Zernike Polynomial Coefficients for a given Wavefront using Matrix Inversion in Matlab

Calculation of Zernike Polynomial Coefficients for a given Wavefront using Matrix Inversion

Represent a wavefront as a sum of Zernike polynomials using a matrix inversion.
This function attempts to solve the a_i's in equation, phi(rho,theta) = SUM(a_i * Z_i(rho,theta), i=1 to M),
where the Z_i(rho,theta)'s are the Zernike polynomials from the zernfun.m file, phi is the wavefront to be represented as a sum of Zernike polynomials, the a_i's are the Zernike coefficients, and M is the number of Zernike polynomials to use.
Input: phi - Phase to be represented as a sum of Zernike polynomials that must be an nXn array (square)
(optional) M - Number of Zernike polynomials to use (Default = 12)
Output: a - Zernike coefficients (a_i's) as a vector Note: zernfun.m is required for use with this file. It is available here: http://www.mathworks.com/matlabcentral/fileexchange/7687