5 December 2001 Estimation of interferogram aberration coefficients using wavelet bases and Zernike polynomials
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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 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. It is shown that decomposition of interferograms into wavelet domains 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.
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Alfredo A. Elias-Juarez, Alfredo A. Elias-Juarez, Noe Razo-Razo, Noe Razo-Razo, Miguel Torres-Cisneros, Miguel Torres-Cisneros, } "Estimation of interferogram aberration coefficients using wavelet bases and Zernike polynomials", Proc. SPIE 4478, Wavelets: Applications in Signal and Image Processing IX, (5 December 2001); doi: 10.1117/12.449733; https://doi.org/10.1117/12.449733

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