## Quantitative fluorescence and elastic scattering tissue polarimetry using an Eigenvalue calibrated spectroscopic Mueller matrix system |

Optics Express, Vol. 21, Issue 13, pp. 15475-15489 (2013)

http://dx.doi.org/10.1364/OE.21.015475

Acrobat PDF (1967 KB)

### 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.

© 2013 OSA

## 1. Introduction

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

23. E. Compain, S. Poirier, and B. Drevillon, “General and self-consistent method for the calibration of polarization modulators, polarimeters, and Mueller-matrix ellipsometers,” Appl. Opt. **38**(16), 3490–3502 (1999). [CrossRef] [PubMed]

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

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

26. M. Dubreuil, S. Rivet, B. Le Jeune, and J. Cariou, “Snapshot Mueller matrix polarimeter by wavelength polarization coding,” Opt. Express **15**(21), 13660–13668 (2007). [CrossRef] [PubMed]

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

22. 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]

28. 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]

*fluorescence and elastic scattering*polarimetric measurements from depolarizing scattering medium such as tissues. In this approach, four required elliptical polarization states are sequentially generated and analyzed by using a PSG unit (comprising of a fixed linear polarizer with its axis oriented at horizontal position followed by a rotatable achromatic quarter wave retarder) and a PSA unit (similar arrangement of fixed linear polarizer with its axis oriented at vertical position and rotatable achromatic quarter wave retarder, but positioned in a reverse order). Sixteen spectrally resolved measurements are combined to construct the sample Mueller matrix. Eigenvalue calibration [28

28. 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]

## 2. Theory

### 2.1. Strategy for constructing 4 × 4 spectral Mueller matrix

**16**(11), 110801 (2011). [CrossRef] [PubMed]

_{i}

^{1}, θ

_{i}

^{2,}θ

_{i}

^{3,}θ

_{i}

^{4}) and the corresponding PSG output can be represented by

**W**, a 4 × 4 matrix whose column vectors are the four generated Stokes vectors

_{o}

^{1}, θ

_{o}

^{2,}θ

_{o}

^{3,}θ

_{o}

^{4}). The corresponding 4 × 4 analysis matrix

**A**can be formed by writing the four basis states (

_{o}) as the row vectors [28

28. 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]

_{i}and θ

_{o}) in the PSG and the PSA units are important for recording stable sample Mueller matrix. Specifically, optimum selection of the basis states of

**W**and

**A**matrices are required to have minimal propagation of errors in the determined Mueller matrix. Theoretical optimization of θ

_{i}and θ

_{o}values was therefore performed. One basic criterion for choosing the polarization basis states, is to maximize the value of the determinant of the 16 × 16 matrix

*Q*, since

*Q*is required to be invertible [6

**16**(11), 110801 (2011). [CrossRef] [PubMed]

*Q*is not binary (i.e., either invertible or not), but rather presents a continuum in which some matrices are more invertible than others. Optimization of

*Q*was therefore performed by maximizing its determinant for varying orientation angles of the quarter wave retarders (achromatic retarders with δ = π/2).Thus, optimized orientation angles for the two retarders were found to be 35°, 70°, 105° and 140°. For simplicity, the orientation angles of the retarders at the PSG and the PSA unit were kept the same (θ

_{i}= θ

_{o}) in the optimization process. A more general criterion for having minimal error propagation has previously been suggested to be based on optimization of the so-called ‘condition number’, defined as the ratio of the smallest to the largest singular values of the individual square matrices

**and**

*W***[29]. The above chosen angles were therefore verified further with this more rigorous approach based on singular value decomposition [29]. Note that the actual forms of the**

*A***and**

*W***matrices of the experimental set-up might differ from the theoretical ones derived above. Specifically, they might also show some wavelength variations, even though the quarter wave retarders used in the experimental set-up are achromatic (over λ = 400 – 800 nm). The experimentally determined**

*A***and**

*W***matrices (determined via Eigenvalue calibration method, discussed subsequently) were thus tested to meet the optimization criteria discussed above.**

*A*### 2.2. Eigenvalue calibration method

**) and the analyzer (**

*W***) matrices of the experimental system may differ from the theoretical ones, and additionally they might also exhibit wavelength response. Fortunately, there exists a method to address this issue, the so-called Eigenvalue calibration method (ECM), which can determine the exact nature of the system**

*A***and**

*W***matrices and their wavelength response [28**

*A***43**(14), 2824–2832 (2004). [CrossRef] [PubMed]

**43**(14), 2824–2832 (2004). [CrossRef] [PubMed]

**) of the form of diattenuating retarder. Let us call these set of measurements as**

*M***. The ECM method requires another set of measurements without any sample (blank), denoted by**

*B***The essential steps of ECM are as follows.**

*B*._{o}**and**

*C***are constructed such that one of them is independent of**

*C*^{/}**and the other is independent of**

*A***Clearly, the matrices**

*W***,**

*C***and**

*C*^{/}**has the same eigenvalues. Thus the eigenvalues of the Mueller matrix**

*M***can be determined from the eigenvalues of either of the matrices**

*M***and**

*C***The actual Mueller matrix**

*C*^{/}.**M**of the reference sample can then be constructed using the determined four set of eigenvalues, through a series of algebraic manipulation, as detailed in references [28

**43**(14), 2824–2832 (2004). [CrossRef] [PubMed]

**M**of the reference sample is determined, in the next step, the system

**and**

*W***matrices are determined from Eq. (8) using**

*A***M**. First the generator

**matrix is determined by solving the following Eq.In order to solve the above Eq.**

*W***,**a linear operator

**K**is built such a way that its only eigenvector associated with null eigenvalue is

**satisfying the Eq.**

*W (*

*– K W*_{16}_{× 1}

**[28**

*= 0)***43**(14), 2824–2832 (2004). [CrossRef] [PubMed]

**are all different from zero except**

*K*_{λ1}, which should actually be null and practically as close to zero as possible (

*W*_{16}_{× 1}) corresponding to the smallest eigenvalue of the matrix

**, is written back in 4 × 4 matrix form to obtain the system polarization state generator matrix**

*K***. Once**

*W***is determined, the polarization state analyzer matrix**

*W***is eventually calculated as**

*A***and**

*W***matrices and their wavelength response. This was performed using four sets of measurements for two different types of calibrating reference samples, Glen Thompson linear polarizer (as diattenuator,**

*A**d*= 1, over λ = 400 – 800 nm) and quarter waveplate (δ = π/2 at 632.8 nm, as retarder). Measurements from the linear polarizer were taken for two different orientations of polarization axis - 28°, 73°, and from the quarter waveplate for two different orientations of the fast axis - 23°, 68° respectively. These sets of orientation angles of the diattenuator and retarder have previously been shown to be optimum for eigenvalue calibration. Since, ECM provides the actual experimental

**and**

*W***matrices, without any prior modeling of the PSG and PSA units, many effects which can modify**

*A***and**

*W***values (misalignment in orientation or configurations, positioning artifacts, beam divergence, non-ideal optical characteristics of the polarizing optics etc.), are automatically taken care off. Moreover, the ratio of the smallest to the largest eigenvalue (λ**

*A*_{min}/λ

_{max}) of the 16 × 16 matrix

**, is an indicator of the accuracy or sensitivity of the system, which was thus determined for our spectral Mueller matrix polarimeter. The performance of the system was further tested by quantitatively determining the medium polarization parameters, diattenuation d, linear retardance δ (and their wavelength response) of standard optical elements. The results of the eigenvalue calibration and the initial exploration of the spectral Mueller matrix polarimeter to record spectral Mueller matrices from biological tissues are presented subsequently, in Section 4.**

*K*### 2.3. Inverse analysis of Mueller matrix using polar decomposition

15. 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**into the product of three ‘basis’ matricesHere, the matrix

**M**contains information on the effects of linear and circular diattenuation,

_{D}**M**

_{R}accounts for linear and circular retardance (or optical rotation) effects, and

**M**includes the effect of any depolarization present in the medium [6

_{Δ}**16**(11), 110801 (2011). [CrossRef] [PubMed]

15. 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]

15. 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]

21. 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]

*d*), depolarization coefficients (

*Δ*), linear retardance (

*δ*), and circular retardance or optical rotation (

*ψ*, circular retardance = 2 × optical rotation), can be determined from the corresponding basis matrices as [6

**16**(11), 110801 (2011). [CrossRef] [PubMed]

**13**(5), 1106–1113 (1996). [CrossRef]

## 3. Experimental methods

_{1}, LPVIS100, Thorlabs, USA) with its axis oriented at horizontal position, followed by a rotatable achromatic quarter wave retarder (Q

_{1}, AQWP05M-600, Thorlabs, USA) mounted on a computer controlled rotational mount (PRM1/M-27E, Thorlabs, USA). The retarders used in the system are achromatic quarter waveplates over λ = 400 – 800 nm, has a retardance accuracy of ~λ/60. Note that these sets of achromatic retarders used in the PSG and the PSA units, are different from the other type of quarter wave retarder (WPQ10M-633, δ = π/2, at λ = 632.8 nm, retardance accuracy of ~λ/300) used in the eigenvalue calibration as a reference sample (discussed in the section 2.2).

_{2}, oriented at vertical position) and a rotatable achromatic quarter wave retarder (Q

_{2}), but positioned in a reverse order. A series of sixteen measurements are performed by sequentially changing the orientation of the fast axis of the quarter wave retarders of the PSG unit and that of the PSA unit, to the four optimized angles 35°, 70°, 105° and 140° (as discussed in Section 2.1). The spectra corresponding to the sixteen combinations of the

*PSG*and

*PSA*are recorded using a fiber optic spectrometer (HR2000, Ocean Optics, USA) in set-up - 1 and using a CCD spectrometer (Shamrock imaging spectrograph, SR-303i-A, ANDOR technology, USA) in set-up-2.

_{em}= 450 – 800 nm) are recorded for sixteen combinations of the

*PSG*and

*PSA*. The set-up was completely automated using Labview so that sixteen spectrally resolved measurements can be performed with relative ease.

_{1}and P

_{2}are always fixed at horizontal and vertical polarization states respectively. This is important particularly, for spectrally resolved (employing a spectrometer) Mueller matrix measurements, since usually spectrometers are associated with complex polarization response (owing to the presence of grating). Never-the-less, eigenvalue calibration was performed following the process discussed in Section 2.2, to yield the exact nature of the system polarization state generator

_{ex}, λ

_{em}= 400 - 800 nm). For constructing fluorescence spectroscopic Mueller matrices (in set-up 2), generator matrix

_{ex}= 405 nm) and analyzer matrix

_{em}= 450 – 800 nm) are used.

## 4. Results and discussion

### 4.1. Results of eigenvalue calibration

**43**(14), 2824–2832 (2004). [CrossRef] [PubMed]

_{12}, M

_{13}and M

_{14}elements) of the Mueller matrix for a quarter wave retarder (orientation angle of fast axis from the horizontal −23°) are shown. The inset shows the element M

_{44}, which ideally should vanish at λ = 632.8 nm (M

_{44}= cos δ, δ = π/2 at 632.8 nm). The small value of the M

_{44}(~0.01) element at 632.8 nm, and the other elements over the entire spectral range (~0.01), ensured reasonably high accuracy of the spectral Mueller matrix system.

*d*(λ), linear retardance

*δ (*λ

*)*, optical rotation

*ψ*(λ) and depolarization coefficients

*Δ*(λ), were determined from polar decomposition (following Section 2.3, Eqs. (11) and (12)) of Mueller matrices recorded from the calibrating diattenuator and the retarder samples. Typical wavelength variation of the extracted

*d*(λ) and

*δ (*λ

*)*for the calibrating linear polarizer (orientation of polarization axis - 28°) and the quarter wave retarder (orientation of fast axis - 23°) sample are shown in Fig. 3(b). As can be seen from the figure, the derived values are in agreement with that expected for an ideal polarizer (

*d*~1) over the spectral range 500 nm – 800 nm. The values for the other derived polarization parameters (

*δ (*λ

*)*,

*ψ*(λ) and

*Δ*(λ)), which are expected to be zero for an ideal polarizer, were also quite negligible (≤ 0.01). Similarly, the determined value for linear retardance

*δ =*1.57 radian at 632.8 nm reasonably agrees with the expected value (

*δ*= π/2), and the corresponding wavelength variation also exhibits the expected 1/λ behavior. Finally, as discussed in Section 2.2, the ratio of the smallest to the largest eigenvalue (λ

_{min}/λ

_{max}) of the 16 × 16 matrix

**, is an indicator of the accuracy or sensitivity of the system. The wavelength variation of λ**

*K*_{min}/λ

_{max}is shown in Fig. 3(c). The considerably small magnitudes of the parameter λ

_{min}/λ

_{max}(~10

^{−3}) confirm high accuracy of the system in acquiring Mueller matrices over a broad wavelength range.

### 4.2. Results of fluorescence and elastic scattering spectroscopic Mueller matrices from tissue sections

31. 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]

31. 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]

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

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

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

35. 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]

_{23}(λ) / M

_{32}(λ), M

_{24}(λ) / M

_{42}(λ),and M

_{34}(λ) / M

_{43}(λ) also show low intensities. While the elements M

_{34}(M

_{43}) and M

_{24}(M

_{42}) represent linear retardance-

*δ*effects for horizontal/ vertical and + 45° /-45° linear polarizations respectively,

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

*δ*(λ) and

*ψ(*λ

*)*(Eq. (12c) and (12d)) were also found to be quite negligible (

*δ,ψ ≤*0.01 radian, within the experimental errors of the system). Interestingly, the elements M

_{12}(λ) / M

_{21}(λ),and M

_{13}(λ) / M

_{31}(λ) show appreciable intensity values and they also preserve the spectral characteristics of the fluorescence emission. The magnitudes of the remaining M

_{41}(λ) / M

_{41}(λ) elements, on the other hand, are relatively weaker. Analogous to the retardation effects, while the elements M

_{12}(M

_{21}) and M

_{13}(M

_{31}) represent linear diattenuation effect for horizontal/ vertical and + 45° /-45° linear polarizations respectively, the elements M

_{41}(M

_{41}) represent circular diattenuation (between left and right circular polarization states). Accordingly, the values for the diattenuation parameter

*d*(λ) (derived using Eq. (12a) of Section 2.3) were found to be appreciable (subsequent results shown in Fig. 5), with major contribution arising from linear diattenuation (negligible circular diattenuation contribution).

**37**(14), 2835–2837 (2012). [CrossRef] [PubMed]

**M**includes the polarizing transfer function of the absorption process at the excitation wavelength (due to the ground molecular state), the matrix

_{A}**M**accounts for the effect of ground state to the excited state transformation and the remaining matrix

_{G→E}**M**includes the effects of the excited state on the resulting fluorescence emission [33

_{EM}**37**(14), 2835–2837 (2012). [CrossRef] [PubMed]

**M**of Eq. (13) can be assumed to be a diattenuating depolarizer matrix [32, 33

_{G→E}**37**(14), 2835–2837 (2012). [CrossRef] [PubMed]

**M**arise from various processes such as the random orientation of the fluorophore molecules, rotational diffusion of fluorophore, radiation less energy transfer among fluorophores etc., the diattenuation effect is characteristic of dipolar absorption / emission and has geometric origin [32, 33

_{G→E}**37**(14), 2835–2837 (2012). [CrossRef] [PubMed]

_{12}/ M

_{21}elements of the matrix

**M**is maximum at a scattering angle of θ = 90° and vanishes at exact forward or backward scattering angles (θ = 0° / 180°, as should be the case for our experimental geometry of backscattering Mueller matrix measurement - θ = 180°) [33

_{G→E}**37**(14), 2835–2837 (2012). [CrossRef] [PubMed]

**M**and

_{A}**M**may possess intrinsic diattenuation and retardance properties of the ground molecular state and the excited state respectively [33

_{EM}**37**(14), 2835–2837 (2012). [CrossRef] [PubMed]

**37**(14), 2835–2837 (2012). [CrossRef] [PubMed]

**M**will possess diattenuation property in addition to depolarization. The observed appreciable intensities of M

_{F}_{12}(λ) / M

_{21}(λ),and M

_{13}(λ) / M

_{31}(λ) elements of the fluorescence Mueller matrices (and accordingly significant value of linear diattenuation) from tissue are thus manifestation of the intrinsic linear anisotropy (linear dichroism) of the emitting fluorophores (collagen). The weak magnitudes of M

_{41}(λ) / M

_{41}(λ), on the other hand, indicate that the emitting molecules exhibit very little / or no circular anisotropy (circular dichroism).

*d*(λ)for normal and precancerous tissue sections. Results are once again shown for the connective tissue region of the tissue sections. Here, the mean values of

_{FL}*d*(λ) for normal (three samples) and precancerous (five samples of pooled Grade I, Grade II and Grade III tissues) tissues are plotted. As previously mentioned, significant magnitude of

_{FL}*d*(λ) and its spectral variation (which resembles characteristic fluorescence spectra of collagen) clearly arise due to the (linear) anisotropic orientation / organization of collagen structures in either the normal or precancerous connective tissues. Importantly, the magnitude of

_{FL}*d*(λ) is observed to be reduced for the precancerous tissue specimens. This might arise due to the fact that progression of precancer is accompanied by destruction of the collagen cross-links, resulting in a loss of the anisotropic organization [35

_{FL}35. 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]

*d*(λ) for normal and precancerous connective tissues are shown in Fig. 5(b). Elastic scattering of light from anisotropically organized scattering structures is also expected to yield diattenuation effects, as is evident from the Fig. Once again, the qualitative trends in the fluorescence and elastic scattering diattenuation are similar, the values for

_{ES}*d*(λ) decreases in precancer, indicating randomization of the fibrous collagen structures [35

35. 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]

## 5. Conclusions

*fluorescence and elastic scattering*Mueller matrices over a broad wavelength range. The performance of the system has been calibrated using Eigenvalue calibration method that also yielded the exact values of the system polarization state generator and polarization state analyzer matrices over the entire wavelength range. The accuracy of the system for measuring sample Mueller matrices were tested on various calibrating reference samples. Following successful evaluation, the system was used to acquire

*fluorescence*and

*elastic scattering*spectroscopic Mueller matrices from biological tissue sections. Initial exploration of the system for quantitative fluorescence spectral polarimetric studies on normal and precancerous human cervical tissue sections has yielded promising results. Specifically, the polar decomposition analysis on fluorescence Mueller matrix from connective tissue region yielded an interesting spectral diattenuation effect, which was attributed to the anisotropic molecular structure of collagen. Note that the results presented here are on thin tissue sections. The potential of this fluorescence spectral diattenuation parameter for probing precancerous alterations in connective tissue however, needs to be rigorously investigated from intact tissues. Our current studies are thus directed towards – (i) development of a more encompassing approach for the analysis / interpretation of fluorescence Mueller matrix and (ii) comprehensive evaluation and exploration of the quantitative fluorescence Mueller matrix polarimetry (and the derived intrinsic fluorescence polarimetry characteristics) for the detection of precancerous changes from intact tissues. The novel spectral Mueller matrix polarimetry system is also being explored for other interdisciplinary applications [38

38. 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. B **116**(47), 13913–13921 (2012). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | D. S. Kliger, J. W. Lewis, and C. E. Randall, |

2. | W. S. Bickel and W. M. Bailey, “Stokes vectors, Mueller matrices, and polarization of scattered light,” Am. J. Phys. |

3. | R. A. Chipman, “Polarimetry,” |

4. | V. V. Tuchin, L. Wang, and D. À. Zimnyakov, |

5. | L. V. Wang, G. L. Coté, and S. L. Jacques, “Special section guest editorial: tissue polarimetry,” J. Biomed. Opt. |

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

7. | R. J. McNichols and G. L. Coté, “Optical glucose sensing in biological fluids: an overview,” J. Biomed. Opt. |

8. | 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. |

9. | A. Pierangelo, A. Benali, M.-R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “Ex-vivo characterization of human colon cancer by Mueller polarimetric imaging,” Opt. Express |

10. | N. Ghosh, A. Banerjee, and J. Soni, “Turbid medium polarimetry in biomedical imaging and diagnosis,” Eur. Phys. J. Appl. Phys. |

11. | P. J. Wu and J. T. Walsh Jr., “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. |

12. | N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Polarized light assessment of complex turbid media such as biological tissues using Mueller matrix decomposition,” |

13. | P. Shukla and A. Pradhan, “Mueller decomposition images for cervical tissue: Potential for discriminating normal and dysplastic states,” Opt. Express |

14. | 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 |

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

16. | R. Ossikovski, A. De Martino, and S. Guyot, “Forward and reverse product decompositions of depolarizing Mueller matrices,” Opt. Lett. |

17. | O. Arteaga and A. Canillas, “Psuedopolar decomposition of the Jones and Mueller-Jones exponential polarization matrices,” J. Opt. Soc. Am. A |

18. | 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. |

19. | R. Ossikovski, “Differential matrix formalism for depolarizing anisotropic media,” Opt. Lett. |

20. | N. Ortega-Quijano and J. L. Arce-Diego, “Mueller matrix differential decomposition,” Opt. Lett. |

21. | 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. |

22. | 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. |

23. | E. Compain, S. Poirier, and B. Drevillon, “General and self-consistent method for the calibration of polarization modulators, polarimeters, and Mueller-matrix ellipsometers,” Appl. Opt. |

24. | M. Mujat and A. Dogariu, “Real-time measurement of the polarization transfer function,” Appl. Opt. |

25. | M. H. Smith, “Optimization of a dual-rotating-retarder Mueller matrix polarimeter,” Appl. Opt. |

26. | M. Dubreuil, S. Rivet, B. Le Jeune, and J. Cariou, “Snapshot Mueller matrix polarimeter by wavelength polarization coding,” Opt. Express |

27. | C.-Y. Han and Y.-F. Chao, “Photoelastic modulated imaging ellipsometry by stroboscopic illumination technique,” Rev. Sci. Instrum. |

28. | B. Laude-Boulesteix, A. De Martino, B. Drévillon, and L. Schwartz, “Mueller polarimetric imaging system with liquid crystals,” Appl. Opt. |

29. | A. De Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, “General methods for optimized design and calibration of Mueller polarimeters,” Thin Solid Films |

30. | F. Stabo-Eeg, “Development of instrumentation for Mueller matrix ellipsometry,” PhD dissertation, Norwegian University of Science and Technology, (2009). |

31. | S. K. Mohanty, N. Ghosh, S. K. Majumder, and P. K. Gupta, “Depolarization of autofluorescence from malignant and normal human breast tissues,” Appl. Opt. |

32. | J. Lackowicz, “Principles of Fluorescence Spectroscopy,” New York, (Plenum Press, 1983). |

33. | O. Arteaga, S. Nichols, and B. Kahr, “Mueller matrices in fluorescence scattering,” Opt. Lett. |

34. | N. Ramanujam, “Fluorescence spectroscopy of neoplastic and non-neoplastic tissues,” Neoplasia |

35. | 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. |

36. | Y. Wu and J. Y. Qu, “Autofluorescence spectroscopy of epithelial tissues,” J. Biomed. Opt. |

37. | 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. Topics |

38. | 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. B |

**OCIS Codes**

(120.5410) Instrumentation, measurement, and metrology : Polarimetry

(170.3660) Medical optics and biotechnology : Light propagation in tissues

(170.4580) Medical optics and biotechnology : Optical diagnostics for medicine

(170.6510) Medical optics and biotechnology : Spectroscopy, tissue diagnostics

(170.7050) Medical optics and biotechnology : Turbid media

(260.5430) Physical optics : Polarization

(300.6280) Spectroscopy : Spectroscopy, fluorescence and luminescence

(170.6935) Medical optics and biotechnology : Tissue characterization

(240.2130) Optics at surfaces : Ellipsometry and polarimetry

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: February 25, 2013

Revised Manuscript: May 13, 2013

Manuscript Accepted: May 13, 2013

Published: June 21, 2013

**Virtual Issues**

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

**Citation**

Jalpa Soni, Harsh Purwar, Harshit Lakhotia, Shubham Chandel, Chitram Banerjee, Uday Kumar, and Nirmalya Ghosh, "Quantitative fluorescence and elastic scattering tissue polarimetry using an Eigenvalue calibrated spectroscopic Mueller matrix system," Opt. Express **21**, 15475-15489 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-13-15475

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### References

- D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic Press, 1990).
- 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]
- R. A. Chipman, “Polarimetry,” Handbook of Optics, 2nd ed., M. Bass, Ed. (McGraw-Hill, 1994) chap. 22, pp. 22.1–22.37
- V. V. Tuchin, L. Wang, and D. À. Zimnyakov, Optical Polarization in Biomedical Applications, (Springer-Verlag, 2006).
- L. V. Wang, G. L. Coté, and S. L. Jacques, “Special section guest editorial: tissue polarimetry,” J. Biomed. Opt.7(3), 278 (2002). [CrossRef]
- N. Ghosh and I. A. Vitkin, “Tissue polarimetry: concepts, challenges, applications, and outlook,” J. Biomed. Opt.16(11), 110801 (2011). [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]
- 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]
- A. Pierangelo, A. Benali, M.-R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “Ex-vivo characterization of human colon cancer by Mueller polarimetric imaging,” Opt. Express19(2), 1582–1593 (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]
- 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]
- N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Polarized light assessment of complex turbid media such as biological tissues using Mueller matrix decomposition,” Handbook of Photonics for Biomedical Science, Valery V. Tuchin, Ed. (Taylor and Francis Publishing, 2010) chap. 9, pp. 253 – 282.
- P. Shukla and A. Pradhan, “Mueller decomposition images for cervical tissue: Potential for discriminating normal and dysplastic states,” Opt. Express17(3), 1600–1609 (2009). [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]
- S. Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A13(5), 1106–1113 (1996). [CrossRef]
- 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]
- O. Arteaga and A. Canillas, “Psuedopolar decomposition of the Jones and Mueller-Jones exponential polarization matrices,” J. Opt. Soc. Am. A26(4), 783–793 (2009). [CrossRef]
- 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]
- R. Ossikovski, “Differential matrix formalism for depolarizing anisotropic media,” Opt. Lett.36(12), 2330–2332 (2011). [CrossRef] [PubMed]
- N. Ortega-Quijano and J. L. Arce-Diego, “Mueller matrix differential decomposition,” Opt. Lett.36(10), 1942–1944 (2011). [CrossRef] [PubMed]
- 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]
- 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]
- E. Compain, S. Poirier, and B. Drevillon, “General and self-consistent method for the calibration of polarization modulators, polarimeters, and Mueller-matrix ellipsometers,” Appl. Opt.38(16), 3490–3502 (1999). [CrossRef] [PubMed]
- M. Mujat and A. Dogariu, “Real-time measurement of the polarization transfer function,” Appl. Opt.40(1), 34–44 (2001). [CrossRef] [PubMed]
- M. H. Smith, “Optimization of a dual-rotating-retarder Mueller matrix polarimeter,” Appl. Opt.41(13), 2488–2493 (2002). [CrossRef] [PubMed]
- M. Dubreuil, S. Rivet, B. Le Jeune, and J. Cariou, “Snapshot Mueller matrix polarimeter by wavelength polarization coding,” Opt. Express15(21), 13660–13668 (2007). [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]
- 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).
- F. Stabo-Eeg, “Development of instrumentation for Mueller matrix ellipsometry,” PhD dissertation, Norwegian University of Science and Technology, (2009).
- 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]
- J. Lackowicz, “Principles of Fluorescence Spectroscopy,” New York, (Plenum Press, 1983).
- O. Arteaga, S. Nichols, and B. Kahr, “Mueller matrices in fluorescence scattering,” Opt. Lett.37(14), 2835–2837 (2012). [CrossRef] [PubMed]
- N. Ramanujam, “Fluorescence spectroscopy of neoplastic and non-neoplastic tissues,” Neoplasia2(1-2), 89–117 (2000). [CrossRef] [PubMed]
- 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]
- Y. Wu and J. Y. Qu, “Autofluorescence spectroscopy of epithelial tissues,” J. Biomed. Opt.11(5), 054023 (2006). [CrossRef] [PubMed]
- 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]
- 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]

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