Complex signal recovery from two fractional Fourier transform intensities: order and noise dependence

Cataloged from PDF version of article.The problem of recovering a complex signal from the magnitudes of two of its fractional Fourier transforms is addressed. This corresponds to phase retrieval from the transverse intensity profiles of an optical field at two arbitrary locations along the optical axis. The convergence of the iterative algorithm, the effects of noise or measurement errors, and their dependence on the fractional transform order are investigated. It is observed that in general, better results are obtained when the fractional transform order is close to unity and poorer results are obtained when the order is close to zero. It follows that to the extent that conditions allow, the fractional order between the two measurement planes should be chosen as close to unity (or other odd integer) as possible for best results. (C) 2004 Elsevier B.V. All rights reserved

Complex signal recovery from multiple fractional Fourier-transform intensities

Cataloged from PDF version of article.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. (c) 2005 Optical Society of Americ

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. © 2005 Optical Society of America

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