Zernike decomposition

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

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

The author wishes to acknowledge the following in the creation of this submission:
Zernike polynomials

• MATLAB release: MATLAB 7.5 (R2007b)
• Other requirements: Code ID#7687 by Paul Fricker

[Greg Noder]

Thank you, runs smoothly.

[aaaa bbbb]

Very well done, thanks!

[Xame Earnest]

This helps, thanks!

[Shalin Mehta]

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

[Alex Kararg]

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

[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().