Abstract

A novel spectroscopic Mueller matrix system has been developed and explored for both fluorescence and elastic scattering polarimetric measurements from biological tissues. The 4 × 4 Mueller matrix measurement strategy is based on sixteen spectrally resolved (λ = 400 - 800 nm) measurements performed by sequentially generating and analyzing four elliptical polarization states. Eigenvalue calibration of the system ensured high accuracy of Mueller matrix measurement over a broad wavelength range, either for forward or backscattering geometry. The system was explored for quantitative fluorescence and elastic scattering spectroscopic polarimetric studies on normal and precancerous tissue sections from human uterine cervix. The fluorescence spectroscopic Mueller matrices yielded an interesting diattenuation parameter, exhibiting differences between normal and precancerous tissues.

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    [CrossRef] [PubMed]

2012 (3)

S. Kumar, H. Purwar, R. Ossikovski, I. A. Vitkin, and N. Ghosh, “Comparative study of differential matrix and extended polar decomposition formalisms for polarimetric characterization of complex tissue-like turbid media,” J. Biomed. Opt.17(10), 105006 (2012).
[CrossRef] [PubMed]

N. Patil, J. Soni, N. Ghosh, and P. De, “Swelling-induced optical anisotropy of thermoresponsive hydrogels based on poly(2-(2-methoxyethoxy)ethyl methacrylate): Deswelling kinetics probed by quantitative Mueller matrix polarimetry,” J. Phys. Chem. B116(47), 13913–13921 (2012).
[CrossRef] [PubMed]

O. Arteaga, S. Nichols, and B. Kahr, “Mueller matrices in fluorescence scattering,” Opt. Lett.37(14), 2835–2837 (2012).
[CrossRef] [PubMed]

2011 (5)

2009 (3)

2008 (1)

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Mueller matrix decomposition for extraction of individual polarization parameters from complex turbid media exhibiting multiple scattering, optical activity, and linear birefringence,” J. Biomed. Opt.13(4), 044036 (2008).
[CrossRef] [PubMed]

2007 (3)

2006 (3)

Y. Wu and J. Y. Qu, “Autofluorescence spectroscopy of epithelial tissues,” J. Biomed. Opt.11(5), 054023 (2006).
[CrossRef] [PubMed]

C.-Y. Han and Y.-F. Chao, “Photoelastic modulated imaging ellipsometry by stroboscopic illumination technique,” Rev. Sci. Instrum.77(2), 023107 (2006).
[CrossRef]

P. J. Wu and J. T. Walsh., “Stokes polarimetry imaging of rat tail tissue in a turbid medium: degree of linear polarization image maps using incident linearly polarized light,” J. Biomed. Opt.11(1), 014031 (2006).
[CrossRef] [PubMed]

2004 (2)

A. De Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, “General methods for optimized design and calibration of Mueller polarimeters,” Thin Solid Films455−456, 112-119 (2004).

B. Laude-Boulesteix, A. De Martino, B. Drévillon, and L. Schwartz, “Mueller polarimetric imaging system with liquid crystals,” Appl. Opt.43(14), 2824–2832 (2004).
[CrossRef] [PubMed]

2002 (3)

M. H. Smith, “Optimization of a dual-rotating-retarder Mueller matrix polarimeter,” Appl. Opt.41(13), 2488–2493 (2002).
[CrossRef] [PubMed]

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt.7(3), 341–349 (2002).
[CrossRef] [PubMed]

L. V. Wang, G. L. Coté, and S. L. Jacques, “Special section guest editorial: tissue polarimetry,” J. Biomed. Opt.7(3), 278 (2002).
[CrossRef]

2001 (3)

2000 (2)

R. J. McNichols and G. L. Coté, “Optical glucose sensing in biological fluids: an overview,” J. Biomed. Opt.5(1), 5–16 (2000).
[CrossRef] [PubMed]

N. Ramanujam, “Fluorescence spectroscopy of neoplastic and non-neoplastic tissues,” Neoplasia2(1-2), 89–117 (2000).
[CrossRef] [PubMed]

1999 (1)

1996 (1)

1994 (1)

D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, “Depolarization of Multiply Scattered Waves by Spherical Diffusers: Influence of the Size Parameter,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics49(2), 1767–1770 (1994).
[CrossRef] [PubMed]

1985 (1)

W. S. Bickel and W. M. Bailey, “Stokes vectors, Mueller matrices, and polarization of scattered light,” Am. J. Phys.53(5), 468–478 (1985).
[CrossRef]

Antonelli, M.-R.

Arce-Diego, J. L.

Arifler, D.

D. Arifler, I. Pavlova, A. Gillenwater, and R. Richards-Kortum, “Light scattering from collagen fiber networks: micro-optical properties of normal and neoplastic stroma,” Biophys. J.92(9), 3260–3274 (2007).
[CrossRef] [PubMed]

Arteaga, O.

Baba, J. S.

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt.7(3), 341–349 (2002).
[CrossRef] [PubMed]

Backman, V.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med.7(11), 1245–1248 (2001).
[CrossRef] [PubMed]

Badizadegan, K.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med.7(11), 1245–1248 (2001).
[CrossRef] [PubMed]

Bailey, W. M.

W. S. Bickel and W. M. Bailey, “Stokes vectors, Mueller matrices, and polarization of scattered light,” Am. J. Phys.53(5), 468–478 (1985).
[CrossRef]

Banerjee, A.

N. Ghosh, A. Banerjee, and J. Soni, “Turbid medium polarimetry in biomedical imaging and diagnosis,” Eur. Phys. J. Appl. Phys.54(3), 30001 (2011).
[CrossRef]

Benali, A.

Bickel, W. S.

W. S. Bickel and W. M. Bailey, “Stokes vectors, Mueller matrices, and polarization of scattered light,” Am. J. Phys.53(5), 468–478 (1985).
[CrossRef]

Bicout, D.

D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, “Depolarization of Multiply Scattered Waves by Spherical Diffusers: Influence of the Size Parameter,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics49(2), 1767–1770 (1994).
[CrossRef] [PubMed]

Brosseau, C.

D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, “Depolarization of Multiply Scattered Waves by Spherical Diffusers: Influence of the Size Parameter,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics49(2), 1767–1770 (1994).
[CrossRef] [PubMed]

Cameron, B. D.

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt.7(3), 341–349 (2002).
[CrossRef] [PubMed]

Canillas, A.

Cariou, J.

Chao, Y.-F.

C.-Y. Han and Y.-F. Chao, “Photoelastic modulated imaging ellipsometry by stroboscopic illumination technique,” Rev. Sci. Instrum.77(2), 023107 (2006).
[CrossRef]

Chipman, R. A.

Chung, J. R.

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt.7(3), 341–349 (2002).
[CrossRef] [PubMed]

Compain, E.

Coté, G. L.

L. V. Wang, G. L. Coté, and S. L. Jacques, “Special section guest editorial: tissue polarimetry,” J. Biomed. Opt.7(3), 278 (2002).
[CrossRef]

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt.7(3), 341–349 (2002).
[CrossRef] [PubMed]

R. J. McNichols and G. L. Coté, “Optical glucose sensing in biological fluids: an overview,” J. Biomed. Opt.5(1), 5–16 (2000).
[CrossRef] [PubMed]

Dasari, R. R.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med.7(11), 1245–1248 (2001).
[CrossRef] [PubMed]

De, P.

N. Patil, J. Soni, N. Ghosh, and P. De, “Swelling-induced optical anisotropy of thermoresponsive hydrogels based on poly(2-(2-methoxyethoxy)ethyl methacrylate): Deswelling kinetics probed by quantitative Mueller matrix polarimetry,” J. Phys. Chem. B116(47), 13913–13921 (2012).
[CrossRef] [PubMed]

De Martino, A.

DeLaughter, A. H.

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt.7(3), 341–349 (2002).
[CrossRef] [PubMed]

Dogariu, A.

Drevillon, B.

Drévillon, B.

B. Laude-Boulesteix, A. De Martino, B. Drévillon, and L. Schwartz, “Mueller polarimetric imaging system with liquid crystals,” Appl. Opt.43(14), 2824–2832 (2004).
[CrossRef] [PubMed]

A. De Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, “General methods for optimized design and calibration of Mueller polarimeters,” Thin Solid Films455−456, 112-119 (2004).

Dubreuil, M.

Feld, M. S.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med.7(11), 1245–1248 (2001).
[CrossRef] [PubMed]

Garcia-Caurel, E.

A. De Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, “General methods for optimized design and calibration of Mueller polarimeters,” Thin Solid Films455−456, 112-119 (2004).

Gayet, B.

Georgakoudi, I.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med.7(11), 1245–1248 (2001).
[CrossRef] [PubMed]

Ghosh, N.

S. Kumar, H. Purwar, R. Ossikovski, I. A. Vitkin, and N. Ghosh, “Comparative study of differential matrix and extended polar decomposition formalisms for polarimetric characterization of complex tissue-like turbid media,” J. Biomed. Opt.17(10), 105006 (2012).
[CrossRef] [PubMed]

N. Patil, J. Soni, N. Ghosh, and P. De, “Swelling-induced optical anisotropy of thermoresponsive hydrogels based on poly(2-(2-methoxyethoxy)ethyl methacrylate): Deswelling kinetics probed by quantitative Mueller matrix polarimetry,” J. Phys. Chem. B116(47), 13913–13921 (2012).
[CrossRef] [PubMed]

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

N. Ghosh, A. Banerjee, and J. Soni, “Turbid medium polarimetry in biomedical imaging and diagnosis,” Eur. Phys. J. Appl. Phys.54(3), 30001 (2011).
[CrossRef]

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, “Mueller matrix decomposition for extraction of individual polarization parameters from complex turbid media exhibiting multiple scattering, optical activity, and linear birefringence,” J. Biomed. Opt.13(4), 044036 (2008).
[CrossRef] [PubMed]

S. K. Mohanty, N. Ghosh, S. K. Majumder, and P. K. Gupta, “Depolarization of autofluorescence from malignant and normal human breast tissues,” Appl. Opt.40(7), 1147–1154 (2001).
[CrossRef] [PubMed]

Gillenwater, A.

D. Arifler, I. Pavlova, A. Gillenwater, and R. Richards-Kortum, “Light scattering from collagen fiber networks: micro-optical properties of normal and neoplastic stroma,” Biophys. J.92(9), 3260–3274 (2007).
[CrossRef] [PubMed]

Gupta, P. K.

Gurjar, R. S.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med.7(11), 1245–1248 (2001).
[CrossRef] [PubMed]

Guyot, S.

Han, C.-Y.

C.-Y. Han and Y.-F. Chao, “Photoelastic modulated imaging ellipsometry by stroboscopic illumination technique,” Rev. Sci. Instrum.77(2), 023107 (2006).
[CrossRef]

Itzkan, I.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med.7(11), 1245–1248 (2001).
[CrossRef] [PubMed]

Jacques, S. L.

L. V. Wang, G. L. Coté, and S. L. Jacques, “Special section guest editorial: tissue polarimetry,” J. Biomed. Opt.7(3), 278 (2002).
[CrossRef]

Kahr, B.

Kumar, S.

S. Kumar, H. Purwar, R. Ossikovski, I. A. Vitkin, and N. Ghosh, “Comparative study of differential matrix and extended polar decomposition formalisms for polarimetric characterization of complex tissue-like turbid media,” J. Biomed. Opt.17(10), 105006 (2012).
[CrossRef] [PubMed]

Laude, B.

A. De Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, “General methods for optimized design and calibration of Mueller polarimeters,” Thin Solid Films455−456, 112-119 (2004).

Laude-Boulesteix, B.

Le Jeune, B.

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]

Lu, S. Y.

Majumder, S. K.

Martinez, A. S.

D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, “Depolarization of Multiply Scattered Waves by Spherical Diffusers: Influence of the Size Parameter,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics49(2), 1767–1770 (1994).
[CrossRef] [PubMed]

McNichols, R. J.

R. J. McNichols and G. L. Coté, “Optical glucose sensing in biological fluids: an overview,” J. Biomed. Opt.5(1), 5–16 (2000).
[CrossRef] [PubMed]

Mohanty, S. K.

Mujat, M.

Nichols, S.

Novikova, T.

Ortega-Quijano, N.

Ossikovski, R.

S. Kumar, H. Purwar, R. Ossikovski, I. A. Vitkin, and N. Ghosh, “Comparative study of differential matrix and extended polar decomposition formalisms for polarimetric characterization of complex tissue-like turbid media,” J. Biomed. Opt.17(10), 105006 (2012).
[CrossRef] [PubMed]

R. Ossikovski, “Differential matrix formalism for depolarizing anisotropic media,” Opt. Lett.36(12), 2330–2332 (2011).
[CrossRef] [PubMed]

R. Ossikovski, A. De Martino, and S. Guyot, “Forward and reverse product decompositions of depolarizing Mueller matrices,” Opt. Lett.32(6), 689–691 (2007).
[CrossRef] [PubMed]

Patil, N.

N. Patil, J. Soni, N. Ghosh, and P. De, “Swelling-induced optical anisotropy of thermoresponsive hydrogels based on poly(2-(2-methoxyethoxy)ethyl methacrylate): Deswelling kinetics probed by quantitative Mueller matrix polarimetry,” J. Phys. Chem. B116(47), 13913–13921 (2012).
[CrossRef] [PubMed]

Pavlova, I.

D. Arifler, I. Pavlova, A. Gillenwater, and R. Richards-Kortum, “Light scattering from collagen fiber networks: micro-optical properties of normal and neoplastic stroma,” Biophys. J.92(9), 3260–3274 (2007).
[CrossRef] [PubMed]

Perelman, L. T.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med.7(11), 1245–1248 (2001).
[CrossRef] [PubMed]

Pierangelo, A.

Poirier, S.

Pradhan, A.

Purwar, H.

S. Kumar, H. Purwar, R. Ossikovski, I. A. Vitkin, and N. Ghosh, “Comparative study of differential matrix and extended polar decomposition formalisms for polarimetric characterization of complex tissue-like turbid media,” J. Biomed. Opt.17(10), 105006 (2012).
[CrossRef] [PubMed]

Qu, J. Y.

Y. Wu and J. Y. Qu, “Autofluorescence spectroscopy of epithelial tissues,” J. Biomed. Opt.11(5), 054023 (2006).
[CrossRef] [PubMed]

Ramanujam, N.

N. Ramanujam, “Fluorescence spectroscopy of neoplastic and non-neoplastic tissues,” Neoplasia2(1-2), 89–117 (2000).
[CrossRef] [PubMed]

Richards-Kortum, R.

D. Arifler, I. Pavlova, A. Gillenwater, and R. Richards-Kortum, “Light scattering from collagen fiber networks: micro-optical properties of normal and neoplastic stroma,” Biophys. J.92(9), 3260–3274 (2007).
[CrossRef] [PubMed]

Rivet, S.

Schmitt, J. M.

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[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).
[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).
[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).
[CrossRef] [PubMed]

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P. J. Wu and J. T. Walsh., “Stokes polarimetry imaging of rat tail tissue in a turbid medium: degree of linear polarization image maps using incident linearly polarized light,” J. Biomed. Opt.11(1), 014031 (2006).
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[CrossRef]

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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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S. Kumar, H. Purwar, R. Ossikovski, I. A. Vitkin, and N. Ghosh, “Comparative study of differential matrix and extended polar decomposition formalisms for polarimetric characterization of complex tissue-like turbid media,” J. Biomed. Opt.17(10), 105006 (2012).
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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef] [PubMed]

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D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, “Depolarization of Multiply Scattered Waves by Spherical Diffusers: Influence of the Size Parameter,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics49(2), 1767–1770 (1994).
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Figures (5)

Fig. 1
Fig. 1

Schematic of the experimental systems (a) for angle resolved elastic scattering spectral Mueller matrix measurement (set-up 1) and (b) for elastic scattering and fluorescence spectral Mueller matrix measurement in the exact backscattering configuration (set-up 2). P1 and P2 are linear polarizers; QWP1 and QWP2 are rotatable achromatic quarter wavw retarders; L1, L2, L3, L4, L5 are lenses, A1, A2, A3 are variable apertures; BS1, BS2 are beam splitters; MO is microscope objective (in set-up2). In both the set-ups, P1, QWP1 form the PSG unit and P2, QWP2 form the PSA unit. The Xe-lamp is used as excitation source for recording elastic scattering spectral Mueller matrices (in both the set-ups), whereas the 405 nm line of a diode laser is used as excitation source for recording fluorescence spectral Mueller matrices (in set-up 2).

Fig. 2
Fig. 2

The Eigenvalue calibration-derived wavelength variation of the individual elements of the (a) polarization state generator W(λ) matrices and (b) polarization state analyzer A(λ) matrices (for set-up 2, operating in exact backscattering configuration). The results are shown here for the wavelength range λ = 475–800 nm.

Fig. 3
Fig. 3

Wavelength variations of (a) expected null elements (M12, M13 and M14 elements) of the Mueller matrix for a calibrating quarter wave retarder sample (fast axis oriented at 23°). The inset shows the element M44, which ideally should vanish at λ = 632.8 nm (M44~0.01, noted inside the figure). The results are shown here for λ = 475 – 800 nm. (b) Diattenuation d (λ) (left axis, dotted line) and linear retardanceδ (λ) (right axis, solid line) for the calibrating linear polarizer (orientation of polarization axis - 28°) and the quarter wave retarder (δ = π/2 at 632.8 nm, orientation of fast axis - 23°) samples respectively (shown for λ = 500 – 800 nm). The value of d for the linear polarizer is close to unity over the entire wavelength range (mean value ~0.984). The determined value for δ of the quarter wave retarder is 1.57 radian at 632.8 nm. (c) The ratio of the smallest to the largest eigenvalue (λminmax) of the 16 × 16 matrix K (shown for λ = 475 – 800 nm).

Fig. 4
Fig. 4

The 4 × 4 fluorescence spectroscopic (λem = 475 – 800 nm) Mueller matrix recorded (in the exact backscattering configuration using set-up 2) with 405 nm excitation, from the connective tissue region (stroma) of a typical Grade I precancerous tissue section.

Fig. 5
Fig. 5

The Mueller matrix-derived (a) fluorescence diattenuation parameter dFL(λ) and (b) elastic scattering diattenuation parameter dES(λ) as a function of wavelength (λ = 475 – 800 nm) for normal (open circle) and precancerous (open square) tissue sections. Results are shown for the connective tissue region (stroma) of the tissue sections. Mean values of three normal tissue samples and five precancerous tissue samples respectively, are shown here.

Equations (16)

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W(θi)=( 1 0 0 0 0 Cθi2+Sθi2cosδ SθiCθi(1cosδ) Sθisinδ 0 SθiCθi(1cosδ) Sθi2+Cθi2cosδ Cθisinδ 0 Sθisinδ Cθisinδ cosδ )×( 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 )×( 1 0 0 0 )=( 1 Cθi2+Sθi2cosδ SθiCθi(1cosδ) Sθisinδ )
PSA(θo)=( 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 )×( 1 0 0 0 0 Cθo2+Sθo2cosδ SθoCθo(1cosδ) Sθosinδ 0 SθoCθi(1cosδ) Sθo+Cθo2cosδ Cθosinδ 0 Sθosinδ Cθosinδ cosδ ) =( 1 (Cθo2+Sθo2cosδ) SθoCθo(1cosδ) Sθosinδ 1 (Cθo2+Sθo2cosδ) SθoCθo(1cosδ) Sθosinδ 0 0 0 0 0 0 0 0 )
A(θo)=[ 1,(Cθo2+Sθo2cosδ),SθoCθo(1cosδ),Sθosinδ ]
M i =AMW
M i vec =Q M vec
Q=A W T
B=AMW, B 0 =AW
C= C 0 1 B= W 1 MW, C ' = B 0 1 =AM A 1
MWWC=0
A= B 0 W 1
M M Δ M R . M D
d= 1 M D (1,1) M D (1,2) 2 + M D (1,3) 2 + M D (1,4) 2
Δ=1 | tr( M Δ 1) | 3 ,0Δ1
δ= cos 1 ( M R (2,2)+ M R (3,3) ) 2 + ( M R (3,2) M R (2,3) ) 2 1
Ψ= tan 1 ( M R (3,2) M R (2,3) M R (2,2)+ M R (3,3) )
M F = M EM M GE M A

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