## Speckle contrast in near field scattering limited by time coherence |

Optics Express, Vol. 19, Issue 4, pp. 3694-3702 (2011)

http://dx.doi.org/10.1364/OE.19.003694

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### Abstract

The relationship between the speckle contrast of scattered light in near field and longitudinal distance that is perpendicular to scattering surface is investigated. The experiment indicates that when using the laser illumination source with proper time coherence length, the curve of speckle contrast vs. longitudinal distance appears minimum turning point. The position and value of minimum point are decided by the coherence of light and scattering matter. It is easy to obtain the correlation area of scattered light by measuring the minimum point position and the illuminated area. Comparing to traditional scattering technique, this method can simultaneously measure the roughness parameters of surface height variance and surface height correlation area.

© 2011 OSA

## 1. Introduction

1. 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]

8. F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Use of dynamic schlieren interferometry to study fluctuations during free diffusion,” Appl. Opt. **45**(10), 2166–2173 (2006). [CrossRef] [PubMed]

1. 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]

2. M. Giglio, M. Carpineti, A. Vailati, and D. Brogioli, “Near-field intensity correlations of scattered light,” Appl. Opt. **40**(24), 4036–4040 (2001). [CrossRef]

3. D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near field scattering,” Appl. Phys. Lett. **81**(22), 4109 (2002). [CrossRef]

4. D. Brogioli, A. Vailati, and M. Giglio, “A schlieren method for ultra-low angle light scattering measurements,” Europhys. Lett. **63**(2), 220–225 (2003). [CrossRef]

5. R. Cerbino, S. Mazzoni, A. Vailati, and M. Giglio, “Scaling behavior for the onset of convection in a colloidal suspension,” Phys. Rev. Lett. **94**(6), 064501 (2005). [CrossRef] [PubMed]

6. A. Vailati, R. Cerbino, S. Mazzoni, M. Giglio, G. Nikolaenko, C. J. Takacs, D. S. Cannell, W. V. Meyer, and A. E. Smart, “Gradient-driven fluctuations experiment: fluid fluctuations in microgravity,” Appl. Opt. **45**(10), 2155–2165 (2006). [CrossRef] [PubMed]

7. F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **70**(4 Pt 1), 041405 (2004). [CrossRef] [PubMed]

8. F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Use of dynamic schlieren interferometry to study fluctuations during free diffusion,” Appl. Opt. **45**(10), 2166–2173 (2006). [CrossRef] [PubMed]

## 2. Experiments

_{00}Ar + laser (U.S., Spectra-Physics Inc., Model 177-G12), the 532nm CW TEM

_{00}green diode laser (China, Photon Technologies, Inc., GDL8100) and the 520nm green LED (China, HongKe Optoelectronic Co.,LTD, H10- A21GHC5-G10-3P) were used respectively, their coherence lengths are about 50mm, 2mm and 0.01mm. A variable optical expander was used before the scattering screen. The incident angle was set as 60° in order to avoid the influence of mirror reflecting into CCD camera. The length of major axis of the ellipse illumination spot was 2cm and the minor axis was 1cm, and white painted board was used as scattering screen in our experiment. The microscope (Japan, Nikon Inc., ST100) is reconstructed and laid perpendicularly to the scattering screen. Its micro objective magnification is 10X and N.A. is 0.25. The CCD camera (Japan, Nikon Inc., DS-U2) take the place of microscopic ocular and its active area is adjusted to image plane. The time of CCD exposure is 1/60s and the digital gain is 1.0X.

^{+}laser doesn’t represent this character. When the 488nm Ar + laser illuminates the scattering screen, the speckle contrast curve keeps steadily at a close distance and increases slowly with increasing distance. While taking the LED as illumination source, the speckle contrast keeps nearly constant.

## 3. Theoretical analysis

_{00}mode has good space coherence, so its coherence area is restricted by the time coherence length. To simplify the analysis without injuring reasonability of experimental results, we only take the center area of illumination region into consideration. As shown in Fig. 5(a) , the relation between the coherent length

*δ*of illumination source and the linear dimension

*α*is the light incidence angle. z is the distance between the plane of the scattering spot and the observation plane. According to the geometry, the ETCA can be written as (see in Fig. 5(b)):where

1. 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]

*n*th ETCA.

*N*is the number of the ETCA in the effective scattering area. Namely

*N*increases according to Eq. (7) while the speckle contrast keeps decreasing. The effective scattering area remains unchanged after it equals to the area of illumination region, but the ETCA expands continuously with increasing distance. Then the value of

*N*decreases and the speckle contrast starts to rise up. When the ETCA equals to the area of illumination region, the speckle contrast keeps steadily and rises slowly. They are concordant with experimental results (see Fig. 2).

*λ*are known, the correlation area of scattered light

*m*th circle of ETCA (see Fig. 9 ). For details, please refer to appendix.

## 4. Application

9. J. Ohtsubo and T. Asakura, “Statistical properties of speckle intensity variations in the diffraction field under illumination of coherent light,” Opt. Commun. **14**(1), 30–34 (1975). [CrossRef]

10. H. Fujii and T. Asakura, “Effect of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. **11**(1), 35–38 (1974). [CrossRef]

9. J. Ohtsubo and T. Asakura, “Statistical properties of speckle intensity variations in the diffraction field under illumination of coherent light,” Opt. Commun. **14**(1), 30–34 (1975). [CrossRef]

10. H. Fujii and T. Asakura, “Effect of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. **11**(1), 35–38 (1974). [CrossRef]

*ε*is Euler’s constant. The speckle contrast can be deduced to [11]:where

## 5. Conclusion

## Appendix

*m*th circle of time coherence area relativing to observation point, and

*m*th circle.

*M*is the number of time coherence area. According to the geometry in Fig. 9, we have recursive relation on

## Acknowledgments

## References and links

1. | 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. |

2. | M. Giglio, M. Carpineti, A. Vailati, and D. Brogioli, “Near-field intensity correlations of scattered light,” Appl. Opt. |

3. | D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near field scattering,” Appl. Phys. Lett. |

4. | D. Brogioli, A. Vailati, and M. Giglio, “A schlieren method for ultra-low angle light scattering measurements,” Europhys. Lett. |

5. | R. Cerbino, S. Mazzoni, A. Vailati, and M. Giglio, “Scaling behavior for the onset of convection in a colloidal suspension,” Phys. Rev. Lett. |

6. | A. Vailati, R. Cerbino, S. Mazzoni, M. Giglio, G. Nikolaenko, C. J. Takacs, D. S. Cannell, W. V. Meyer, and A. E. Smart, “Gradient-driven fluctuations experiment: fluid fluctuations in microgravity,” Appl. Opt. |

7. | F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

8. | F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Use of dynamic schlieren interferometry to study fluctuations during free diffusion,” Appl. Opt. |

9. | J. Ohtsubo and T. Asakura, “Statistical properties of speckle intensity variations in the diffraction field under illumination of coherent light,” Opt. Commun. |

10. | H. Fujii and T. Asakura, “Effect of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. |

11. | J. W. Goodman, |

**OCIS Codes**

(030.6140) Coherence and statistical optics : Speckle

(290.5820) Scattering : Scattering measurements

(180.4243) Microscopy : Near-field microscopy

**ToC Category:**

Coherence and Statistical Optics

**History**

Original Manuscript: December 21, 2010

Revised Manuscript: February 4, 2011

Manuscript Accepted: February 4, 2011

Published: February 10, 2011

**Virtual Issues**

Vol. 6, Iss. 3 *Virtual Journal for Biomedical Optics*

**Citation**

Gaoming Li, Yishen Qiu, Hui Li, Yan Huang, Shou Liu, and Zhiyun Huang, "Speckle contrast in near field scattering limited by time coherence," Opt. Express **19**, 3694-3702 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-4-3694

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### References

- 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]
- M. Giglio, M. Carpineti, A. Vailati, and D. Brogioli, “Near-field intensity correlations of scattered light,” Appl. Opt. 40(24), 4036–4040 (2001). [CrossRef]
- D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near field scattering,” Appl. Phys. Lett. 81(22), 4109 (2002). [CrossRef]
- D. Brogioli, A. Vailati, and M. Giglio, “A schlieren method for ultra-low angle light scattering measurements,” Europhys. Lett. 63(2), 220–225 (2003). [CrossRef]
- R. Cerbino, S. Mazzoni, A. Vailati, and M. Giglio, “Scaling behavior for the onset of convection in a colloidal suspension,” Phys. Rev. Lett. 94(6), 064501 (2005). [CrossRef] [PubMed]
- A. Vailati, R. Cerbino, S. Mazzoni, M. Giglio, G. Nikolaenko, C. J. Takacs, D. S. Cannell, W. V. Meyer, and A. E. Smart, “Gradient-driven fluctuations experiment: fluid fluctuations in microgravity,” Appl. Opt. 45(10), 2155–2165 (2006). [CrossRef] [PubMed]
- F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4 Pt 1), 041405 (2004). [CrossRef] [PubMed]
- F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Use of dynamic schlieren interferometry to study fluctuations during free diffusion,” Appl. Opt. 45(10), 2166–2173 (2006). [CrossRef] [PubMed]
- J. Ohtsubo and T. Asakura, “Statistical properties of speckle intensity variations in the diffraction field under illumination of coherent light,” Opt. Commun. 14(1), 30–34 (1975). [CrossRef]
- H. Fujii and T. Asakura, “Effect of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. 11(1), 35–38 (1974). [CrossRef]
- J. W. Goodman, Speckle Phenonmena in optics:theory and applications (Ben Roberts & Company, 2007).

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