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Optics Letters

Optics Letters


  • Vol. 21, Iss. 18 — Sep. 15, 1996
  • pp: 1427–1429

Optical heterodyne imaging and Wigner phase space distributions

A. Wax and J. E. Thomas  »View Author Affiliations

Optics Letters, Vol. 21, Issue 18, pp. 1427-1429 (1996)

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We demonstrate that optical heterodyne imaging directly measures smoothed Wigner phase space distributions. This method may be broadly applicable to fundamental studies of light propagation and tomographic imaging. Basic physical properties of Wigner distributions are illustrated by experimental measurements.

© 1996 Optical Society of America

Original Manuscript: May 6, 1996
Published: September 15, 1996

A. Wax and J. E. Thomas, "Optical heterodyne imaging and Wigner phase space distributions," Opt. Lett. 21, 1427-1429 (1996)

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  1. E. P. Wigner, Phys. Rev. Lett. 40, 749 (1932).
  2. M. Hillery, R. F. O'Connel, M. O. Scully, E. P. Wigner, Phys. Rep. 106, 121 (1984). [CrossRef]
  3. D. F. McAlister, M. Beck, L. Clarke, A. Mayer, M. G. Raymer, Opt. Lett. 20, 1181 (1995). [CrossRef] [PubMed]
  4. M. G. Raymer, C. Cheng, D. M. Toloudis, M. Anderson, M. Beck, in Advances in Optical Imaging and Photon Migration (Optical Society of America, Washington, D.C., 1996), pp. 236–238.
  5. S. John, G. Pang, Y. Yang, Proc. SPIE 2389, 64 (1995). [CrossRef]
  6. See, for example, V. J. Corcoran, J. Appl. Phys. 36, 1819 (1965); A. E. Siegman, Appl. Opt. 5, 1588 (1966); S. Cohen, Appl. Opt. 14, 1953 (1975); A. Migdall, B. Roop, Y. C. Zheng, J. E. Hardis, G. J. Xia, Appl. Opt. 29, 5136 (1990). [CrossRef] [PubMed]
  7. Recent heterodyne studies in turbid media include K. P. Chan, M. Yamada, B. Devaraj, H. Inaba, Opt. Lett. 20, 492 (1995); M. Toida, M. Kondo, T. Ichimura, H. Inaba, Appl. Phys. B 52, 391 (1991). [CrossRef] [PubMed]
  8. The mean-square beat is positive definite and takes the form of a smoothed Wigner distribution. See N. D. Cartwright, Physica 83A, 210 (1976).
  9. H. P. Yuen, V. W. S. Chan, Opt. Lett. 8, 177 (1983). [CrossRef] [PubMed]
  10. This method has been used in light beating spectroscopy; see H. Z. Cummins, H. L. Swinney, in Progress in Optics, E. Wolf, ed. (North-Holland, New York, 1970), Vol. VIII, Chap. 3, pp. 133–200. [CrossRef]
  11. This method has been used by G. L. Abbas, V. W. S. Chan, T. K. Yee, IEEE J. Lightwave Technol. 3, 1110 (1985). [CrossRef]
  12. A. Yariv, Introduction to Optical Electronics (Holt, Rinehart, & Winston, New York, 1976), Chap. 3, p. 35.
  13. A. Wax, J. E. Thomas, in Advances in Optical Imaging and Photon Migration (Optical Society of America, Washington, D.C., 1996), pp. 238–242.
  14. The magnitude of the mean beat amplitude (rather than the mean square) is usually measured in this case. See, for example, J. A. Izatt, H. R. Hee, G. M. Owen, E. A. Swanson, J. G. Fujimoto, Opt. Lett. 19, 590 (1994). [CrossRef] [PubMed]

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