Two-dimensional phase retrieval using the logarithmic Hilbert transform and the estimation technique of zero information
- 14 March 1986
- journal article
- Published by IOP Publishing in Journal of Physics D: Applied Physics
- Vol. 19 (3) , 319-331
- https://doi.org/10.1088/0022-3727/19/3/005
Abstract
This paper studies the two-dimensional phase retrieval problem based on the theory of entire functions. A method to retrieve the two-dimensional phase distribution from the observed moduli is proposed by utilising the mathematical properties of entire functions. This method consists of the logarithmic Hilbert transform in one dimension and the estimation technique for the influence of zeros in the complex lower half-plane. The usefulness of the method is shown in a computer simulation study of the reconstruction of the two-dimensional real and positive object from the observable moduli at the Fourier transform plane of the object.Keywords
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