It is shown that a priori knowledge of the edges of an object is not sufficient to ensure that it can be uniquely reconstructed from the modulus of its Fourier transform (or from its autocorrelation function). Furthermore, even in those cases for which the ultimate solution is unique, in intermediate steps in the solution by the recursive Hayes–Quatieri algorithm there can be ambiguities. An extension of the recursive algorithm that finds the solution (or solutions) is suggested, and it is shown that the recursive method can be applied to complex-valued objects.
© 1986 Optical Society of America
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