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
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.
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 ?!?!
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().