Comparison of B-spline and Zernike fitting techniques in complex wavefront surfaces

Zernike polynomial fitting has been the commonplace alternative for assigning a measured wavefront a given shape. However, Zernike polynomials have intrinsic limitations under given conditions, mainly in complex wavefronts with for instance decentered double-peaks or with relevant undulations. The main goal of this paper is analyzing an alternative to Zernike fitting based in B-Spline fitting, comparing the strengths and weaknesses of each representation when applied to wavefront fitting. Simple and complex wavefront cases will be presented and studied, and the quality of their fitted representations using Zernike and B-Spline polynomials will be compared, presenting the main factors relevant in their comparison. Moreover, the case of random white noise added to the estimated data will allow an insight into the expected behavior of both representations when applied to experimental data.