Abstract

A hybrid model comprising the differential Mueller matrix formalism and the Mueller matrix decomposition method is proposed for extracting the linear birefringence (LB), linear dichroism (LD), circular birefringence (CB), circular dichroism (CD), and depolarization properties (Dep) of turbid optical samples. In contrast to the differential-based Mueller matrix method, the proposed hybrid model provides full-range measurements of all the anisotropic properties of the optical sample. Furthermore, compared to the decomposition-based Mueller matrix method, the proposed model is insensitive to the multiplication order of the constituent basis matrices. The validity of the proposed method is confirmed by extracting the anisotropic properties of a compound chitosan-glucose-microsphere sample with LB/CB/Dep properties and two ferrofluidic samples with CB/CD/Dep and LB/LD/Dep properties, respectively. It is shown that the proposed hybrid model not only yields full-range measurements of all the anisotropic parameters, but is also more accurate and more stable than the decomposition method. Moreover, compared to the decomposition method, the proposed model more accurately reflects the dependency of the phase retardation angle and linear dichroism angle on the direction of the external magnetic field for ferrofluidic samples. Overall, the results presented in this study confirm that the proposed model has significant potential for extracting the optical parameters of real-world samples characterized by either single or multiple anisotropic properties.

© 2013 OSA

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2010

2009

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 Biophotonics2(3), 145–156 (2009).
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[CrossRef] [PubMed]

2007

2006

T. Moffitt, Y. C. Chen, and S. A. Prahl, “Preparation and characterization of polyurethane optical phantoms,” J. Biomed. Opt. 11, 041103 (2006).

G. Pal, S. Basu, K. Mitra, and T. Vo-Dinh, “Time-resolved optical tomography using short-pulse laser for tumor detection,” Appl. Opt.45(24), 6270–6282 (2006).
[CrossRef] [PubMed]

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, F. Paglia, and R. Cubeddu, “Multi-channel time-resolved system for functional near infrared spectroscopy,” Opt. Express14(12), 5418–5432 (2006).
[CrossRef] [PubMed]

C. L. Darling, G. D. Huynh, and D. Fried, “Light scattering properties of natural and artificially demineralized dental enamel at 1310 nm,” J. Biomed. Opt.11(3), 034023 (2006).
[CrossRef] [PubMed]

B. D. Cameron, Y. Li, and A. Nezhuvingal, “Determination of optical scattering properties in turbid media using Mueller matrix imaging,” J. Biomed. Opt. 11, 054031 (2006).

2005

A. Dimofte, J. C. Finlay, and T. C. Zhu, “A method for determination of the absorption and scattering properties interstitially in turbid media,” Phys. Med. Biol.50(10), 2291–2311 (2005).
[CrossRef] [PubMed]

P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt.10(3), 034018 (2005).
[CrossRef] [PubMed]

R. A. Chipman, “Depolarization index and the average degree of polarization,” Appl. Opt.44(13), 2490–2495 (2005).
[CrossRef] [PubMed]

B. J. DeBoo, J. M. Sasian, and R. A. Chipman, “Depolarization of diffusely reflecting man-made objects,” Appl. Opt.44(26), 5434–5445 (2005).
[CrossRef] [PubMed]

H. C. Cheng and Y. L. Lo, “The synthesis of multiple parameters of arbitrary FBGs via a genetic algorithm, and two thermally modulated intensity,” J. Lightwave Technol.23(6), 2158–2168 (2005).
[CrossRef]

2004

S. Sun, H. Zeng, D. B. Robinson, S. Raoux, P. M. Rice, S. X. Wang, and G. Li, “Monodisperse MFe2O4 (M = Fe, Co, Mn) nanoparticles,” J. Am. Chem. Soc.126(1), 273–279 (2004).
[CrossRef] [PubMed]

R. O. Esenaliev, Y. Y. Petrov, O. Hartrumpf, D. J. Deyo, and D. S. Prough, “Continuous, noninvasive monitoring of total hemoglobin concentration by an optoacoustic technique,” Appl. Opt.43(17), 3401–3407 (2004).
[CrossRef] [PubMed]

N. Shah, A. E. Cerussi, D. Jakubowski, D. Hsiang, J. Butler, and B. J. Tromberg, “Spatial variations in optical and physiological properties of healthy breast tissue,” J. Biomed. Opt.9(3), 534–540 (2004).
[CrossRef] [PubMed]

2003

S. J. Yeh, O. S. Khalil, C. F. Hanna, and S. Kantor, “Near-infrared thermo-optical response of the localized reflectance of intact diabetic and nondiabetic human skin,” J. Biomed. Opt.8(3), 534–544 (2003).
[CrossRef] [PubMed]

2002

X. Wang, G. Yao, and L. V. Wang, “Monte Carlo Model and Single-Scattering Approximation of the Propagation of Polarized Light in Turbid Media Containing Glucose,” Appl. Opt.41(4), 792–801 (2002).
[CrossRef] [PubMed]

X. Wang and L. V. Wang, “Propagation of polarized light in birefringent turbid media: A Monte Carlo study,” J. Biomed. Opt.7(3), 279–290 (2002).
[CrossRef] [PubMed]

G. L. Liu, Y. Li, and B. D. Cameron, “Polarization-based optical imaging and processing techniques with application to the cancer diagnostics,” Proc. SPIE4617, 208–220 (2002).
[CrossRef]

2001

1998

1997

1995

S. Fantini, M.-A. Franceschini, J. S. Maier, S. A. Walker, B. B. Barbieri, and E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng.34(1), 32–42 (1995).
[CrossRef]

1993

1986

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta (Lond.)33(2), 185–189 (1986).
[CrossRef]

1978

Alexandrakis, G.

Arce-Diego, J. L.

Azzam, R. M. A.

Barbieri, B. B.

S. Fantini, M.-A. Franceschini, J. S. Maier, S. A. Walker, B. B. Barbieri, and E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng.34(1), 32–42 (1995).
[CrossRef]

Bargo, P. R.

P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt.10(3), 034018 (2005).
[CrossRef] [PubMed]

Basu, S.

Beek, J. F.

Bernabeu, E.

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta (Lond.)33(2), 185–189 (1986).
[CrossRef]

Blair, G.

P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt.10(3), 034018 (2005).
[CrossRef] [PubMed]

Busch, D. R.

Butler, J.

N. Shah, A. E. Cerussi, D. Jakubowski, D. Hsiang, J. Butler, and B. J. Tromberg, “Spatial variations in optical and physiological properties of healthy breast tissue,” J. Biomed. Opt.9(3), 534–540 (2004).
[CrossRef] [PubMed]

Cameron, B. D.

B. D. Cameron, Y. Li, and A. Nezhuvingal, “Determination of optical scattering properties in turbid media using Mueller matrix imaging,” J. Biomed. Opt. 11, 054031 (2006).

G. L. Liu, Y. Li, and B. D. Cameron, “Polarization-based optical imaging and processing techniques with application to the cancer diagnostics,” Proc. SPIE4617, 208–220 (2002).
[CrossRef]

B. D. Cameron, M. J. Rakovic, M. Mehrübeoglu, 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]

Cerussi, A. E.

N. Shah, A. E. Cerussi, D. Jakubowski, D. Hsiang, J. Butler, and B. J. Tromberg, “Spatial variations in optical and physiological properties of healthy breast tissue,” J. Biomed. Opt.9(3), 534–540 (2004).
[CrossRef] [PubMed]

Chen, P. C.

Chen, Y. C.

T. Moffitt, Y. C. Chen, and S. A. Prahl, “Preparation and characterization of polyurethane optical phantoms,” J. Biomed. Opt. 11, 041103 (2006).

Cheng, H. C.

Chipman, R. A.

Contini, D.

Cope, M.

Coté, G. L.

Cubeddu, R.

Darling, C. L.

C. L. Darling, G. D. Huynh, and D. Fried, “Light scattering properties of natural and artificially demineralized dental enamel at 1310 nm,” J. Biomed. Opt.11(3), 034023 (2006).
[CrossRef] [PubMed]

DeBoo, B. J.

Delpy, D. T.

Deyo, D. J.

Dimofte, A.

A. Dimofte, J. C. Finlay, and T. C. Zhu, “A method for determination of the absorption and scattering properties interstitially in turbid media,” Phys. Med. Biol.50(10), 2291–2311 (2005).
[CrossRef] [PubMed]

Esenaliev, R. O.

Fantini, S.

S. Fantini, M.-A. Franceschini, J. S. Maier, S. A. Walker, B. B. Barbieri, and E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng.34(1), 32–42 (1995).
[CrossRef]

Faris, G. W.

Finlay, J. C.

A. Dimofte, J. C. Finlay, and T. C. Zhu, “A method for determination of the absorption and scattering properties interstitially in turbid media,” Phys. Med. Biol.50(10), 2291–2311 (2005).
[CrossRef] [PubMed]

Franceschini, M.-A.

S. Fantini, M.-A. Franceschini, J. S. Maier, S. A. Walker, B. B. Barbieri, and E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng.34(1), 32–42 (1995).
[CrossRef]

Fried, D.

C. L. Darling, G. D. Huynh, and D. Fried, “Light scattering properties of natural and artificially demineralized dental enamel at 1310 nm,” J. Biomed. Opt.11(3), 034023 (2006).
[CrossRef] [PubMed]

Ghosh, N.

N. Ghosh and I.A. Vitkin, “Tissue polarimetry: concepts, challenges, applications, and outlook,” J. Biomed. Opt. 16, 110801 (2011).

X. Guo, M. F. G. Wood, N. Ghosh, and I. A. Vitkin, “Depolarization of light in turbid media: a scattering event resolved Monte Carlo study,” Appl. Opt.49(2), 153–162 (2010).
[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 Biophotonics2(3), 145–156 (2009).
[CrossRef] [PubMed]

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, 102023 (2009).

Gil, J. J.

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta (Lond.)33(2), 185–189 (1986).
[CrossRef]

Goodell, T. T.

P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt.10(3), 034018 (2005).
[CrossRef] [PubMed]

Gratton, E.

S. Fantini, M.-A. Franceschini, J. S. Maier, S. A. Walker, B. B. Barbieri, and E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng.34(1), 32–42 (1995).
[CrossRef]

Guo, X.

Hanna, C. F.

S. J. Yeh, O. S. Khalil, C. F. Hanna, and S. Kantor, “Near-infrared thermo-optical response of the localized reflectance of intact diabetic and nondiabetic human skin,” J. Biomed. Opt.8(3), 534–544 (2003).
[CrossRef] [PubMed]

Hartrumpf, O.

Hsiang, D.

N. Shah, A. E. Cerussi, D. Jakubowski, D. Hsiang, J. Butler, and B. J. Tromberg, “Spatial variations in optical and physiological properties of healthy breast tissue,” J. Biomed. Opt.9(3), 534–540 (2004).
[CrossRef] [PubMed]

Huynh, G. D.

C. L. Darling, G. D. Huynh, and D. Fried, “Light scattering properties of natural and artificially demineralized dental enamel at 1310 nm,” J. Biomed. Opt.11(3), 034023 (2006).
[CrossRef] [PubMed]

Jacques, S. L.

P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt.10(3), 034018 (2005).
[CrossRef] [PubMed]

A. A. Oraevsky, S. L. Jacques, and F. K. Tittel, “Measurement of tissue optical properties by time-resolved detection of laser-induced transient stress,” Appl. Opt.36(1), 402–415 (1997).
[CrossRef] [PubMed]

Jakubowski, D.

N. Shah, A. E. Cerussi, D. Jakubowski, D. Hsiang, J. Butler, and B. J. Tromberg, “Spatial variations in optical and physiological properties of healthy breast tissue,” J. Biomed. Opt.9(3), 534–540 (2004).
[CrossRef] [PubMed]

Kantor, S.

S. J. Yeh, O. S. Khalil, C. F. Hanna, and S. Kantor, “Near-infrared thermo-optical response of the localized reflectance of intact diabetic and nondiabetic human skin,” J. Biomed. Opt.8(3), 534–544 (2003).
[CrossRef] [PubMed]

Kattawar, G. W.

Khalil, O. S.

S. J. Yeh, O. S. Khalil, C. F. Hanna, and S. Kantor, “Near-infrared thermo-optical response of the localized reflectance of intact diabetic and nondiabetic human skin,” J. Biomed. Opt.8(3), 534–544 (2003).
[CrossRef] [PubMed]

Koval, G.

P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt.10(3), 034018 (2005).
[CrossRef] [PubMed]

Li, G.

S. Sun, H. Zeng, D. B. Robinson, S. Raoux, P. M. Rice, S. X. Wang, and G. Li, “Monodisperse MFe2O4 (M = Fe, Co, Mn) nanoparticles,” J. Am. Chem. Soc.126(1), 273–279 (2004).
[CrossRef] [PubMed]

Li, R. K.

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 Biophotonics2(3), 145–156 (2009).
[CrossRef] [PubMed]

Li, S. H.

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 Biophotonics2(3), 145–156 (2009).
[CrossRef] [PubMed]

Li, Y.

B. D. Cameron, Y. Li, and A. Nezhuvingal, “Determination of optical scattering properties in turbid media using Mueller matrix imaging,” J. Biomed. Opt. 11, 054031 (2006).

G. L. Liu, Y. Li, and B. D. Cameron, “Polarization-based optical imaging and processing techniques with application to the cancer diagnostics,” Proc. SPIE4617, 208–220 (2002).
[CrossRef]

Lin, J. F.

Liu, G. L.

G. L. Liu, Y. Li, and B. D. Cameron, “Polarization-based optical imaging and processing techniques with application to the cancer diagnostics,” Proc. SPIE4617, 208–220 (2002).
[CrossRef]

Lo, Y. L.

Lo, Y.-L.

T.-T.-H. Pham and Y.-L. Lo, “Extraction of effective parameters of turbid media utilizing Mueller matrix approach -A study of glucose sensing,” J. Biomed. Opt.17(9), 097002 (2012).
[CrossRef]

Maier, J. S.

S. Fantini, M.-A. Franceschini, J. S. Maier, S. A. Walker, B. B. Barbieri, and E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng.34(1), 32–42 (1995).
[CrossRef]

Matcher, S. J.

Mehrübeoglu, M.

Mitra, K.

Moffitt, T.

T. Moffitt, Y. C. Chen, and S. A. Prahl, “Preparation and characterization of polyurethane optical phantoms,” J. Biomed. Opt. 11, 041103 (2006).

Nezhuvingal, A.

B. D. Cameron, Y. Li, and A. Nezhuvingal, “Determination of optical scattering properties in turbid media using Mueller matrix imaging,” J. Biomed. Opt. 11, 054031 (2006).

Oraevsky, A. A.

Ortega-Quijano, N.

Ossikovski, R.

Paglia, F.

Pal, G.

Patterson, M. S.

Petrov, Y. Y.

Pham, T. T. H.

Pham, T.-T.-H.

T.-T.-H. Pham and Y.-L. Lo, “Extraction of effective parameters of turbid media utilizing Mueller matrix approach -A study of glucose sensing,” J. Biomed. Opt.17(9), 097002 (2012).
[CrossRef]

Pickering, J. W.

Pifferi, A.

Prahl, S. A.

T. Moffitt, Y. C. Chen, and S. A. Prahl, “Preparation and characterization of polyurethane optical phantoms,” J. Biomed. Opt. 11, 041103 (2006).

P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt.10(3), 034018 (2005).
[CrossRef] [PubMed]

J. W. Pickering, S. A. Prahl, N. van Wieringen, J. F. Beek, H. J. C. M. Sterenborg, and M. J. C. van Gemert, “Double-Integrating-Sphere System for Measuring the Optical Properties of Tissue,” Appl. Opt.32(4), 399–410 (1993).
[CrossRef] [PubMed]

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Rakovic, M. J.

Raoux, S.

S. Sun, H. Zeng, D. B. Robinson, S. Raoux, P. M. Rice, S. X. Wang, and G. Li, “Monodisperse MFe2O4 (M = Fe, Co, Mn) nanoparticles,” J. Am. Chem. Soc.126(1), 273–279 (2004).
[CrossRef] [PubMed]

Rastegar, S.

Rice, P. M.

S. Sun, H. Zeng, D. B. Robinson, S. Raoux, P. M. Rice, S. X. Wang, and G. Li, “Monodisperse MFe2O4 (M = Fe, Co, Mn) nanoparticles,” J. Am. Chem. Soc.126(1), 273–279 (2004).
[CrossRef] [PubMed]

Robinson, D. B.

S. Sun, H. Zeng, D. B. Robinson, S. Raoux, P. M. Rice, S. X. Wang, and G. Li, “Monodisperse MFe2O4 (M = Fe, Co, Mn) nanoparticles,” J. Am. Chem. Soc.126(1), 273–279 (2004).
[CrossRef] [PubMed]

Sasian, J. M.

Shah, N.

N. Shah, A. E. Cerussi, D. Jakubowski, D. Hsiang, J. Butler, and B. J. Tromberg, “Spatial variations in optical and physiological properties of healthy breast tissue,” J. Biomed. Opt.9(3), 534–540 (2004).
[CrossRef] [PubMed]

Sleven, R. A.

P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt.10(3), 034018 (2005).
[CrossRef] [PubMed]

Spinelli, L.

Sterenborg, H. J. C. M.

Sun, S.

S. Sun, H. Zeng, D. B. Robinson, S. Raoux, P. M. Rice, S. X. Wang, and G. Li, “Monodisperse MFe2O4 (M = Fe, Co, Mn) nanoparticles,” J. Am. Chem. Soc.126(1), 273–279 (2004).
[CrossRef] [PubMed]

Tittel, F. K.

Torricelli, A.

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N. Shah, A. E. Cerussi, D. Jakubowski, D. Hsiang, J. Butler, and B. J. Tromberg, “Spatial variations in optical and physiological properties of healthy breast tissue,” J. Biomed. Opt.9(3), 534–540 (2004).
[CrossRef] [PubMed]

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van Wieringen, N.

Vitkin, I. A.

X. Guo, M. F. G. Wood, N. Ghosh, and I. A. Vitkin, “Depolarization of light in turbid media: a scattering event resolved Monte Carlo study,” Appl. Opt.49(2), 153–162 (2010).
[CrossRef] [PubMed]

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, 102023 (2009).

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 Biophotonics2(3), 145–156 (2009).
[CrossRef] [PubMed]

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N. Ghosh and I.A. Vitkin, “Tissue polarimetry: concepts, challenges, applications, and outlook,” J. Biomed. Opt. 16, 110801 (2011).

Vo-Dinh, T.

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S. Fantini, M.-A. Franceschini, J. S. Maier, S. A. Walker, B. B. Barbieri, and E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng.34(1), 32–42 (1995).
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S. Sun, H. Zeng, D. B. Robinson, S. Raoux, P. M. Rice, S. X. Wang, and G. Li, “Monodisperse MFe2O4 (M = Fe, Co, Mn) nanoparticles,” J. Am. Chem. Soc.126(1), 273–279 (2004).
[CrossRef] [PubMed]

Wang, X.

Weisel, R. D.

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 Biophotonics2(3), 145–156 (2009).
[CrossRef] [PubMed]

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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 Biophotonics2(3), 145–156 (2009).
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Wood, M. F. G.

X. Guo, M. F. G. Wood, N. Ghosh, and I. A. Vitkin, “Depolarization of light in turbid media: a scattering event resolved Monte Carlo study,” Appl. Opt.49(2), 153–162 (2010).
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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, 102023 (2009).

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 Biophotonics2(3), 145–156 (2009).
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Yao, G.

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S. J. Yeh, O. S. Khalil, C. F. Hanna, and S. Kantor, “Near-infrared thermo-optical response of the localized reflectance of intact diabetic and nondiabetic human skin,” J. Biomed. Opt.8(3), 534–544 (2003).
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S. Sun, H. Zeng, D. B. Robinson, S. Raoux, P. M. Rice, S. X. Wang, and G. Li, “Monodisperse MFe2O4 (M = Fe, Co, Mn) nanoparticles,” J. Am. Chem. Soc.126(1), 273–279 (2004).
[CrossRef] [PubMed]

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A. Dimofte, J. C. Finlay, and T. C. Zhu, “A method for determination of the absorption and scattering properties interstitially in turbid media,” Phys. Med. Biol.50(10), 2291–2311 (2005).
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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Determination of optical scattering properties in turbid media using Mueller matrix imaging

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J Biophotonics

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 Biophotonics2(3), 145–156 (2009).
[CrossRef] [PubMed]

J. Am. Chem. Soc.

S. Sun, H. Zeng, D. B. Robinson, S. Raoux, P. M. Rice, S. X. Wang, and G. Li, “Monodisperse MFe2O4 (M = Fe, Co, Mn) nanoparticles,” J. Am. Chem. Soc.126(1), 273–279 (2004).
[CrossRef] [PubMed]

J. Biomed. Opt.

X. Wang and L. V. Wang, “Propagation of polarized light in birefringent turbid media: A Monte Carlo study,” J. Biomed. Opt.7(3), 279–290 (2002).
[CrossRef] [PubMed]

T.-T.-H. Pham and Y.-L. Lo, “Extraction of effective parameters of turbid media utilizing Mueller matrix approach -A study of glucose sensing,” J. Biomed. Opt.17(9), 097002 (2012).
[CrossRef]

P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt.10(3), 034018 (2005).
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[CrossRef] [PubMed]

S. J. Yeh, O. S. Khalil, C. F. Hanna, and S. Kantor, “Near-infrared thermo-optical response of the localized reflectance of intact diabetic and nondiabetic human skin,” J. Biomed. Opt.8(3), 534–544 (2003).
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[CrossRef] [PubMed]

Polarimetry in turbid, birefringent, optically active media: A Monte Carlo study of Mueller matrix decomposition in the backscattering geometry

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, 102023 (2009).

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Figures (16)

Fig. 1
Fig. 1

Schematic illustration of experimental Mueller-Stokes measurement system.

Fig. 2
Fig. 2

Schematic illustration of composite sample with LB, CB and Dep properties.

Fig. 3
Fig. 3

Schematic illustration of composite sample with CB, CD and Dep properties.

Fig. 4
Fig. 4

Schematic illustration of composite sample with LB/LD and Dep properties.

Fig. 5
Fig. 5

Flow chart of a modified algorithm based on using the differential calculation method and the hybrid model

Fig. 6
Fig. 6

Extracted values of α, β and γ for LB/CB/Dep sample using hybrid model, differential calculation method and decomposition method. Note that theoretical input parameters are as follows: (a) α: 0~180°, β = 60°, γ = 15°, Δ = 0.4; (b) β: 0~360°, α = 30°, γ = 15°, Δ = 0.4; and (c) γ: 0~180°, α = 30°, β = 60°, Δ = 0.4.

Fig. 7
Fig. 7

Extracted values of γ and R for CB/CD/Dep sample using hybrid model, differential calculation method and decomposition method. Note that theoretical input parameters are as follows: (a) γ: 0~180°, R = 0.2 and Δ = 0.4; and (b) R = −1~1, γ = 15° and Δ = 0.4.

Fig. 8
Fig. 8

Extracted values of α, β, θd, and D for LB/LD/Dep composite sample using hybrid model (GA), differential calculation method and decomposition method. Note that theoretical input parameters are as follows: (a) α: 0~180°, β = 60°, θd = 35°, D = 0.5, Δ = 0.4; (b) β: 0~360°, α = 30°, θd = 35°, D = 0.5, Δ = 0.4; (c) θd: 0~180°, α = 30°, β = 60°, D = 0.5, Δ = 0.4; and (d) D: 0~1, α = 30°, β = 60°, θd = 35°, Δ = 0.4.

Fig. 9
Fig. 9

Extracted values of α, β, γ, θd, D, and R for LB/CB/LD/CD/Dep sample using differential calculation method, and exactly β and γ are modified by the hybrid model. Note that theoretical input parameters are as follows: (a) α: 0~180°, β = 60°, γ = 15°, θd = 35°, D = 0.5, R = 0.2, Δ = 0.4; (b) θd: 0~180°, α = 30°, β = 60°, γ = 15°, D = 0.5, R = 0.2, Δ = 0.4; (c) D: 0~1, α = 30°, β = 60°, γ = 15°, θd = 35°, R = 0.2, Δ = 0.4; (d) R = −1~1, α = 30°, β = 60°, γ = 15°, θd = 35°, D = 0.5, Δ = 0.4; (e) β: 0~360°, α = 30°, γ = 15°, θd = 35°, D = 0.5, R = 0.2, Δ = 0.4; and (f) γ: 0~180°, α = 30°, β = 60°, θd = 35°, D = 0.5, R = 0.2, Δ = 0.4.

Fig. 10
Fig. 10

Schematic illustration of experimental measurement system (NDF: Neutral Density Filter).

Fig. 11
Fig. 11

Experimental results for LB/CB/Dep properties of chitosan/glucose solutions with various chitosan concentrations. Note that figures (a)~(d) relate to chitosan / glucose samples containing suspended particles, while figures (e)~(h) relate to chitosan / glucose samples with no suspended particles.

Fig. 12
Fig. 12

Experimental results for LB/CB/Dep properties of chitosan/glucose solutions with various glucose concentrations. Note that figures (a)~(d) relate to chitosan / glucose samples containing suspended particles, while figures (e)~(h) relate to chitosan / glucose samples with no suspended particles.

Fig. 13
Fig. 13

Transmission electron microscopy image of the Fe3O4 nanoparticles

Fig. 14
Fig. 14

Ferrofluidic samples with (a) CB and CD properties, and (b) LB and LD properties

Fig. 15
Fig. 15

Experimental results for CB/CD/Dep properties of ferrofluidic sample with Fe3O4 concentration of 0.01 M.

Fig. 16
Fig. 16

Experimental results for LB/LD/Dep properties of ferrofluidic sample with Fe3O4 concentration of 0.025 M.

Equations (54)

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S output = [ S 0 S 1 S 2 S 3 ] output = M sample S input =[ M 11 M 12 M 13 M 14 M 21 M 22 M 23 M 24 M 31 M 32 M 33 M 34 M 41 M 42 M 43 M 44 ] [ S ^ 0 S ^ 1 S ^ 2 S ^ 3 ] input
M sample =[ M 11 M 12 M 13 M 14 M 21 M 22 M 23 M 24 M 31 M 32 M 33 M 34 M 41 M 42 M 43 M 44 ]= S output[ 0°,45°,90°,RHC ] S input[ 0°,45°,90°,RHC ] 1
m=( dM dz ) M 1
λ m = ln( λ M ) z
m= V M m λ V M 1 =[ m 11 m 12 m 13 m 14 m 21 m 22 m 23 m 24 m 31 m 32 m 33 m 34 m 41 m 42 m 43 m 44 ]
m BD = 1 d [ ln[ (1 R 2 ) 1D 1+D ] ln 1D 1+D cos(2 θ d ) ln 1D 1+D sin(2 θ d ) ln( 1+R 1R ) ln 1D 1+D cos(2 θ d ) ln[ (1 R 2 ) 1D 1+D ] 2γ βsin(2α) ln 1D 1+D sin(2 θ d ) 2γ ln[ (1 R 2 ) 1D 1+D ] βcos(2α) ln( 1+R 1R ) βsin(2α) βcos(2α) ln[ (1 R 2 ) 1D 1+D ] ]
m Δ = 1 d [ 0 κ q ' κ u ' κ v ' κ q ' κ iq ' η v ' η u ' κ u ' η v ' κ iu ' η q ' κ v ' η u ' η q ' κ iv ' ]
m BDΔ = m BD + m Δ = 1 d [ ln[ (1 R 2 ) 1D 1+D ] ln 1D 1+D cos(2 θ d )+ κ q ' ln 1D 1+D sin(2 θ d )+ κ u ' ln( 1+R 1R )+ κ v ' ln 1D 1+D cos(2 θ d ) κ q ' ln[ (1 R 2 ) 1D 1+D ] κ iq ' 2γ+ η v ' βsin(2α)+ η u ' ln 1D 1+D sin(2 θ d ) κ u ' 2γ+ η v ' ln[ (1 R 2 ) 1D 1+D ] κ iu ' βcos(2α)+ η q ' ln( 1+R 1R ) κ v ' βsin(2α)+ η u ' βcos(2α)+ η q ' ln[ (1 R 2 ) 1D 1+D ] κ iv ' ]
α= 1 2 tan 1 ( m 42 m 24 m 34 m 43 )
β= [ ( m 42 m 24 ) 2 ] 2 + [ ( m 34 m 43 ) 2 ] 2
γ= ( m 23 m 32 ) 4
θ d = 1 2 tan 1 ( m 13 + m 31 m 12 + m 21 )
D= 1 e 2 ( m 12 + m 21 ) 2 + ( m 13 + m 31 ) 2 1+ e 2 ( m 12 + m 21 ) 2 + ( m 13 + m 31 ) 2
R= e ( m 14 + m 41 2 ) 1 e ( m 14 + m 41 2 ) +1
m Δ =[ 0 ( m 12 m 21 ) 2 ( m 13 m 31 ) 2 ( m 14 m 41 ) 2 ( m 21 m 12 ) 2 m 22 m 11 ( m 23 + m 32 ) 2 ( m 24 + m 42 ) 2 ( m 31 m 13 ) 2 ( m 23 + m 32 ) 2 m 33 m 11 ( m 34 + m 43 ) 2 ( m 41 m 14 ) 2 ( m 24 + m 42 ) 2 ( m 34 + m 43 ) 2 m 44 m 11 ]
Μ Δ =[ 1 K 12 K 13 K 14 K 12 K 22 K 23 K 24 K 13 K 23 K 33 K 34 K 14 K 24 K 34 K 44 ]
Δ=1 K 22 2 + K 33 2 + K 44 2 3 ,0Δ1
M BΔ = M B M Δ or M Δ M B
M B = M BΔ M Δ 1 or M Δ 1 M BΔ =[ M 11 M 12 M 13 M 14 M 21 M 22 M 23 M 24 M 31 M 32 M 33 M 34 M 41 M 42 M 43 M 44 ]
M B =[ 1 0 0 0 0 B 22 B 23 B 24 0 B 32 B 33 B 34 0 B 42 B 43 B 44 ]
where B 22 =cos( β 2 +4 γ 2 )+ β 2 cos 2 (2α) β 2 +4 γ 2 [ 1cos( β 2 +4 γ 2 ) ], B 33 =cos( β 2 +4 γ 2 )+ β 2 sin 2 (2α) β 2 +4 γ 2 [ 1cos( β 2 +4 γ 2 ) ], B 44 =cos( β 2 +4 γ 2 )+ 4 γ 2 β 2 +4 γ 2 [ 1cos( β 2 +4 γ 2 ) ], B 23 = 2γ β 2 +4 γ 2 sin( β 2 +4 γ 2 )+ β 2 sin(4α) 2( β 2 +4 γ 2 ) [ 1cos( β 2 +4 γ 2 ) ], B 32 = 2γ β 2 +4 γ 2 sin( β 2 +4 γ 2 )+ β 2 sin(4α) 2( β 2 +4 γ 2 ) [ 1cos( β 2 +4 γ 2 ) ], B 24 = βsin(2α) β 2 +4 γ 2 sin( β 2 +4 γ 2 )+ 2γβcos(2α) β 2 +4 γ 2 [ 1cos( β 2 +4 γ 2 ) ], B 42 = βsin(2α) β 2 +4 γ 2 sin( β 2 +4 γ 2 )+ 2γβcos(2α) β 2 +4 γ 2 [ 1cos( β 2 +4 γ 2 ) ], B 34 = βcos(2α) β 2 +4 γ 2 sin( β 2 +4 γ 2 )+ 2γβsin(2α) β 2 +4 γ 2 [ 1cos( β 2 +4 γ 2 ) ], B 43 = βcos(2α) β 2 +4 γ 2 sin( β 2 +4 γ 2 )+ 2γβsin(2α) β 2 +4 γ 2 [ 1cos( β 2 +4 γ 2 ) ].
γ= cos 1 ( M 22 + M 33 + M 44 1 2 )( M 23 M 32 4 ) sin[ cos 1 ( M 22 + M 33 + M 44 1 2 ) ]
βsin(2α)= cos 1 ( M 22 + M 33 + M 44 1 2 )( M 42 M 24 ) 2sin[ cos 1 ( M 22 + M 33 + M 44 1 2 ) ] =P
βcos(2α)= cos 1 ( M 22 + M 33 + M 44 1 2 )( M 34 M 43 ) 2sin[ cos 1 ( M 22 + M 33 + M 44 1 2 ) ] =Q
α= 1 2 tan 1 P Q
β= P 2 + Q 2
M CΔ = M C M Δ or M Δ M C
M C = M CΔ M Δ 1 or M Δ 1 M CΔ =[ N 11 N 12 N 13 N 14 N 21 N 22 N 23 N 24 N 31 N 32 N 33 N 34 N 41 N 42 N 43 N 44 ]
M C =[ 1+ R 2 0 0 2R 0 ( 1 R 2 )cos(2γ) ( 1 R 2 )sin(2γ) 0 0 ( 1 R 2 )sin(2γ) ( 1 R 2 )cos(2γ) 0 2R 0 0 1+ R 2 ]
γ= 1 2 tan 1 ( N 23 N 22 )
R= N 11 ( N 12 / cos2γ ) N 14
M LΔ = M L M Δ or M Δ M L
M L = M LΔ M Δ 1 or M Δ 1 Μ LΔ =[ L 11 L 12 L 13 L 14 L 21 L 22 L 23 L 24 L 31 L 32 L 33 L 34 L 41 L 42 L 43 L 44 ]
m L = 1 d [ ln 1D 1+D ln 1D 1+D cos(2 θ d ) ln 1D 1+D sin(2 θ d ) 0 ln 1D 1+D cos(2 θ d ) ln 1D 1+D 0 βsin(2α) ln 1D 1+D sin(2 θ d ) 0 ln 1D 1+D βcos(2α) 0 βsin(2α) βcos(2α) ln 1D 1+D ] Inverse differential calculation M L
M L =[ L 11 L 12 L 13 L 14 L 21 L 22 L 23 L 24 L 31 L 32 L 33 L 34 L 41 L 42 L 43 L 44 ]
A= ( lnP ) 4 + β 4 +2 ( lnP ) 2 β 2 cos[ 4( α θ d ) ]
B= ( lnP ) 2 β 2 + A
C= ( lnP ) 2 β 2 A
L 11 = P{ [ ( lnP ) 2 + β 2 ]( cosh B 2 cosh C 2 )+ A ( cosh B 2 +cosh C 2 ) } 2 A
L 12 = PlnP{ B 2 sinh C 2 [ β 2 cos( 4α2 θ d )+( A ( lnP ) 2 )cos(2 θ d ) ]+ C 2 sinh B 2 [ β 2 cos( 4α2 θ d )+( A + ( lnP ) 2 )cos(2 θ d ) ] } ABC
L 13 = PlnP{ B 2 sinh C 2 [ β 2 sin( 4α2 θ d )+( A ( lnP ) 2 )sin(2 θ d ) ]+ C 2 sinh B 2 [ β 2 sin( 4α2 θ d )+( A + ( lnP ) 2 )sin(2 θ d ) ] } ABC
L 14 = PlnPβsin[ 2( α θ d ) ]{ cosh B 2 cosh C 2 } A
L 21 = PlnP{ B 2 sinh C 2 [ β 2 cos( 4α2 θ d )+( A ( lnP ) 2 )cos(2 θ d ) ]+ C 2 sinh B 2 [ β 2 cos( 4α2 θ d )+( A + ( lnP ) 2 )cos(2 θ d ) ] } ABC
L 22 = P{ [ β 2 cos4α+ ( lnP ) 2 cos4 θ d ]( cosh B 2 cosh C 2 )+ A ( cosh B 2 +cosh C 2 ) } 2 A
L 23 = P[ β 2 sin(4α)+ ( lnP ) 2 sin(4 θ d ) ][ cosh B 2 cosh C 2 ] 2 A
L 24 = P{ B 2 sinh B 2 [ β 2 sin( 4α2 θ d )+[ A ( lnP ) 2 ]sin(2 θ d ) ]+ C 2 sinh C 2 [ β 2 sin( 4α2 θ d )+[ A + ( lnP ) 2 ]sin(2 θ d ) ] } 2βcos[ 2( α θ d ) ] A
L 31 = PlnP{ B 2 sinh C 2 [ β 2 sin( 4α2 θ d )+( A ( lnP ) 2 )sin(2 θ d ) ]+ C 2 sinh B 2 [ β 2 sin( 4α2 θ d )+( A + ( lnP ) 2 )sin(2 θ d ) ] } ABC
L 32 = P[ β 2 sin(4α)+ ( lnP ) 2 sin(4 θ d ) ][ cosh B 2 cosh C 2 ] 2 A
L 33 = P{ [ β 2 cos4α+ ( lnP ) 2 cos4 θ d ]( cosh B 2 cosh C 2 )+ A ( cosh B 2 +cosh C 2 ) } 2 A
L 34 = P{ B 2 sinh B 2 [ β 2 cos( 4α2 θ d )+[ A ( lnP ) 2 ]cos(2 θ d ) ]+ C 2 sinh C 2 [ β 2 cos( 4α2 θ d )+[ A + ( lnP ) 2 ]cos(2 θ d ) ] } 2βcos[ 2( α θ d ) ] A
L 41 = PlnPβsin[ 2( α θ d ) ]{ cosh B 2 cosh C 2 } A
L 42 = P{ B 2 sinh B 2 [ β 2 sin( 4α2 θ d )+[ A ( lnP ) 2 ]sin(2 θ d ) ]+ C 2 sinh C 2 [ β 2 sin( 4α2 θ d )+[ A + ( lnP ) 2 ]sin(2 θ d ) ] } 2βcos[ 2( α θ d ) ] A
L 43 = P{ B 2 sinh B 2 [ β 2 cos( 4α2 θ d )+[ A ( lnP ) 2 ]cos(2 θ d ) ]+ C 2 sinh C 2 [ β 2 cos( 4α2 θ d )+[ A + ( lnP ) 2 ]cos(2 θ d ) ] } 2βcos[ 2( α θ d ) ] A
L 44 = P{ [ ( lnP ) 2 + β 2 ]( cosh B 2 cosh C 2 )+ A ( cosh B 2 +cosh C 2 ) } 2 A

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