Bz. Dong et al., NUMERICAL INVESTIGATION OF PHASE RETRIEVAL IN A FRACTIONAL FOURIER-TRANSFORM, Journal of the Optical Society of America. A, Optics, image science,and vision., 14(10), 1997, pp. 2709-2714
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.