Abstract

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 Moré’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.

© 2008 Optical Society of America

Recursive algorithm for phase retrieval in the fractional Fourier transform domain

Wen-Xiang Cong, Nan-Xian Chen, and Ben-Yuan Gu
Appl. Opt. 37(29) 6906-6910 (1998)

Quantitative phase retrieval of a complex-valued object using variable function orders in the fractional Fourier domain

Wen Chen and Xudong Chen
Opt. Express 18(13) 13536-13541 (2010)

Efficient computation of joint fractional Fourier domain signal representation

Lutfiye Durak, Ahmet Kemal Özdemir, and Orhan Arikan
J. Opt. Soc. Am. A 25(3) 765-772 (2008)

Fractional Fourier domain optical image hiding using phase retrieval algorithm based on iterative nonlinear double random phase encoding

Xiaogang Wang, Wen Chen, and Xudong Chen
Opt. Express 22(19) 22981-22995 (2014)

Improved discrete fractional Fourier transform

Soo-Chang Pei and Min-Hung Yeh
Opt. Lett. 22(14) 1047-1049 (1997)