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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 6 — Jun. 1, 1999
  • pp: 1402–1412

Three-dimensional speckle dynamics in paraxial optical systems

H. T. Yura, S. G. Hanson, R. S. Hansen, and B. Rose  »View Author Affiliations


JOSA A, Vol. 16, Issue 6, pp. 1402-1412 (1999)
http://dx.doi.org/10.1364/JOSAA.16.001402


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Abstract

Three-dimensional (3D) speckle dynamics are investigated within the paraxial approximation as represented by ABCD-matrix theory. Within the paraxial approximation, exact expressions are derived for the space–time-lagged intensity covariance that results from an in-plane translation, an out-of-plane rotation, or an in-plane rotation of a diffuse scattering object that is illuminated by a Gaussian-shaped laser beam. As illustrative examples we consider the 3D dynamical nature of speckles that are formed in free space and in Fourier transform and imaging systems. The spatiotemporal characteristics of the observed 3D speckle patterns are interpreted in terms of boiling, decorrelation, rotation, translation, and tilting. Experimental results, which support the quantitative theory, are presented and discussed.

© 1999 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(030.6140) Coherence and statistical optics : Speckle
(030.6600) Coherence and statistical optics : Statistical optics
(110.1220) Imaging systems : Apertures
(110.6150) Imaging systems : Speckle imaging
(290.5880) Scattering : Scattering, rough surfaces

History
Original Manuscript: October 29, 1998
Revised Manuscript: February 16, 1999
Manuscript Accepted: February 18, 1999
Published: June 1, 1999

Citation
H. T. Yura, S. G. Hanson, R. S. Hansen, and B. Rose, "Three-dimensional speckle dynamics in paraxial optical systems," J. Opt. Soc. Am. A 16, 1402-1412 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-6-1402


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References

  1. See, for example, J. C. Dainty, “The statistics of speckle patterns,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. XIV, Chap. 1; S. M. Kozel, G. R. Lokshin, “Longitudinal correlation properties of coherent radiation scattered from a rough surface,” Opt. Spectrosc. 33, 89–90 (1972); T. Asakura, N. Takai, “Dynamic laser speckles and their application to velocity measurements of the diffuse object,” Appl. Phys. 25, 179–194 (1981); T. Yoshimura, “Statistical properties of dynamic speckles,” J. Opt. Soc. Am. A 3, 1032–1054 (1986); B. Rose, H. Imam, S. G. Hanson, H. T. Yura, R. S. Hansen, “Laser-speckle angular-displacement sensor: theoretical and experimental study,” Appl. Opt. 37, 2119–2129 (1998); T. Okamoto, T. Asakura, “The statistics of dynamic speckles,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1995), Vol. XXXIV, Chap. 3; H. T. Yura, S. G. Hanson, T. P. Grum, “Speckle: statistics and interferometric decorrelation effects in complex ABCD optical systems,” J. Opt. Soc. Am. A 10, 316–323 (1993). [CrossRef]
  2. T. Yoshimura, S. Iwamoto, “Dynamic properties of three-dimensional speckles,” J. Opt. Soc. Am. A 10, 324–328 (1993). [CrossRef]
  3. H. T. Yura, S. G. Hanson, “Optical beam wave propagation through complex optical systems,” J. Opt. Soc. Am. A 4, 1931–1948 (1987). [CrossRef]
  4. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), Chap. 2.
  5. A. S. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 20.
  6. H. T. Yura, S. G. Hanson, “Optical beam wave propagation through complex optical systems,” J. Opt. Soc. Am. A 4, 1931–1948 (1987). [CrossRef]
  7. The generalization of the results derived here to systems that are not cylindrically symmetric is straightforward.
  8. H. T. Yura, B. Rose, S. G. Hanson, “Dynamic laser speckle in complex ABCD systems,” J. Opt. Soc. Am. A 15, 1160–1166 (1998). [CrossRef]
  9. S. Wolfram, Mathematica: A System for Doing Mathematics by Computer (Addison-Wesley, Redwood City, Calif., 1991).
  10. H. T. Yura, S. G. Hanson, T. P. Grum, “Speckle: statistics and interferometric decorrelation effects in complex ABCD optical systems,” J. Opt. Soc. Am. A 10, 316–323 (1993). [CrossRef]
  11. J. H. Churnside, “Speckle from a rotating diffuse object,” J. Opt. Soc. Am. 72, 1464–1469 (1982). [CrossRef]
  12. Because each scatterer appears in the same position in the illuminated region once with each revolution of the object, the speckle pattern exhibits a periodicity with a frequency equal to the frequency of revolution.
  13. Substituting Eqs. (4.6a) and (4.6b) into Eq. (4.1) yields that the maximum value of the space–time cross covariance equals unity.
  14. This because the orientation of the (static) speckles is independent of the motion of the object.
  15. H. T. Yura, B. Rose, S. G. Hanson, “Speckle dynamics from in-plane rotating diffuse objects in complex ABCD optical systems,” J. Opt. Soc. Am. A 15, 1167–1171 (1998). [CrossRef]
  16. Note that the complex cross covariance is proportional to exp[ikJ-ik(J-vZτ)]=exp[iωDτ], where J is the path length along the optic axis and ωD=kvZ is the Doppler shift caused by the longitudinal motion of the object.

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