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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 29, Iss. 6 — Jun. 1, 2012
  • pp: 1188–1198

Speckle contrast of the sum of N partially correlated speckle patterns

Sigbjørn Vindenes Egge, Ulf Österberg, and Astrid Aksnes  »View Author Affiliations

JOSA A, Vol. 29, Issue 6, pp. 1188-1198 (2012)

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In this paper a general method is presented for calculating the theoretical speckle contrast of a sum of correlated speckle patterns, motivated by the need to suppress the presence of speckle in laser projection displays. The method is applied to a specific example, where correlated speckle patterns are created by sequentially passing light through partially overlapping areas on a diffuser, before being projected onto a screen. This design makes it possible to find a simple expression for the correlation between speckle patterns. When the set of correlations involves symmetry, it is shown that the expression for the speckle contrast becomes simpler. The difference in performance between discretely and continuously varying speckle patterns is also investigated. In an example with speckle reduction by a rotating sinusoidal grating, it is found that continuous variation gives a speckle contrast that is 0.61 times the contrast obtained by discretely summing the maximum number of independent patterns.

© 2012 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
(050.1970) Diffraction and gratings : Diffractive optics
(110.1650) Imaging systems : Coherence imaging
(120.2040) Instrumentation, measurement, and metrology : Displays

ToC Category:
Coherence and Statistical Optics

Original Manuscript: October 18, 2011
Revised Manuscript: December 25, 2011
Manuscript Accepted: January 6, 2012
Published: June 1, 2012

Sigbjørn Vindenes Egge, Ulf Österberg, and Astrid Aksnes, "Speckle contrast of the sum of N partially correlated speckle patterns," J. Opt. Soc. Am. A 29, 1188-1198 (2012)

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  1. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2006).
  2. S. V. Egge, M. N. Akram, V. Kartashov, K. Welde, Z. Tong, U. Österberg, and A. Aksnes, “Sinusoidal rotating grating for speckle reduction in laser projectors: feasibility study,” Opt. Eng. 50, 083202 (2011). [CrossRef]
  3. J. W. Goodman, Introduction to Fourier Optics3rd ed. (McGraw-Hill, 2005).
  4. V. Kartashov and M. N. Akram, “Speckle suppression in projection displays by using a motionless changing diffuser,” J. Opt. Soc. Am. A 27, 2593–2601 (2010). [CrossRef]
  5. J. W. Goodman, “Probability density function of the sum of N partially correlated speckle patterns,” Opt. Commun. 13, 244–247 (1975). [CrossRef]
  6. R. Barakat, “The brightness distribution of the sum of two correlated speckle patterns,” Opt. Commun. 8, 14–16 (1973). [CrossRef]
  7. J. W. Goodman, Statistical Optics (Wiley, 1985).
  8. J. Ohtsubo and T. Asakura, “Statistical properties of the sum of partially-developed, correlated speckle patterns,” Appl. Phys. A 17, 159–164 (1978). [CrossRef]
  9. J. Ohtsubo and T. Asakura, “Statistical properties of the sum of two partially correlated speckle patterns,” Appl. Phys. 14, 183–187 (1977). [CrossRef]
  10. A. Valberg, Light Vision Color (Wiley, 2005).
  11. R. J. Larsen and M. L. Marx, An Introduction to Mathematical Statistics and Its Applications, 3rd ed. (Prentice-Hall, 2001).
  12. J. W. Goodman, “Some fundamental properties of speckle,” J. Opt. Soc. Am. 66, 1145–1150 (1976). [CrossRef]
  13. J. F. Power, “Fresnel diffraction model for the point spread of a laser light profile microscope (LPM),” Appl. Phys. B 78, 693–703 (2004). [CrossRef]
  14. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, 1968).
  15. C. Meneses-Fabian and G. Rodriguez-Zurita, “Carrier fringes in the two-aperture common-path interferometer,” Opt. Lett. 36, 642–644 (2011). [CrossRef]

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