Complex signal recovery from multiple fractional Fourier-transform intensities

The problem of recovering a complex signal from the magnitudes of any number of its fractional Fourier transforms at any set of fractional orders is addressed. This problem corresponds to the problem of phase retrieval from the transverse intensity profiles of an optical field at arbitrary locations in an optical system involving arbitrary concatenations of lenses and sections of free space. The dependence of the results on the number of orders, their spread, and the noise is investigated. Generally, increasing the number of orders improves the results, but with diminishing return beyond a certain point. Selecting the measurement planes such that their fractional orders are well separated or spread as much as possible also leads to better results.