Two phase retrieval methods are used for the reconstruction of a 2-D object function from its. Fourier transformed moduli obtained with and without an exponential filter at the object plane. One of the methods is a phase retrieval method using only the Fourier series expansion, and the other is a phase retrieval method using the logarithmic Hilbert transform and the Fourier series expansion. These methods extend the range that successful reconstructions of 2-D objects can be obtained by making use of the properties of entire functions of the exponential type. The usefulness of these methods is shown in computer simulation studies of the reconstructions of 2-D real and phase objects from their Fourier moduli.
© 1989 Optical Society of America
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