NUMERICAL INVESTIGATION OF PHASE RETRIEVAL IN A FRACTIONAL FOURIER-TRANSFORM

Recently the combination of the Gerchberg-Saxton (GS) algorithm and a fractional Fourier transform was proposed to implement beam shaping in the fractional Fourier domain [Zalevsky et al., Opt. Lett. 21, 842 (1 996)]. We generalize this idea to deal with the problem of phase retri eval from two intensity measurements in a fractional Fourier transform system. The relevant equations for determining the unknown phases are derived, based on the general theory of amplitude-phase retrieval in an optical system. The unitarity condition of the fractional Fourier t ransform in a practical optical system with finite aperture is discuss ed. For different fractional orders P, the phase retrieval of several typical model images is studied in detail. A comparison of the GS and our algorithms is given, based on numerical simulations. It follows th at our algorithm can offer the desired phase in all cases considered. However, the GS algorithm may fail when the transform system is nonuni tary. (C) 1997 Optical Society of America.