## Experimental study on the existence and properties of speckle phase vortices in the diffraction region near random surfaces |

Optics Express, Vol. 20, Issue 16, pp. 17833-17842 (2012)

http://dx.doi.org/10.1364/OE.20.017833

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### Abstract

We design an optical setup to extract phase vortices in which the interference intensity of reference light wave and speckle fields produced by random screens with different roughness values in the diffraction region near random screens is obtained. Random screens with different roughness are used as samples. Fourier transform is used to extract speckle phase vortices from the interference intensity, and the experimental results show that the phase vortices can be produced when the roughness of the screen is large enough, and they even may appear on the surface. The density of phase vortices would become larger with an increase of the distances in the diffraction region near the random screen. When the distance is certain, the density of phase vortices becomes larger with the increase of roughness. These results would be helpful for understanding the formation of phase vortices.

© 2012 OSA

## 1. Introduction

2. J. F. Nye and M. V. Berry, “Dislocations in Wave Trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. **336**(1605), 165–190 (1974). [CrossRef]

2. J. F. Nye and M. V. Berry, “Dislocations in Wave Trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. **336**(1605), 165–190 (1974). [CrossRef]

4. M. Giglio, M. Carpineti, and A. Vailati, “Space intensity correlations in the near field of the scattered light: A direct measurement of the density correlation function g(r),” Phys. Rev. Lett. **85**(7), 1416–1419 (2000). [CrossRef] [PubMed]

5. G. M. Li, Y. S. Qiu, H. Li, Y. Huang, S. Liu, and Z. Y. Huang, “Speckle contrast in near field scattering limited by time coherence,” Opt. Express **19**(4), 3694–3702 (2011). [CrossRef] [PubMed]

6. K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, “Fractality of light’s darkness,” Phys. Rev. Lett. **100**(5), 053902 (2008). [CrossRef] [PubMed]

11. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer- based topography and interferometry,” J. Opt. Soc. Am. **72**(1), 156–160 (1982). [CrossRef]

14. E. Wolf, “Solution of the Phase Problem in the Theory of Structure Determination of Crystals from X-Ray Diffraction Experiments,” Phys. Rev. Lett. **103**(7), 075501 (2009). [CrossRef] [PubMed]

7. W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental Investigation of Local Properties and Statistics of Optical Vortices in Random Wave Fields,” Phys. Rev. Lett. **94**(10), 103902 (2005). [CrossRef] [PubMed]

16. N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A **73**(5), 525–528 (1983). [CrossRef]

## 2. Experiments and extraction of the speckle wave field in the diffraction region near random screens

## 3. The existence and properties of speckle phase vortices in the diffraction region near random screens

16. N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A **73**(5), 525–528 (1983). [CrossRef]

## 4. Conclusions

## Acknowledgments

## References and links

1. | J. W. Goodman, |

2. | J. F. Nye and M. V. Berry, “Dislocations in Wave Trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. |

3. | P. S. Liu, |

4. | M. Giglio, M. Carpineti, and A. Vailati, “Space intensity correlations in the near field of the scattered light: A direct measurement of the density correlation function g(r),” Phys. Rev. Lett. |

5. | G. M. Li, Y. S. Qiu, H. Li, Y. Huang, S. Liu, and Z. Y. Huang, “Speckle contrast in near field scattering limited by time coherence,” Opt. Express |

6. | K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, “Fractality of light’s darkness,” Phys. Rev. Lett. |

7. | W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental Investigation of Local Properties and Statistics of Optical Vortices in Random Wave Fields,” Phys. Rev. Lett. |

8. | F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Polarization Singularities in 2D and 3D Speckle Fields,” Phys. Rev. Lett. |

9. | O. V. Angelsky, A. P. Maksimyak, P. P. Maksimyak, and S. G. Hanson, “Interference diagnostics of white-light vortices,” Opt. Express |

10. | H. S. Song, C. F. Cheng, S. Y. Teng, M. Liu, G. Y. Liu, and N. Y. Zhang, “Experimental studies on the statistical functions of speckle fields based on the extraction of the complex amplitudes by use of interference beam,” Acta Phys. Sin. |

11. | M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer- based topography and interferometry,” J. Opt. Soc. Am. |

12. | D. J. Bone, H. A. Bachor, and R. J. Sandeman, “Fringe-pattern analysis using a 2-D Fourier transform,” Appl. Opt. |

13. | M. H. Zhang, J. F. Xu, X. F. Wang, and Q. Wei, “Complex-valued acquisition of the diffraction imaging by incoherent quasi-monochromatic light without a support constraint,” Phys. Rev. A |

14. | E. Wolf, “Solution of the Phase Problem in the Theory of Structure Determination of Crystals from X-Ray Diffraction Experiments,” Phys. Rev. Lett. |

15. | N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetsky, and V. V. Shkukov, “Dislocation of the wave-front of a speckle-inhomogeneous field,” JETP Lett. |

16. | N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A |

17. | M. V. Berry and M. R. Dennis, “Phase singularities in isotropic random waves,” Proc. R. Soc. Lond. A |

**OCIS Codes**

(030.6140) Coherence and statistical optics : Speckle

(100.5070) Image processing : Phase retrieval

(260.6042) Physical optics : Singular optics

**ToC Category:**

Coherence and Statistical Optics

**History**

Original Manuscript: May 17, 2012

Revised Manuscript: July 6, 2012

Manuscript Accepted: July 9, 2012

Published: July 20, 2012

**Citation**

Xiaoyi Chen, Zhenhua Li, Haixia Li, Meina Zhang, and Chuanfu Cheng, "Experimental study on the existence and properties of speckle phase vortices in the diffraction region near random surfaces," Opt. Express **20**, 17833-17842 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-16-17833

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### References

- J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Ben Roberts & Company, 2007).
- J. F. Nye and M. V. Berry, “Dislocations in Wave Trains,” Proc. R. Soc. Lond. A Math. Phys. Sci.336(1605), 165–190 (1974). [CrossRef]
- P. S. Liu, Fundamentals of Statistical Optics of Speckles (Science Press, 1987), p.7.
- M. Giglio, M. Carpineti, and A. Vailati, “Space intensity correlations in the near field of the scattered light: A direct measurement of the density correlation function g(r),” Phys. Rev. Lett.85(7), 1416–1419 (2000). [CrossRef] [PubMed]
- G. M. Li, Y. S. Qiu, H. Li, Y. Huang, S. Liu, and Z. Y. Huang, “Speckle contrast in near field scattering limited by time coherence,” Opt. Express19(4), 3694–3702 (2011). [CrossRef] [PubMed]
- K. O’Holleran, M. R. Dennis, F. Flossmann, and M. J. Padgett, “Fractality of light’s darkness,” Phys. Rev. Lett.100(5), 053902 (2008). [CrossRef] [PubMed]
- W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental Investigation of Local Properties and Statistics of Optical Vortices in Random Wave Fields,” Phys. Rev. Lett.94(10), 103902 (2005). [CrossRef] [PubMed]
- F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Polarization Singularities in 2D and 3D Speckle Fields,” Phys. Rev. Lett.100(20), 203902 (2008). [CrossRef] [PubMed]
- O. V. Angelsky, A. P. Maksimyak, P. P. Maksimyak, and S. G. Hanson, “Interference diagnostics of white-light vortices,” Opt. Express13(20), 8179–8183 (2005). [CrossRef] [PubMed]
- H. S. Song, C. F. Cheng, S. Y. Teng, M. Liu, G. Y. Liu, and N. Y. Zhang, “Experimental studies on the statistical functions of speckle fields based on the extraction of the complex amplitudes by use of interference beam,” Acta Phys. Sin.58(11), 7654–7661 (2009).
- M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer- based topography and interferometry,” J. Opt. Soc. Am.72(1), 156–160 (1982). [CrossRef]
- D. J. Bone, H. A. Bachor, and R. J. Sandeman, “Fringe-pattern analysis using a 2-D Fourier transform,” Appl. Opt.25(10), 1653–1660 (1986). [CrossRef] [PubMed]
- M. H. Zhang, J. F. Xu, X. F. Wang, and Q. Wei, “Complex-valued acquisition of the diffraction imaging by incoherent quasi-monochromatic light without a support constraint,” Phys. Rev. A82(4), 043839 (2010). [CrossRef]
- E. Wolf, “Solution of the Phase Problem in the Theory of Structure Determination of Crystals from X-Ray Diffraction Experiments,” Phys. Rev. Lett.103(7), 075501 (2009). [CrossRef] [PubMed]
- N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetsky, and V. V. Shkukov, “Dislocation of the wave-front of a speckle-inhomogeneous field,” JETP Lett.33, 195–199 (1981).
- N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A73(5), 525–528 (1983). [CrossRef]
- M. V. Berry and M. R. Dennis, “Phase singularities in isotropic random waves,” Proc. R. Soc. Lond. A456(2001), 2059–2079 (2000). [CrossRef]

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