## Speckle size of light scattered from 3D rough objects |

Optics Express, Vol. 20, Issue 4, pp. 4726-4737 (2012)

http://dx.doi.org/10.1364/OE.20.004726

Acrobat PDF (1016 KB)

### Abstract

From scalar Helmholtz integral relation and by coordinate system transformation, this paper begins with a derivation of the far-zone speckle field in the observation plane perpendicular to the scattering direction from an arbitrarily shaped conducting rough object illuminated by a plane wave illumination, followed by the spatial correlation function of the speckle intensity to obtain the speckle size from the objects. Especially, the specific expressions for the speckle sizes of light backscattered from spheres, cylinders and cones are obtained in detail showing that the speckle size along one direction in the observation plane is proportional to the incident wavelength and the distance between the object and the observation plane, and is inverse proportional to the maximal illuminated dimension of the object parallel to the direction. In addition, the shapes of the speckle of the rough objects with different shapes are different. The investigation on the speckle size in this paper will be useful for the statistical properties of speckle from complicated rough objects and the speckle imaging to target detection and identification.

© 2012 OSA

## 1. Introduction

20. R. Berlasso, F. Perez Quintián, M. A. Rebollo, C. A. Raffo, and N. G. Gaggioli, “Study of speckle size of light scattered from cylindrical rough surfaces,” Appl. Opt. **39**(31), 5811–5819 (2000). [CrossRef] [PubMed]

21. R. G. Berlasso, F. P. Quintián, M. A. Rebollo, N. G. Gaggioli, B. L. Sánchez, and M. E. Bernabeu, “Speckle size of light scattered from slightly rough cylindrical surfaces,” Appl. Opt. **41**(10), 2020–2027 (2002). [CrossRef] [PubMed]

## 2. Speckle field from rough objects in the observation plane perpendicular to the scattered direction

*P*in the far field can be expressed as [22, 23

23. G. Zhang and Z. Wu, “Two-frequency mutual coherence function of scattering from arbitrarily shaped rough objects,” Opt. Express **19**(8), 7007–7019 (2011). [CrossRef] [PubMed]

*P*( x r , y r , z r ) and the origin of the object while

*P*and the point on the object surfacewhere

*P*close to the

## 3. Speckle size for 3D various shaped rough objects

*et al*[25]. The geometry of the speckle size is shown by Fig. 3 below, where

26. L. G. Shirley and N. George, “Speckle from a cascade of two thin diffusers,” J. Opt. Soc. Am. A **6**(6), 765–781 (1989). [CrossRef]

### 3.1 Rough spheres

*a*, as in Fig. 5 below. The coordinate of the point is

### 3.2 Rough cylinders

*a*and length

*b*, as in Fig. 7 , with the point (

### 3.3 Rough cones

*h*. The coordinate system of the cone is shown in Fig. 9 .

20. R. Berlasso, F. Perez Quintián, M. A. Rebollo, C. A. Raffo, and N. G. Gaggioli, “Study of speckle size of light scattered from cylindrical rough surfaces,” Appl. Opt. **39**(31), 5811–5819 (2000). [CrossRef] [PubMed]

## 4. Conclusion

## Acknowledgments

## References and links

1. | J. W. Goodman, “Statistical properties of laser speckle patterns,” in |

2. | Q. B. Li and F. P. Chiang, “A new formula for fringe localization in holographic interferometry,” Opt. Lasers Eng. |

3. | D. W. Li, F. P. Chiang, and J. B. Chen, “Statistical analysis of one-beam subjective laser speckle interferometry,” J. Opt. Soc. Am. A |

4. | T. Asakura and N. Takai, “Dynamic laser speckles and their application to velocity measurements of the diffuse object,” Appl. Phys. (Berl.) |

5. | T. Yoshimura, “Statistical properties of dynamic speckles,” J. Opt. Soc. Am. A |

6. | L. Leushacke and M. Kirchner, “Three-dimensional correlation coefficient of speckle intensity for rectangular and circular apertures,” J. Opt. Soc. Am. A |

7. | Q. B. Li and F. P. Chiang, “Three-dimensional dimension of laser speckle,” Appl. Opt. |

8. | T. Yoshimura and S. Iwamoto, “Dynamic properties of three-dimensional speckles,” J. Opt. Soc. Am. A |

9. | M. Ibrahim, J. Uozumi, and T. Asakura, “Longitudinal correlation properties of speckles produced by Ring-Slit illumination,” Opt. Rev. |

10. | H. T. Yura, B. Rose, and S. G. Hanson, “Dynamic laser speckle in complex ABCD optical systems,” J. Opt. Soc. Am. A |

11. | 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 |

12. | G. J. Guo, S. K. Li, and Q. L. Tan, “Statistical properties of laser speckles generated from far rough surfaces,” Int. J. Infrared Millim. Waves |

13. | K. Chu and N. George, “Correlation function for speckle size in the right-half-space,” Opt. Commun. |

14. | D. V. Semenov, S. V. Miridonov, E. Nippolainen, and A. A. Kamshilin, “Statistical properties of dynamic speckles formed by a deflecting laser beam,” Opt. Express |

15. | T. Xu and G. R. Bashford, “Further progress on lateral flow estimation using speckle size variation with scan direction,” in |

16. | J. E. Ward, D. P. Kelly, and J. T. Sheridan, “Three-dimensional speckle size in generalized optical systems with limiting apertures,” J. Opt. Soc. Am. A |

17. | D. Li, D. P. Kelly, and J. T. Sheridan, “Three-dimensional static speckle fields. Part I. theory and numerical investigation,” J. Opt. Soc. Am. A |

18. | D. Li, D. P. Kelly, and J. T. Sheridan, “Three-dimensional static speckle fields. Part II. experimental investigation,” J. Opt. Soc. Am. A |

19. | D. R. Dunmeyer, |

20. | R. Berlasso, F. Perez Quintián, M. A. Rebollo, C. A. Raffo, and N. G. Gaggioli, “Study of speckle size of light scattered from cylindrical rough surfaces,” Appl. Opt. |

21. | R. G. Berlasso, F. P. Quintián, M. A. Rebollo, N. G. Gaggioli, B. L. Sánchez, and M. E. Bernabeu, “Speckle size of light scattered from slightly rough cylindrical surfaces,” Appl. Opt. |

22. | A. Ishimaru, |

23. | G. Zhang and Z. Wu, “Two-frequency mutual coherence function of scattering from arbitrarily shaped rough objects,” Opt. Express |

24. | R. K. Erf, |

25. | L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, and J. R. Vivilecchia, “Advanced techniques for target discirmination using laser speckle,” Linc. Lab. J. |

26. | L. G. Shirley and N. George, “Speckle from a cascade of two thin diffusers,” J. Opt. Soc. Am. A |

27. | J. S. Gradshteyn and J. M. Ryzhik, |

**OCIS Codes**

(030.6140) Coherence and statistical optics : Speckle

(030.6600) Coherence and statistical optics : Statistical optics

(290.5880) Scattering : Scattering, rough surfaces

**ToC Category:**

Coherence and Statistical Optics

**History**

Original Manuscript: January 3, 2012

Revised Manuscript: February 2, 2012

Manuscript Accepted: February 7, 2012

Published: February 9, 2012

**Citation**

Geng Zhang, Zhensen Wu, and Yanhui Li, "Speckle size of light scattered from 3D rough objects," Opt. Express **20**, 4726-4737 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-4726

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### References

- J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena (Springer, 1975), vol. 9, pp. 9–75.
- Q. B. Li and F. P. Chiang, “A new formula for fringe localization in holographic interferometry,” Opt. Lasers Eng.8, 1–21 (1988).
- D. W. Li, F. P. Chiang, and J. B. Chen, “Statistical analysis of one-beam subjective laser speckle interferometry,” J. Opt. Soc. Am. A2(5), 657–666 (1985). [CrossRef]
- T. Asakura and N. Takai, “Dynamic laser speckles and their application to velocity measurements of the diffuse object,” Appl. Phys. (Berl.)25(3), 179–194 (1981). [CrossRef]
- T. Yoshimura, “Statistical properties of dynamic speckles,” J. Opt. Soc. Am. A3(7), 1032–1054 (1986). [CrossRef]
- L. Leushacke and M. Kirchner, “Three-dimensional correlation coefficient of speckle intensity for rectangular and circular apertures,” J. Opt. Soc. Am. A7(5), 827–832 (1990). [CrossRef]
- Q. B. Li and F. P. Chiang, “Three-dimensional dimension of laser speckle,” Appl. Opt.31(29), 6287–6291 (1992). [CrossRef] [PubMed]
- T. Yoshimura and S. Iwamoto, “Dynamic properties of three-dimensional speckles,” J. Opt. Soc. Am. A10(2), 324–328 (1993). [CrossRef]
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- H. T. Yura, B. Rose, and S. G. Hanson, “Dynamic laser speckle in complex ABCD optical systems,” J. Opt. Soc. Am. A15(5), 1160–1166 (1998). [CrossRef]
- H. T. Yura, S. G. Hanson, R. S. Hansen, and B. Rose, “Three-dimensional speckle dynamics in paraxial optical systems,” J. Opt. Soc. Am. A16(6), 1402–1412 (1999). [CrossRef]
- G. J. Guo, S. K. Li, and Q. L. Tan, “Statistical properties of laser speckles generated from far rough surfaces,” Int. J. Infrared Millim. Waves22(8), 1177–1191 (2001). [CrossRef]
- K. Chu and N. George, “Correlation function for speckle size in the right-half-space,” Opt. Commun.276(1), 1–7 (2007). [CrossRef]
- D. V. Semenov, S. V. Miridonov, E. Nippolainen, and A. A. Kamshilin, “Statistical properties of dynamic speckles formed by a deflecting laser beam,” Opt. Express16(2), 1238–1249 (2008). [CrossRef] [PubMed]
- T. Xu and G. R. Bashford, “Further progress on lateral flow estimation using speckle size variation with scan direction,” in IEEE International Ultrosonics Symposium Proceedings, pp. 1383–1386 (2009).
- J. E. Ward, D. P. Kelly, and J. T. Sheridan, “Three-dimensional speckle size in generalized optical systems with limiting apertures,” J. Opt. Soc. Am. A26(8), 1855–1864 (2009). [CrossRef] [PubMed]
- D. Li, D. P. Kelly, and J. T. Sheridan, “Three-dimensional static speckle fields. Part I. theory and numerical investigation,” J. Opt. Soc. Am. A28(9), 1896–1903 (2011). [CrossRef]
- D. Li, D. P. Kelly, and J. T. Sheridan, “Three-dimensional static speckle fields. Part II. experimental investigation,” J. Opt. Soc. Am. A28(9), 1904–1908 (2011). [CrossRef]
- D. R. Dunmeyer, Laser Speckle Modeling for Three-Dimensional Metrology and LADAR, M. Eng. dissertation (Massachusetts Institute of Technology, 2001).
- R. Berlasso, F. Perez Quintián, M. A. Rebollo, C. A. Raffo, and N. G. Gaggioli, “Study of speckle size of light scattered from cylindrical rough surfaces,” Appl. Opt.39(31), 5811–5819 (2000). [CrossRef] [PubMed]
- R. G. Berlasso, F. P. Quintián, M. A. Rebollo, N. G. Gaggioli, B. L. Sánchez, and M. E. Bernabeu, “Speckle size of light scattered from slightly rough cylindrical surfaces,” Appl. Opt.41(10), 2020–2027 (2002). [CrossRef] [PubMed]
- A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic Press,1978).
- G. Zhang and Z. Wu, “Two-frequency mutual coherence function of scattering from arbitrarily shaped rough objects,” Opt. Express19(8), 7007–7019 (2011). [CrossRef] [PubMed]
- R. K. Erf, Speckle Metrology (Speckle Metrology, 1978).
- L. G. Shirley, E. D. Ariel, G. R. Hallerman, H. C. Payson, and J. R. Vivilecchia, “Advanced techniques for target discirmination using laser speckle,” Linc. Lab. J.5(3), 367–440 (1992).
- L. G. Shirley and N. George, “Speckle from a cascade of two thin diffusers,” J. Opt. Soc. Am. A6(6), 765–781 (1989). [CrossRef]
- J. S. Gradshteyn and J. M. Ryzhik, Table of Integrals, Series and Products (Academic,1965).

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