OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 12, Iss. 9 — Sep. 1, 1995
  • pp: 1942–1946

Partially coherent fields, the transport-of-intensity equation, and phase uniqueness

T. E. Gureyev, A. Roberts, and K. A. Nugent  »View Author Affiliations


JOSA A, Vol. 12, Issue 9, pp. 1942-1946 (1995)
http://dx.doi.org/10.1364/JOSAA.12.001942


View Full Text Article

Enhanced HTML    Acrobat PDF (322 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Recent papers have shown that there are different coherent and partially coherent fields that may have identical intensity distributions throughout space. On the other hand, the well-known transport-of-intensity equation allows the phase of a coherent field to be recovered from intensity measurements, and the solution is widely held to be unique. A discussion is given on the recovery of the structure of both coherent and partially coherent fields from intensity measurements, and we reconcile the uniqueness question by showing that the transport-of-intensity equation has a unique solution for the phase only if the intensity distribution has no zeros.

© 1995 Optical Society of America

History
Original Manuscript: September 9, 1994
Revised Manuscript: February 24, 1995
Manuscript Accepted: March 31, 1995
Published: September 1, 1995

Citation
T. E. Gureyev, A. Roberts, and K. A. Nugent, "Partially coherent fields, the transport-of-intensity equation, and phase uniqueness," J. Opt. Soc. Am. A 12, 1942-1946 (1995)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-12-9-1942


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. R. Teague, “Irradiance moments: their propagation and use for unique retrieval of phases,” J. Opt. Soc. Am. 72, 1199–1209 (1982). [CrossRef]
  2. M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. 73, 1434–1441 (1983). [CrossRef]
  3. N. Striebl, “Phase imaging by the transport of intensity equation,” Opt. Commun. 49, 6–10 (1984). [CrossRef]
  4. K. Ichikawa, A. W. Lohmann, M. Takeda, “Phase retrieval based on the irradiance transport equation and the Fourier transport method,” Appl. Opt. 27, 3433–3436 (1988). [CrossRef] [PubMed]
  5. F. Roddier, “Wavefront intensity and the irradiance transport equation,” Appl. Opt. 29, 1402–1403 (1990). [CrossRef] [PubMed]
  6. S. R. Restaino, “Wavefront sensing and image deconvolution of solar data,” Appl. Opt. 31, 7442–7449 (1992). [CrossRef] [PubMed]
  7. K. A. Nugent, “Wave field determination using three-dimensional intensity information,” Phys. Rev. Lett. 68, 2261–2264 (1992); see also the comment by G. Hazak, Phys. Rev. Lett. 69, 2874 (1992). [CrossRef] [PubMed]
  8. M. G. Rayner, M. Beck, D. F. MacAlister, “Complex wavefield reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994). [CrossRef]
  9. V. Bagini, F. Gori, M. Santarsiero, G. Guattari, G. Schirripa Spagnolo, “Space intensity distribution and projections of the cross spectral density,” Opt. Commun. 102, 495–504 (1993). [CrossRef]
  10. G. Gori, M. Santarsiero, G. Guattari, “Coherence and the spatial distribution of intensity,” J. Opt. Soc. Am. A 10, 673–679 (1993). [CrossRef]
  11. M. J. Bastiaans, “Application of the Wigner distribution function to partially coherent light,” J. Opt. Soc. Am. A 3, 1227–1238 (1986). [CrossRef]
  12. K. Dutta, J. W. Goodman, “Reconstructions of images of partially coherent objects from samples of mutual intensity,” J. Opt. Soc. Am. 67, 796–803 (1977). [CrossRef]
  13. K. A. Nugent, “Coherence induced spectral changes and generalised radiance,” Opt. Commun. 91, 13–17 (1992). [CrossRef]
  14. D. L. Fried, J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31, 2865–2882 (1992). [CrossRef] [PubMed]
  15. D. Gilbarg, N. S. Trudinger, Elliptic Partial Differential Equations of Second Order (Springer-Verlag, Berlin, 1977), Chap. 8. [CrossRef]
  16. P. Coullett, L. Gil, F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989). [CrossRef]
  17. G. A. Swartzlander, C. T. Law, “Optical vortex solitons in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992). [CrossRef] [PubMed]
  18. J. F. Nye, M. V. Berry, “Dislocation in wave trains,” Proc. R. Soc. London A336, 165–190 (1974).
  19. H. He, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical particle trapping with higher order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995). [CrossRef]
  20. N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, B. Ya. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. 73, 525–528 (1983). [CrossRef]

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.

Figures

Fig. 1 Fig. 2 Fig. 3
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited