OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 22, Iss. 5 — May. 1, 2005
  • pp: 899–906

Correlation between intensity and phase in monochromatic light

Ervin Kolenović  »View Author Affiliations

JOSA A, Vol. 22, Issue 5, pp. 899-906 (2005)

View Full Text Article

Enhanced HTML    Acrobat PDF (307 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Analytical expressions to describe the phase gradient of monochromatic light by means of the three-dimensional intensity distribution are derived. With these formulas it is shown that the two-dimensional phase gradient in a plane can be completely determined from noninterferometric intensity measurements if the light propagates strictly in one direction. The analytical expressions are verified by means of numerical investigations on simulated speckle fields, and the results are discussed with respect to common deterministic phase retrieval approaches.

© 2005 Optical Society of America

OCIS Codes
(030.6140) Coherence and statistical optics : Speckle
(100.5070) Image processing : Phase retrieval
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

Original Manuscript: June 29, 2004
Revised Manuscript: November 21, 2004
Manuscript Accepted: November 10, 2004
Published: May 1, 2005

Ervin Kolenović, "Correlation between intensity and phase in monochromatic light," J. Opt. Soc. Am. A 22, 899-906 (2005)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, B. Y. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. 73, 525–528 (1983). [CrossRef]
  2. G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993). [CrossRef]
  3. N. Shvartsman, I. Freund, “Speckle spots ride phase saddles sidesaddle,” Opt. Commun. 117, 228–234 (1995). [CrossRef]
  4. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982). [CrossRef] [PubMed]
  5. G. Vdovin, “Reconstruction of an object shape from the near-field intensity of a reflected paraxial beam,” Appl. Opt. 36, 5508–5513 (1997). [CrossRef] [PubMed]
  6. 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]
  7. M. R. Teague, “Irradiance moments: their propagation and use for unique retrieval of phase,” J. Opt. Soc. Am. 72, 1199–1209 (1982). [CrossRef]
  8. M. R. Teague, “Deterministic phase retrieval: a Green’s 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 (1983). [CrossRef]
  10. K. Ichikawa, A. W. Lohmann, M. Takeda, “Phase retrieval based on irradiance transport equation and the Fourier transform method: experiments,” Appl. Opt. 27, 3433–3436 (1988). [CrossRef] [PubMed]
  11. K. G. Larkin, C. J. R. Sheppard, “Direct method for phase retrieval from the intensity of cylindrical wave fronts,” J. Opt. Soc. Am. A 16, 1838–1844 (1999). [CrossRef]
  12. M. J. Bastiaans, K. B. Wolf, “Phase reconstruction from intensity measurements in linear systems,” J. Opt. Soc. Am. A 20, 1046–1049 (2003). [CrossRef]
  13. G. Ade, “On the validity of the transport equation for the intensity in optics,” Opt. Commun. 52, 307–310 (1985). [CrossRef]
  14. M. R. Teague, “Image formation in terms of the transport equation,” J. Opt. Soc. Am. A 2, 2019–2026 (1985). [CrossRef]
  15. F. Roddier, “Wavefront sensing and the irradiance transport equation,” Appl. Opt. 29, 1402–1403 (1990). [CrossRef] [PubMed]
  16. T. E. Gureyev, A. Roberts, K. A. Nugent, “Phase retrieval with the transport-of-intensity equation: matrix solution with the use of Zernike polynomials,” J. Opt. Soc. Am. A 12, 1932–1941 (1995). [CrossRef]
  17. T. E. Gureyev, 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]
  18. M. Fernández-Guasti, J. L. Jiménez, F. Granados-Augustín, A. Cornejo-Rodríguez, “Amplitude and phase representation of monochromatic fields in physical optics,” J. Opt. Soc. Am. A 20, 1629–1634 (2003). [CrossRef]
  19. G. Weigelt, B. Stoffregen, “The longitudinal correlation of a three-dimensional speckle intensity distribution,” Optik (Stuttgart) 48, 399–407 (1977).
  20. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), p. 402.
  21. B. Saleh, M. Teich, Fundamentals of Photonics, 1st ed. (Wiley-Interscience, New York, 1991), p. 52.

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.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited