Different types of nonredundant sampling patterns are shown to guarantee completeness of the basis formed by the sampled partial derivatives of Zernike polynomials, commonly used to reconstruct the wavefront from its slopes (wavefront sensing). In the ideal noise-free case, this enables one to recover double the number of modes J than sampling points I (critical sampling ). With real data, noise amplification makes the optimal number of modes lower . Our computer simulations show that optimized nonredundant sampling provides a significant improvement of wavefront reconstructions, with the number of modes recovered about 2.5 higher than with standard sampling patterns.
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