matlab code for decomposing a 3D shape to Zernike descriptors? Thanks!

31 Dec 2008 Shalin Mehta

This is a good code for illustrating the idea of Zernike decomposition

18 Sep 2008 Xame Earnest

This helps, thanks!

19 May 2008 aaaa bbbb

Very well done, thanks!

03 Jan 2008 Greg Noder

Thank you, runs smoothly.

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