OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 15, Iss. 1 — Jan. 1, 1998
  • pp: 207–216

Detection of movement with laser speckle patterns: statistical properties

U. Schnell, J. Piot, and R. Dändliker  »View Author Affiliations

JOSA A, Vol. 15, Issue 1, pp. 207-216 (1998)

View Full Text Article

Acrobat PDF (362 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present an optical method for detection of in-plane movement of a diffusing object. The technique is based on spatial filtering of the laser speckle pattern, which is produced by illumination of the object with coherent light. Two interlaced differential comb photodetector arrays act as a periodic filter to the spatial-frequency spectrum of the speckle pattern intensity. The detector produces a zero-offset, periodic output signal versus displacement that permits measurement of the movement at arbitrarily low speed. The direction of the movement can be detected with the help of the quadrature signal, which is produced by a second pair of interlaced comb photodetector arrays. When speckle size and period of the comb photodetector arrays are matched, the output signal versus displacement is quasi-sinusoidal with statistical amplitude and phase. First- and second-order statistics of the signal are investigated. First the probability density function and the autocorrelation function of the complex Fourier transform of the speckle pattern intensity are determined. Then the statistical properties of the spectrum of the filtered signal and of the signal itself are calculated. It turns out that the amplitude of the signal is Rayleigh distributed. Both the autocorrelation function of the signal and the probability density function of the measured phase difference for a given displacement are calculated. The potential accuracy of displacement measurements is analyzed. In addition, the signal quality is investigated with respect to the geometry of the detector. The theoretical results are experimentally verified.

© 1998 Optical Society of America

OCIS Codes
(030.6140) Coherence and statistical optics : Speckle
(030.6600) Coherence and statistical optics : Statistical optics
(330.4150) Vision, color, and visual optics : Motion detection

U. Schnell, J. Piot, and R. Dändliker, "Detection of movement with laser speckle patterns: statistical properties," J. Opt. Soc. Am. A 15, 207-216 (1998)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. I. Yamaguchi and S. Komatsu, “Theory and applications of dynamic laser speckles due to in-plane object motion,” Opt. Acta 24, 705–724 (1977).
  2. T. Asakura and N. Takai, “Dynamic laser speckles and their application to velocity measurements of the diffuse object,” Appl. Phys. 25, 179–194 (1981).
  3. B. E. A. Saleh, “Speckle correlation measurement of the velocity of a small rotating rough surface,” Appl. Opt. 14, 2344–2346 (1975).
  4. J. Ohtsubo and T. Asakura, “Velocity measurement of a diffuse object by using time-varying speckles,” Opt. Quantum Electron. 8, 523–529 (1976).
  5. N. Takai, T. Iwai, and T. Asakura, “Real-time velocity measurement for a diffuse object using zero-crossing of laser speckle,” J. Opt. Soc. Am. 70, 450–455 (1980).
  6. M. Naito, M. Ishigami, and A. Kobayashi, “Spatial filter and its application to industrial measurement,” presented at IMEKO-V, Versailles, May 25–30, 1970.
  7. A. Kobayashi, “Measurement and sensors,” Sens. Actuators 13, 29–41 (1988).
  8. H. Ogiwara and H. Ukita, “A speckle pattern velocimeter using a periodical differential detector,” Jpn. J. Appl. Phys. Suppl. 14, 307–310 (1975).
  9. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 9–75.
  10. J. C. Dainty, “The statistics of speckle patterns,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1977), Vol. XIV, pp. 1–46.
  11. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), pp. 60–79.
  12. Hilbert transformation algorithm implemented in the MATLAB function hilbert, in Signal Processing Toolbox for Use with MATLAB (MathWorks, Natick, Mass., 1994).
  13. F. de Coulon, “Théorie et traitement des signaux,” Traité d’Electricité (Presses Polytechniques Romandes, Lausanne, 1984), Vol. VI, pp. 111–144.
  14. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), pp. 33–50.
  15. S. O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J. 24, 46–159 (1945).
  16. A. W. Drake, Fundamentals of Applied Probability Theory (McGraw-Hill, New York, 1967), pp. 203–221.
  17. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1991), pp. 86–102.
  18. S. Lowenthal and H. Arsenault, “Image formation for coherent diffuse objects: statistical properties,” J. Opt. Soc. Am. 60, 1478–1483 (1970).
  19. R. Dändliker and F. M. Mottier, “Determination of coherence length from speckle contrast on a rough surface,” J. Appl. Math. Phys. 22, 369–380 (1971).

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