## Random light scattering by collections of ellipsoids |

Optics Express, Vol. 20, Issue 28, pp. 29296-29307 (2012)

http://dx.doi.org/10.1364/OE.20.029296

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### Abstract

Theory of weak scattering of random optical fields from deterministic collections of particles with soft ellipsoidal scattering potentials of arbitrary shapes and orientations is developed. Far-field intensity distribution produced on scattering is shown to be influenced by source correlation properties as well as by a number, shapes and orientations of scatterers. The theory extends previous results on scattering from collections of spheres with soft Gaussian potentials and is applicable to analysis of a wide range of media including blood cells.

© 2012 OSA

## 1. Introduction

1. E. Wolf, J. T. Foley, and F. Gori, “Frequency shifts of spectral lines produced by scattering from spatially random media,” J. Opt. Soc. Am. A **6**(8), 1142–1149 (1989). [CrossRef]

5. C. Zhao, Y. Cai, X. Lu, and H. T. Eyyuboğlu, “Radiation force of coherent and partially coherent flat-topped beams on a Rayleigh particle,” Opt. Express **17**(3), 1753–1765 (2009). [CrossRef] [PubMed]

6. S. Sahin, G. Gbur, and O. Korotkova, “Scattering of light from particles with semisoft boundaries,” Opt. Lett. **36**(20), 3957–3959 (2011). [CrossRef] [PubMed]

7. G. J. Streekstra, A. G. Hoekstra, E. J. Nijhof, and R. M. Heethaar, “Light scattering by red blood cells in ektacytometry: Fraunhofer versus anomalous diffraction,” Appl. Opt. **32**(13), 2266–2272 (1993). [CrossRef] [PubMed]

10. R. S. Brock, X. H. Hu, P. Yang, and J. Lu, “Evaluation of a parallel FDTD code and application to modeling of light scattering by deformed red blood cells,” Opt. Express **13**(14), 5279–5292 (2005). [CrossRef] [PubMed]

12. O. Korotkova and E. Wolf, “Scattering matrix theory for stochastic scalar fields,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **75**(5), 056609 (2007). [CrossRef] [PubMed]

13. S. Sahin and O. Korotkova, “Scattering of scalar light fields from collections of particles,” Phys. Rev. A **78**(6), 063815 (2008). [CrossRef]

14. S. Sahin and O. Korotkova, “Effect of the pair-structure factor of a particulate medium on scalar wave scattering in the first Born approximation,” Opt. Lett. **34**(12), 1762–1764 (2009). [CrossRef] [PubMed]

15. D. G. Fischer and E. Wolf, “Inverse problems with quasi-homogeneous random media,” J. Opt. Soc. Am. A **11**(3), 1128–1135 (1994). [CrossRef]

17. Z. Tong and O. Korotkova, “Method for tracing the position of an alien object embedded in a random particulate medium,” J. Opt. Soc. Am. A **28**(8), 1595–1599 (2011). [CrossRef] [PubMed]

## 2. Scattering matrix theory for the collection of particles with different types

*ω*can be characterized by the cross-spectral density function [11]the asterisk denoting the complex and the angular brackets denoting the average of the statistical ensemble monochromatic realizations of the incident field. The angular correlation function of the incident field is defined as the four-dimensional Fourier transform of

12. O. Korotkova and E. Wolf, “Scattering matrix theory for stochastic scalar fields,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **75**(5), 056609 (2007). [CrossRef] [PubMed]

*x-y*plane. Within the validity of the first Born approximation the scattering matrix has simple relation with the scattering potential [18]with

10. R. S. Brock, X. H. Hu, P. Yang, and J. Lu, “Evaluation of a parallel FDTD code and application to modeling of light scattering by deformed red blood cells,” Opt. Express **13**(14), 5279–5292 (2005). [CrossRef] [PubMed]

*L*different types, the scattering potential of the whole collection is then given by the formulawhere

*m*th particle,

*l*,

*l*.

## 3. Spectral pair-scattering matrix for the collection of ellipsoids

*ξ*,

*η*,

*ζ*] (see Fig. 1 ), having three-dimensional (soft) Gaussian potentials

12. O. Korotkova and E. Wolf, “Scattering matrix theory for stochastic scalar fields,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **75**(5), 056609 (2007). [CrossRef] [PubMed]

## 4. Example of two correlated plane waves scattering on the collection of ellipsoids

**u**the expression

## 5. Concluding remarks

19. Z. Tong and O. Korotkova, “Pair-structure matrix of random collections of particles: Implications for light scattering,” Opt. Commun. **284**(24), 5598–5600 (2011). [CrossRef]

## Acknowledgments

## References and links

1. | E. Wolf, J. T. Foley, and F. Gori, “Frequency shifts of spectral lines produced by scattering from spatially random media,” J. Opt. Soc. Am. A |

2. | E. Wolf, J. T. Foley, and F. Gori, “Frequency shifts of spectral lines produced by scattering from spatially random media: errata,” J. Opt. Soc. Am. A |

3. | D. G. Fischer and E. Wolf, “Inverse problems with quasi-homogeneous random media,” J. Opt. Soc. Am. A |

4. | A. Dogariu and E. Wolf, “Spectral changes produced by static scattering on a system of particles,” Opt. Lett. |

5. | C. Zhao, Y. Cai, X. Lu, and H. T. Eyyuboğlu, “Radiation force of coherent and partially coherent flat-topped beams on a Rayleigh particle,” Opt. Express |

6. | S. Sahin, G. Gbur, and O. Korotkova, “Scattering of light from particles with semisoft boundaries,” Opt. Lett. |

7. | G. J. Streekstra, A. G. Hoekstra, E. J. Nijhof, and R. M. Heethaar, “Light scattering by red blood cells in ektacytometry: Fraunhofer versus anomalous diffraction,” Appl. Opt. |

8. | G. J. Streekstra, A. G. Hoekstra, and R. M. Heethaar, “Anomalous diffraction by arbitrarily oriented ellipsoids: applications in ektacytometry,” Appl. Opt. |

9. | B. K. Wilson, M. R. Behrend, M. P. Horning, and M. C. Hegg, “Detection of malarial byproduct hemozoin utilizing its unique scattering properties,” Opt. Express |

10. | R. S. Brock, X. H. Hu, P. Yang, and J. Lu, “Evaluation of a parallel FDTD code and application to modeling of light scattering by deformed red blood cells,” Opt. Express |

11. | E. Wolf, |

12. | O. Korotkova and E. Wolf, “Scattering matrix theory for stochastic scalar fields,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

13. | S. Sahin and O. Korotkova, “Scattering of scalar light fields from collections of particles,” Phys. Rev. A |

14. | S. Sahin and O. Korotkova, “Effect of the pair-structure factor of a particulate medium on scalar wave scattering in the first Born approximation,” Opt. Lett. |

15. | D. G. Fischer and E. Wolf, “Inverse problems with quasi-homogeneous random media,” J. Opt. Soc. Am. A |

16. | D. Zhao, O. Korotkova, and E. Wolf, “Application of correlation-induced spectral changes to inverse scattering,” Opt. Lett. |

17. | Z. Tong and O. Korotkova, “Method for tracing the position of an alien object embedded in a random particulate medium,” J. Opt. Soc. Am. A |

18. | M. Born and E. Wolf, |

19. | Z. Tong and O. Korotkova, “Pair-structure matrix of random collections of particles: Implications for light scattering,” Opt. Commun. |

**OCIS Codes**

(290.5850) Scattering : Scattering, particles

(290.5825) Scattering : Scattering theory

**ToC Category:**

Scattering

**History**

Original Manuscript: November 12, 2012

Manuscript Accepted: December 10, 2012

Published: December 17, 2012

**Virtual Issues**

Vol. 8, Iss. 1 *Virtual Journal for Biomedical Optics*

**Citation**

Zhangrong Mei and Olga Korotkova, "Random light scattering by collections of ellipsoids," Opt. Express **20**, 29296-29307 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-28-29296

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### References

- E. Wolf, J. T. Foley, and F. Gori, “Frequency shifts of spectral lines produced by scattering from spatially random media,” J. Opt. Soc. Am. A6(8), 1142–1149 (1989). [CrossRef]
- E. Wolf, J. T. Foley, and F. Gori, “Frequency shifts of spectral lines produced by scattering from spatially random media: errata,” J. Opt. Soc. Am. A7(1), 173–173 (1990). [CrossRef]
- D. G. Fischer and E. Wolf, “Inverse problems with quasi-homogeneous random media,” J. Opt. Soc. Am. A11(3), 1128–1132 (1994). [CrossRef]
- A. Dogariu and E. Wolf, “Spectral changes produced by static scattering on a system of particles,” Opt. Lett.23(17), 1340–1342 (1998). [CrossRef] [PubMed]
- C. Zhao, Y. Cai, X. Lu, and H. T. Eyyuboğlu, “Radiation force of coherent and partially coherent flat-topped beams on a Rayleigh particle,” Opt. Express17(3), 1753–1765 (2009). [CrossRef] [PubMed]
- S. Sahin, G. Gbur, and O. Korotkova, “Scattering of light from particles with semisoft boundaries,” Opt. Lett.36(20), 3957–3959 (2011). [CrossRef] [PubMed]
- G. J. Streekstra, A. G. Hoekstra, E. J. Nijhof, and R. M. Heethaar, “Light scattering by red blood cells in ektacytometry: Fraunhofer versus anomalous diffraction,” Appl. Opt.32(13), 2266–2272 (1993). [CrossRef] [PubMed]
- G. J. Streekstra, A. G. Hoekstra, and R. M. Heethaar, “Anomalous diffraction by arbitrarily oriented ellipsoids: applications in ektacytometry,” Appl. Opt.33(31), 7288–7296 (1994). [CrossRef] [PubMed]
- B. K. Wilson, M. R. Behrend, M. P. Horning, and M. C. Hegg, “Detection of malarial byproduct hemozoin utilizing its unique scattering properties,” Opt. Express19(13), 12190–12196 (2011). [CrossRef] [PubMed]
- R. S. Brock, X. H. Hu, P. Yang, and J. Lu, “Evaluation of a parallel FDTD code and application to modeling of light scattering by deformed red blood cells,” Opt. Express13(14), 5279–5292 (2005). [CrossRef] [PubMed]
- E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, Cambridge, 2007).
- O. Korotkova and E. Wolf, “Scattering matrix theory for stochastic scalar fields,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.75(5), 056609 (2007). [CrossRef] [PubMed]
- S. Sahin and O. Korotkova, “Scattering of scalar light fields from collections of particles,” Phys. Rev. A78(6), 063815 (2008). [CrossRef]
- S. Sahin and O. Korotkova, “Effect of the pair-structure factor of a particulate medium on scalar wave scattering in the first Born approximation,” Opt. Lett.34(12), 1762–1764 (2009). [CrossRef] [PubMed]
- D. G. Fischer and E. Wolf, “Inverse problems with quasi-homogeneous random media,” J. Opt. Soc. Am. A11(3), 1128–1135 (1994). [CrossRef]
- D. Zhao, O. Korotkova, and E. Wolf, “Application of correlation-induced spectral changes to inverse scattering,” Opt. Lett.32(24), 3483–3485 (2007). [CrossRef] [PubMed]
- Z. Tong and O. Korotkova, “Method for tracing the position of an alien object embedded in a random particulate medium,” J. Opt. Soc. Am. A28(8), 1595–1599 (2011). [CrossRef] [PubMed]
- M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, 1999).
- Z. Tong and O. Korotkova, “Pair-structure matrix of random collections of particles: Implications for light scattering,” Opt. Commun.284(24), 5598–5600 (2011). [CrossRef]

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