Previously it was shown that one can solve the phase-retrieval problem from two intensities observed at the Fourier-transform plane of an object in one dimension by using the Fourier-series expansion. In this paper, an improved method using the logarithmic Hilbert transform and the Fourier series expansion is proposed. It is proved from the distribution of zeros in the complex plane that the Fourier-transform phase of Hermitian object functions cannot be retrieved by using the previous method but can be retrieved by using the method in this paper. The results reconstructed by the present method are also shown in computer simulations.
© 1988 Optical Society of America
N. Nakajima, "Phase retrieval using the logarithmic Hilbert transform and the Fourier-series expansion," J. Opt. Soc. Am. A 5, 257-262 (1988)