OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 20, Iss. 6 — Jun. 1, 2003
  • pp: 1046–1049

Phase reconstruction from intensity measurements in linear systems

Martin J. Bastiaans and Kurt Bernardo Wolf  »View Author Affiliations

JOSA A, Vol. 20, Issue 6, pp. 1046-1049 (2003)

View Full Text Article

Enhanced HTML    Acrobat PDF (123 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The phase of a signal at a plane is reconstructed from the intensity profiles at two close parallel screens connected by a small abcd canonical transform; this applies to propagation along harmonic and repulsive fibers and in free media. We analyze the relationship between the local spatial frequency (the signal phase derivative) and the derivative of the squared modulus of the signal under a one-parameter canonical transform with respect to the parameter. We thus generalize to all linear systems the results that have been obtained separately for Fresnel and fractional Fourier transforms.

© 2003 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(100.5070) Image processing : Phase retrieval

Original Manuscript: November 25, 2002
Revised Manuscript: February 13, 2003
Manuscript Accepted: February 13, 2003
Published: June 1, 2003

Martin J. Bastiaans and Kurt Bernardo Wolf, "Phase reconstruction from intensity measurements in linear systems," J. Opt. Soc. Am. A 20, 1046-1049 (2003)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. Z. Zalevsky, D. Mendlovic, R. G. Dorsch, “Gerchberg–Saxton algorithm applied in the fractional Fourier or the Fresnel domain,” Opt. Lett. 21, 842–844 (1996). [CrossRef] [PubMed]
  2. H. M. Ozaktas, Z. Zalevsky, M. A. Kutay, The Fractional Fourier Transform (Wiley, Chichester, UK, 2001).
  3. W. X. Cong, N. X. Chen, B. Y. Gu, “Recursive algorithm for phase retrieval in the fractional Fourier-transform domain,” Appl. Opt. 37, 6906–6910 (1998). [CrossRef]
  4. W. X. Cong, N. X. Chen, B. Y. Gu, “Phase retrieval in the Fresnel transform system:  a recursive algorithm,” J. Opt. Soc. Am. A 16, 1827–1830 (1999). [CrossRef]
  5. K. A. Nugent, D. Paganin, “Matter-wave phase measurement:  a noninterferometric approach,” Phys. Rev. A 61, 063614 (2000). [CrossRef]
  6. D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. (Oxford) 206, 33–40 (2002). [CrossRef]
  7. D. Paganin, K. A. Nugent, “Phase measurement of waves that obey nonlinear equations,” Opt. Lett. 27, 622–624 (2002). [CrossRef]
  8. M. R. Teague, “Deterministic phase retrieval:  a Green function solution,” J. Opt. Soc. Am. 73, 1434–1441 (1983). [CrossRef]
  9. N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–10 (1984). [CrossRef]
  10. K. Ichikawa, A. W. Lohmann, M. Takeda, “Phase retrieval based on the Fourier transport method:  experiments,” Appl. Opt. 27, 3433–3436 (1988). [CrossRef] [PubMed]
  11. T. E. Gureev, A. Roberts, K. A. Nugent, “Partially coherent fields, the transport-of-intensity equation, and phase uniqueness,” J. Opt. Soc. Am. A 12, 1942–1946 (1995). [CrossRef]
  12. T. Alieva, M. J. Bastiaans, “On fractional Fourier transform moments,” IEEE Signal Process. Lett. 7, 320–323 (2000). [CrossRef]
  13. T. Alieva, M. J. Bastiaans, L. J. Stanković, “Signal reconstruction from two close fractional Fourier power spectra,” IEEE Trans. Signal Process. 51, 112–123 (2003). [CrossRef]
  14. M. Moshinsky, C. Quesne, “Oscillator systems,” in Proceedings of the 15th Solvay Conference in Physics (1970) (Gordon and Breach, New York, 1974).
  15. M. Moshinsky, C. Quesne, “Linear canonical transformations and their unitary representation,” J. Math. Phys. 12, 1772–1780 (1971). [CrossRef]
  16. C. Quesne, M. Moshinsky, “Canonical transformations and matrix elements,” J. Math. Phys. 12, 1780–1783 (1971). [CrossRef]
  17. K. B. Wolf, Integral Transforms in Science and Engineering (Plenum, New York, 1979), Chap. 9.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited