Abstract

This study sheds new light on the stagnation problem troubling the iterative Fourier transform algorithm used for phase retrieval. This is implemented by the introduction of two concepts, the territory and the hole, which exist in a relationship in the sense that the creation and the annihilation of a hole results in the annihilation and the creation of a corresponding territory. These concepts are brought about in the parameter space formed by the set of objects satisfying the object-domain constraints by means of topographical investigations of the minimization process by use of the error-reduction algorithm, paying particular attention to the cases of 2×2 and 3×2 objects with L-shaped supports. The effect of noise contained in the Fourier modulus on the stagnation phenomena is also clarified by use of these concepts.

© 1997 Optical Society of America

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