Estimation of interferogram aberration coefficients using wavelet bases and Zernike polynomials

This paper combines the use of wavelet decompositions and Zernike polynomial approximations to extract aberration coefficients associated to an interferogram. Zernike polynomials are well known to represent aberration components 12 of a wave-front. Polynomial approximation properties on a discrete mesh after an orthogonalization process via Gram-Schmidt decompositions are very useful to straightforward estimate aberration coefficients(13). It is shown that decomposition of interferograms into wavelet domains 14 can reduce the number of computations without a significant effect on the estimated aberration coefficients amplitudes if full size interferograms were considered. Haar wavelets because of their non-overlapping and time localization properties appear to be well suited for this application. Aberration coefficients can be computed from multi resolution decompositions schemes and 2-D Zernike polynomial approximations on coarser scales, providing the means to reduce computational complexity on such calculations.