The problem of wave-front estimation from wave-front slope measurements has been examined from a least-squares curve fitting model point of view. It is shown that the slope measurement sampling geometry influences the model selection for the phase estimation. Successive over-relaxation (SOR) is employed to numerically solve the exact zonal phase estimation problem. A new zonal phase gradient model is introduced and its error propagator, which relates the mean-square wavefront error to the noisy slope measurements, has been compared with two previously used models. A technique for the rapid extraction of phase aperture functions is presented. Error propagation properties for modal estimation are evaluated and compared with zonal estimation results.

© 1980 Optical Society of America

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