Abstract

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

Full Article  |  PDF Article
Related Articles
Holographic interferometry and the fractional Fourier transformation

John T. Sheridan and Robert Patten
Opt. Lett. 25(7) 448-450 (2000)

Extended fractional Fourier transforms

Jianwen Hua, Liren Liu, and Guoqiang Li
J. Opt. Soc. Am. A 14(12) 3316-3322 (1997)

Chirp filtering in the fractional Fourier domain

Rainer G. Dorsch, Adolf W. Lohmann, Yigal Bitran, David Mendlovic, and Haldun M. Ozaktas
Appl. Opt. 33(32) 7599-7602 (1994)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (3)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (4)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription