SUPPRESSION OF THE INFLUENCE OF NOISE IN LEAST-SQUARES PHASE ESTIMATION FROM THE PHASE DIFFERENCE

We improve the estimation of the index of the rotational source presented in our previous paper [J. Opt. Soc. Am. A 5, 416 (1988)] for the purpose of extending the applicability of extended least-squares phase estimation (ELPE) from the measured phase difference to larger levels of noise. To this end, a multienclosure estimation method is proposed. For suppressing the influence of noise on the estimation of the index, this method makes use of some of the minimum enclosures in the vicinity of the minimum enclosure encircling the index to be estimated. Computer simulations suggest that, to obtain the best result, one should utilize the four adjoining minimum enclosures. For an object without ir discontinuity in its Fourier phase, a more effective estimation can be achieved by combining our multienclosure estimation method and the single-enclosure estimation method presented in our previous paper. Computer simulations show that, when the proposed methods are used, ELPE contributes to large improvements in the phase retrieval and, as a result, in the reconstruction of the object, as well. © 1990 Optical Society of America.