Solving the phase-retrieval problem of a complex signal in the fractional Fourier domain by nonlinear least-squares

From the viewpoint of unconstrained optimization the phase-retrieval problem of a 1D complex signal in the fractional Fourier domain is formulated as a nonlinear least-squares problem. A definition of the discrete fractional Fourier transform (DFRFT) constructed by a discrete Hermite-Gaussian function is adopted here. The ill-posedness of the problem is stressed, and the Levenberg-Marquardt algorithm of More's form is used to solve it. In contrast to many published references, this method can reconstruct the phase accurately from the amplitude of the original signal and the one of its DFRFT at any order in the interval (0, 2). For amplitudes with low-level noise this method also works well. (C) 2008 Optical Society of America.