Least-squares Fourier phase estimation from the modulo 2r bispectrum phase

The recovery of Fourier phases from measurements of the bispectrum occupies a vital role in many astronomical speckle imaging schemes. In arecent paper [J. Opt. Soc. Am. A 7,14(1990)] it was suggested that a least-squares so-lution to this problem must fail if the bispectrum phase is known only modulo 27r. Here an alternative nonlinear least-squares algorithm is presented that differs from the linear method discussed in the aforementioned paper and that permits the fitting of Fourier phases directly to modulo 27r measurements of the bispectrum phase, thus eliminating any need for phase unwrapping. Numerical simulations of this method confirm that it is reliable and robust in the presence of noise and verify its enhanced performance when compared with a linear least-squares method that includes the unwrapping of the bispectral phase before Fourier phase retrieval. 1