## Polarization studies for backscattering of RBC suspensions based on Mueller matrix decomposition |

Optics Express, Vol. 20, Issue 18, pp. 20771-20782 (2012)

http://dx.doi.org/10.1364/OE.20.020771

Acrobat PDF (1318 KB)

### Abstract

Tissue polarimetry has demonstrated its great potential in biomedical field presently. In this study, the polarization characteristics of red blood cell (RBC) suspensions in a back-detection geometry have been investigated with experimental measurements and Monte Carlo (MC) simulation based on Mueller matrix decomposition. It is revealed that the simulated dependence of degree of polarization (DOP) and diattenuation on the distance away from incident point is qualitatively consistent with experimental result. DOP and diattenuation decay with increasing radial distance except in the region adjacent to the incident point. Further analysis shows that the number of scattering events and the scattering angle simultaneously influence the trends of DOP and diattenuation curves in the central region.

© 2012 OSA

## 1. Introduction

1. F. Boulvert, G. Le Brun, B. Le Jeune, J. Cariou, and L. Martin, “Decomposition algorithm of an experimental Mueller matrix,” Opt. Commun. **282**(5), 692–704 (2009). [CrossRef]

2. M. H. Smith, “Interpreting Mueller matrix images of tissues,” Proc. SPIE **4257**, 82–89 (2001). [CrossRef]

3. J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. **34**(6), 1558–1568 (1995). [CrossRef]

8. M. R. Antonelli, A. Pierangelo, T. Novikova, P. Validire, A. Benali, B. Gayet, and A. De Martino, “Mueller matrix imaging of human colon tissue for cancer diagnostics: how Monte Carlo modeling can help in the interpretation of experimental data,” Opt. Express **18**(10), 10200–10208 (2010). [CrossRef] [PubMed]

1. F. Boulvert, G. Le Brun, B. Le Jeune, J. Cariou, and L. Martin, “Decomposition algorithm of an experimental Mueller matrix,” Opt. Commun. **282**(5), 692–704 (2009). [CrossRef]

9. X. Li and G. Yao, “Mueller matrix decomposition of diffuse reflectance imaging in skeletal muscle,” Appl. Opt. **48**(14), 2625–2631 (2009). [CrossRef] [PubMed]

11. N. Ghosh, M. F. G. Wood, S. H. Li, R. D. Weisel, B. C. Wilson, R. K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J Biophotonics **2**(3), 145–156 (2009). [CrossRef] [PubMed]

9. X. Li and G. Yao, “Mueller matrix decomposition of diffuse reflectance imaging in skeletal muscle,” Appl. Opt. **48**(14), 2625–2631 (2009). [CrossRef] [PubMed]

10. J. Chung, W. Jung, M. J. Hammer-Wilson, P. Wilder-Smith, and Z. Chen, “Use of polar decomposition for the diagnosis of oral precancer,” Appl. Opt. **46**(15), 3038–3045 (2007). [CrossRef] [PubMed]

12. N. Ghosh and I. A. Vitkin, “Tissue polarimetry: concepts, challenges, applications, and outlook,” J. Biomed. Opt. **16**(11), 110801 (2011). [CrossRef] [PubMed]

13. S.-Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A **13**(5), 1106–1113 (1996). [CrossRef]

## 2. Experiment

14. M. Itoh, M. Yamanari, Y. Yasuno, and T. Yatagai, “Polarization characteristics of multiple backscattering in human blood cell suspensions,” Opt. Quantum Electron. **37**(13-15), 1277–1285 (2005). [CrossRef]

^{2}. The receiving angle was about 3 deg in order to make

## 3. Theory

### 3.1 Polarization-sensitive Monte Carlo simulation

^{−1}). In our implementation, the Henyey-Greenstein (HG) phase function was used for sampling the scattering angle, and azimuthal angle was chosen uniformly between 0 and

21. J. Q. Lu, P. Yang, and X. H. Hu, “Simulations of light scattering from a biconcave red blood cell using the finite-difference time-domain method,” J. Biomed. Opt. **10**(2), 024022 (2005). [CrossRef] [PubMed]

^{7}input photon packets.

### 3.2 Polar decomposition of the Mueller matrices

13. S.-Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A **13**(5), 1106–1113 (1996). [CrossRef]

22. J. Morio and F. Goudail, “Influence of the order of diattenuator, retarder, and polarizer in polar decomposition of Mueller matrices,” Opt. Lett. **29**(19), 2234–2236 (2004). [CrossRef] [PubMed]

13. S.-Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A **13**(5), 1106–1113 (1996). [CrossRef]

20. N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Polarimetry in turbid, birefringent, optically active media: A Monte Carlo study of Mueller matrix decomposition in the backscattering geometry,” J. Appl. Phys. **105**(10), 102023 (2009). [CrossRef]

23. S. Manhas, M. K. Swami, P. Buddhiwant, N. Ghosh, P. K. Gupta, and J. Singh, “Mueller matrix approach for determination of optical rotation in chiral turbid media in backscattering geometry,” Opt. Express **14**(1), 190–202 (2006). [CrossRef] [PubMed]

## 4. Results and discussion

24. X. Wang, L. Yang, J. Lai, and Z. Li, “Polar decomposition applied to light back-scattering by erythrocyte suspensions,” Proc. SPIE **8192**, 81924T, 81924T-6 (2011). [CrossRef]

^{−1}to 800 cm

^{−1}). The phase relationship by different scattering events will be randomized. Hence, the coherent backscattering effects are very weak and can be ignored. After polar decomposition for Mueller matrices, distribution of DOP and diattenuation in the backscattering plane can be obtained. As illustrated in Fig. 3 , the distribution of DOP and diattenuation is azimuthally independent. In order to discuss the dependence of DOP and diattenuation on radial distance, Fig. 4 shows the curves along central horizontal axis L

_{A}.

15. X. Wang, L. V. Wang, C. W. Sun, and C. C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments,” J. Biomed. Opt. **8**(4), 608–617 (2003). [CrossRef] [PubMed]

25. A. Roggan, M. Friebel, K. Dörschel, A. Hahn, and G. Müller, “Optical properties of circulating human blood in the wavelength range 400-2500 nm,” J. Biomed. Opt. **4**(1), 36–46 (1999). [CrossRef]

15. X. Wang, L. V. Wang, C. W. Sun, and C. C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments,” J. Biomed. Opt. **8**(4), 608–617 (2003). [CrossRef] [PubMed]

26. X. Guo, M. F. G. Wood, and A. Vitkin, “Monte Carlo study of pathlength distribution of polarized light in turbid media,” Opt. Express **15**(3), 1348–1360 (2007). [CrossRef] [PubMed]

27. M. Friebel, J. Helfmann, and M. C. Meinke, “Influence of osmolarity on the optical properties of human erythrocytes,” J. Biomed. Opt. **15**(5), 055005 (2010). [CrossRef] [PubMed]

## 5. Conclusion

## References and links

1. | F. Boulvert, G. Le Brun, B. Le Jeune, J. Cariou, and L. Martin, “Decomposition algorithm of an experimental Mueller matrix,” Opt. Commun. |

2. | M. H. Smith, “Interpreting Mueller matrix images of tissues,” Proc. SPIE |

3. | J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. |

4. | A. H. Hielscher, A. A. Eick, J. R. Mourant, D. Shen, J. P. Freyer, and I. J. Bigio, “Diffuse backscattering Mueller matricesof highly scattering media,” Opt. Express |

5. | B. D. Cameron, M. J. Raković, M. Mehrübeoğlu, G. W. Kattawar, S. Rastegar, L. V. Wang, and G. L. Coté, “Measurement and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium,” Opt. Lett. |

6. | M. J. Raković, G. W. Kattawar, M. B. Mehrübeoğlu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Coté, “Light backscattering polarization patterns from turbid media: theory and experiment,” Appl. Opt. |

7. | P. Yang, H. Wei, G. W. Kattawar, Y. X. Hu, D. M. Winker, C. A. Hostetler, and B. A. Baum, “Sensitivity of the backscattering Mueller matrix to particle shape and thermodynamic phase,” Appl. Opt. |

8. | M. R. Antonelli, A. Pierangelo, T. Novikova, P. Validire, A. Benali, B. Gayet, and A. De Martino, “Mueller matrix imaging of human colon tissue for cancer diagnostics: how Monte Carlo modeling can help in the interpretation of experimental data,” Opt. Express |

9. | X. Li and G. Yao, “Mueller matrix decomposition of diffuse reflectance imaging in skeletal muscle,” Appl. Opt. |

10. | J. Chung, W. Jung, M. J. Hammer-Wilson, P. Wilder-Smith, and Z. Chen, “Use of polar decomposition for the diagnosis of oral precancer,” Appl. Opt. |

11. | N. Ghosh, M. F. G. Wood, S. H. Li, R. D. Weisel, B. C. Wilson, R. K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J Biophotonics |

12. | N. Ghosh and I. A. Vitkin, “Tissue polarimetry: concepts, challenges, applications, and outlook,” J. Biomed. Opt. |

13. | S.-Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A |

14. | M. Itoh, M. Yamanari, Y. Yasuno, and T. Yatagai, “Polarization characteristics of multiple backscattering in human blood cell suspensions,” Opt. Quantum Electron. |

15. | X. Wang, L. V. Wang, C. W. Sun, and C. C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments,” J. Biomed. Opt. |

16. | D. Côté and I. A. Vitkin, “Robust concentration determination of optically active molecules in turbid media with validated three-dimensional polarization sensitive Monte Carlo calculations,” Opt. Express |

17. | J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part I,” Opt. Express |

18. | J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part II,” Opt. Express |

19. | |

20. | N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Polarimetry in turbid, birefringent, optically active media: A Monte Carlo study of Mueller matrix decomposition in the backscattering geometry,” J. Appl. Phys. |

21. | J. Q. Lu, P. Yang, and X. H. Hu, “Simulations of light scattering from a biconcave red blood cell using the finite-difference time-domain method,” J. Biomed. Opt. |

22. | J. Morio and F. Goudail, “Influence of the order of diattenuator, retarder, and polarizer in polar decomposition of Mueller matrices,” Opt. Lett. |

23. | S. Manhas, M. K. Swami, P. Buddhiwant, N. Ghosh, P. K. Gupta, and J. Singh, “Mueller matrix approach for determination of optical rotation in chiral turbid media in backscattering geometry,” Opt. Express |

24. | X. Wang, L. Yang, J. Lai, and Z. Li, “Polar decomposition applied to light back-scattering by erythrocyte suspensions,” Proc. SPIE |

25. | A. Roggan, M. Friebel, K. Dörschel, A. Hahn, and G. Müller, “Optical properties of circulating human blood in the wavelength range 400-2500 nm,” J. Biomed. Opt. |

26. | X. Guo, M. F. G. Wood, and A. Vitkin, “Monte Carlo study of pathlength distribution of polarized light in turbid media,” Opt. Express |

27. | M. Friebel, J. Helfmann, and M. C. Meinke, “Influence of osmolarity on the optical properties of human erythrocytes,” J. Biomed. Opt. |

**OCIS Codes**

(110.7050) Imaging systems : Turbid media

(120.5410) Instrumentation, measurement, and metrology : Polarimetry

(290.1350) Scattering : Backscattering

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: May 7, 2012

Revised Manuscript: June 27, 2012

Manuscript Accepted: August 20, 2012

Published: August 24, 2012

**Virtual Issues**

Vol. 7, Iss. 10 *Virtual Journal for Biomedical Optics*

**Citation**

Xuezhen Wang, Jiancheng Lai, and Zhenhua Li, "Polarization studies for backscattering of RBC suspensions based on Mueller matrix decomposition," Opt. Express **20**, 20771-20782 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-18-20771

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### References

- F. Boulvert, G. Le Brun, B. Le Jeune, J. Cariou, and L. Martin, “Decomposition algorithm of an experimental Mueller matrix,” Opt. Commun. 282(5), 692–704 (2009). [CrossRef]
- M. H. Smith, “Interpreting Mueller matrix images of tissues,” Proc. SPIE 4257, 82–89 (2001). [CrossRef]
- J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34(6), 1558–1568 (1995). [CrossRef]
- A. H. Hielscher, A. A. Eick, J. R. Mourant, D. Shen, J. P. Freyer, and I. J. Bigio, “Diffuse backscattering Mueller matricesof highly scattering media,” Opt. Express 1(13), 441–453 (1997). [CrossRef] [PubMed]
- B. D. Cameron, M. J. Raković, M. Mehrübeoğlu, G. W. Kattawar, S. Rastegar, L. V. Wang, and G. L. Coté, “Measurement and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium,” Opt. Lett. 23(7), 485–487 (1998). [CrossRef] [PubMed]
- M. J. Raković, G. W. Kattawar, M. B. Mehrübeoğlu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Coté, “Light backscattering polarization patterns from turbid media: theory and experiment,” Appl. Opt. 38(15), 3399–3408 (1999). [CrossRef] [PubMed]
- P. Yang, H. Wei, G. W. Kattawar, Y. X. Hu, D. M. Winker, C. A. Hostetler, and B. A. Baum, “Sensitivity of the backscattering Mueller matrix to particle shape and thermodynamic phase,” Appl. Opt. 42(21), 4389–4395 (2003). [CrossRef] [PubMed]
- M. R. Antonelli, A. Pierangelo, T. Novikova, P. Validire, A. Benali, B. Gayet, and A. De Martino, “Mueller matrix imaging of human colon tissue for cancer diagnostics: how Monte Carlo modeling can help in the interpretation of experimental data,” Opt. Express 18(10), 10200–10208 (2010). [CrossRef] [PubMed]
- X. Li and G. Yao, “Mueller matrix decomposition of diffuse reflectance imaging in skeletal muscle,” Appl. Opt. 48(14), 2625–2631 (2009). [CrossRef] [PubMed]
- J. Chung, W. Jung, M. J. Hammer-Wilson, P. Wilder-Smith, and Z. Chen, “Use of polar decomposition for the diagnosis of oral precancer,” Appl. Opt. 46(15), 3038–3045 (2007). [CrossRef] [PubMed]
- N. Ghosh, M. F. G. Wood, S. H. Li, R. D. Weisel, B. C. Wilson, R. K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J Biophotonics 2(3), 145–156 (2009). [CrossRef] [PubMed]
- N. Ghosh and I. A. Vitkin, “Tissue polarimetry: concepts, challenges, applications, and outlook,” J. Biomed. Opt. 16(11), 110801 (2011). [CrossRef] [PubMed]
- S.-Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A 13(5), 1106–1113 (1996). [CrossRef]
- M. Itoh, M. Yamanari, Y. Yasuno, and T. Yatagai, “Polarization characteristics of multiple backscattering in human blood cell suspensions,” Opt. Quantum Electron. 37(13-15), 1277–1285 (2005). [CrossRef]
- X. Wang, L. V. Wang, C. W. Sun, and C. C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments,” J. Biomed. Opt. 8(4), 608–617 (2003). [CrossRef] [PubMed]
- D. Côté and I. A. Vitkin, “Robust concentration determination of optically active molecules in turbid media with validated three-dimensional polarization sensitive Monte Carlo calculations,” Opt. Express 13(1), 148–163 (2005). [CrossRef] [PubMed]
- J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part I,” Opt. Express 13(12), 4420–4438 (2005). [CrossRef] [PubMed]
- J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part II,” Opt. Express 13(25), 10392–10405 (2005). [CrossRef] [PubMed]
- http://omlc.ogi.edu/software/polarization/
- N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Polarimetry in turbid, birefringent, optically active media: A Monte Carlo study of Mueller matrix decomposition in the backscattering geometry,” J. Appl. Phys. 105(10), 102023 (2009). [CrossRef]
- J. Q. Lu, P. Yang, and X. H. Hu, “Simulations of light scattering from a biconcave red blood cell using the finite-difference time-domain method,” J. Biomed. Opt. 10(2), 024022 (2005). [CrossRef] [PubMed]
- J. Morio and F. Goudail, “Influence of the order of diattenuator, retarder, and polarizer in polar decomposition of Mueller matrices,” Opt. Lett. 29(19), 2234–2236 (2004). [CrossRef] [PubMed]
- S. Manhas, M. K. Swami, P. Buddhiwant, N. Ghosh, P. K. Gupta, and J. Singh, “Mueller matrix approach for determination of optical rotation in chiral turbid media in backscattering geometry,” Opt. Express 14(1), 190–202 (2006). [CrossRef] [PubMed]
- X. Wang, L. Yang, J. Lai, and Z. Li, “Polar decomposition applied to light back-scattering by erythrocyte suspensions,” Proc. SPIE 8192, 81924T, 81924T-6 (2011). [CrossRef]
- A. Roggan, M. Friebel, K. Dörschel, A. Hahn, and G. Müller, “Optical properties of circulating human blood in the wavelength range 400-2500 nm,” J. Biomed. Opt. 4(1), 36–46 (1999). [CrossRef]
- X. Guo, M. F. G. Wood, and A. Vitkin, “Monte Carlo study of pathlength distribution of polarized light in turbid media,” Opt. Express 15(3), 1348–1360 (2007). [CrossRef] [PubMed]
- M. Friebel, J. Helfmann, and M. C. Meinke, “Influence of osmolarity on the optical properties of human erythrocytes,” J. Biomed. Opt. 15(5), 055005 (2010). [CrossRef] [PubMed]

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