A method to solve the phase-retrieval problem from two intensities observed at the Fourier transform of an object function in one dimension is proposed. This method involves the solution of the linear equations consisting of the data of two intensities, obtained with and without an exponential filter at the object plane, and unknown coefficients in the Fourier series expansion of phase. There is no need to treat the nonlinear equation for zero location in the complex plane. The usefulness of the method is shown in computer simulation studies of the reconstruction of the one-dimensional phase object from the observable moduli at the Fourier-transform plane of the object.
© 1987 Optical Society of America
Original Manuscript: April 4, 1986
Manuscript Accepted: August 22, 1986
Published: January 1, 1987
N. Nakajima, "Phase retrieval from two intensity measurements using the Fourier series expansion," J. Opt. Soc. Am. A 4, 154-158 (1987)