The Question of Phase Retrieval in Optics
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It is generally asserted that valuable phase information is irretrievably lost in the squaring operation required to obtain the intensity from the amplitude distribution in the image of a star formed by a lens. In this paper the phase reconstruction is studied under the constraint that the aperture of the lens be finite. It is shown that in some cases the phase reconstruction is unique; and that in other cases there is finite or denumerable infinite number of discrete solutions. Conversely, it is proved that every non-negative function that is integrable and band-limited can be realized as the intensity distribution in the image of a star formed by a lens.
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