Demonstration of full 4×4 Mueller polarimetry through an optical fiber for endoscopic applications Sandeep Manhas,1,4 J´er´emy Vizet,1,4 Stanislas Deby,2 Jean-Charles Vanel,2 Paola Boito,1 Mireille Verdier,3 Antonello De Martino,2 and Dominique Pagnoux1,∗ 1 Xlim institute, University of Limoges, UMR CNRS 7252, 123 Avenue Albert Thomas, 87060 Limoges CEDEX, France 2 LPICM, Ecole Polytechnique, UMR CNRS 7647, 91128 Palaiseau, France 3 Cellular homeostasis and pathologies laboratory, Faculty of Medicine, University of Limoges, EA 3842, 2 rue du Dr Marcland, 87025 Limoges CEDEX, France 4 These authors contributed equally to this work. ∗ [email protected]

Abstract: A novel technique to measure the full 4 × 4 Mueller matrix of a sample through an optical fiber is proposed, opening the way for endoscopic applications of Mueller polarimetry for biomedical diagnosis. The technique is based on two subsequent Mueller matrices measurements: one for characterizing the fiber only, and another for the assembly of fiber and sample. From this differential measurement, we proved theoretically that the polarimetric properties of the sample can be deduced. The proof of principle was experimentally validated by measuring various polarimetric parameters of known optical components. Images of manufactured and biological samples acquired by using this approach are also presented. © 2015 Optical Society of America OCIS codes: (110.5405) Polarimetric imaging; (120.5410) Polarimetry; (260.5430) Polarization; (260.1440) Birefringence; (170.6935) Tissue characterization; (060.2430) Fibers, single-mode; (110.2350) Fiber optics imaging.

References and links 1. 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 19, 1582–1593 (2011). 2. S. L. Jacques, J. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340 (2002). 3. A. Pierangelo, A. Nazac, A. Benali, P. Validire, H. Cohen, T. Novikova, B. H. Ibrahim, S. Manhas, C. Fallet, M.-R. Antonelli, and A. De Martino, “Polarimetric imaging of uterine cervix: a case study,” Opt. Express 21, 14120–14130 (2013). 4. N. Ghosh and I. A. Vitkin, “Tissue polarimetry: concepts, challenges, applications, and outlook,” J. Biomed. Opt. 16, 110801 (2011). 5. 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, 1245– 1248 (2001). 6. J. Qi, M. Ye, M. Singh, N. T. Clancy, and D. S. Elson, “Narrow band 3 × 3 Mueller polarimetric endoscopy,” Biomed. Opt. Express 4, 2433–2449 (2013). 7. M. H. Smith, P. D. Burke, A. Lompado, E. A. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3911, 210–216 (2000). 8. J. Chung, W. Jung, M. J. Hammer-Wilson, P Wilder-Smith, and Z. Chen, “Use of polar decomposition for the diagnosis of oral precancer,” Appl. Opt. 46, 3038–3045 (2007).

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9. M. Dubreuil, P. Babilotte, L. Martin, D. Sevrain, S. Rivet, Y. Le Grand, G. Le Brun, B. Turlin, and B. Le Jeune, “Mueller matrix polarimetry for improved liver fibrosis diagnosis,” Opt. Lett. 37, 1061–1063 (2012). 10. D. Goldstein, Polarized Light, Revised and Expanded (Taylor & Francis, 2003). 11. J. Fade and M. Alouini, “Depolarization remote sensing by orthogonality breaking,” Phys. Rev. Lett. 109, 043901 (2012). 12. J. Desroches, D. Pagnoux, F. Louradour, and A. Barth´el´emy, “Fiber-optic device for endoscopic polarization imaging,” Opt. Lett. 34, 3409–3411 (2009). 13. A. Myakov, L. Nieman, L. Wicky, U. Utzinger, R. Richards-Kortum, and K. Sokolov, “Fiber optic probe for polarized reflectance spectroscopy in vivo: Design and performance,” J. Biomed. Opt. 7, 388–397 (2002). 14. E. Garcia-Caurel, A. De Martino, J.-P. Gaston, and L. Yan, “Application of spectroscopic ellipsometry and Mueller ellipsometry to optical characterization,” Appl. Spectrosc. 67, 1–21 (2013). 15. 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, 3490–3502 (1999). 16. A. Peinado, A. Lizana, and Juan Campos, “Optimization and tolerance analysis of a polarimeter with ferroelectric liquid crystals,” Appl. Opt. 52, 5748–5757 (2013). ¨ 17. T. Chartier, A. Hideur, C. Ozkul, F. Sanchez, and G. M. St´ephan, “Measurement of the elliptical birefringence of single-mode optical fibers,” Appl. Opt. 40, 5343–5353 (2001). 18. S. Delvaux and M. V. Barel, “Eigenvalue computation for unitary rank structured matrices,” J. Comput. Appl. Math. 213, 268–287 (2008). 19. S.-Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A 13, 1106–1113 (1996). 20. D. J. Maitland and J. T. Walsh, “Quantitative measurements of linear birefringence during heating of native collagen,” Lasers Surg. Med. 20, 310–318 (1997). 21. M. Dubreuil, S. Rivet, B. Le Jeune, and J. Cariou, “Snapshot Mueller matrix polarimeter by wavelength polarization coding,” Opt. Express 15, 13660–13668 (2007).

1.

Introduction

Over the past few decades, optical polarimetry has received considerable attention for biomedical diagnosis, as it can provide additional information compared to intensity based measurements [1–9]. Among the different polarimetric techniques, Mueller polarimetry is the only one able to determine the full polarimetric response of any sample, giving access to its birefringence, diattenuation and depolarization [3, 4, 9, 10]. When considering inner tissues, in vivo in situ accurate characterization involving endoscopic techniques is of paramount importance to perform early diseases diagnosis. Current endoscopic tools are based on intensity imaging. Therefore, polarimetry can be a very attractive candidate to improve the diagnostic performance of endoscopy. Unfortunately, the optical fibers used in endoscopes modify the polarization states of the guided light in an uncontrolled manner all along the path. Obviously, polarization maintaining fibers also cannot overcome this problem as they only preserve two orthogonal linear polarization states. Thus, the probing polarization states and the analyzed ones are no longer those emitted by the source and reflected/scattered by the sample, as in the case of usual polarimetric techniques. For this reason, the implementation of polarimetric techniques with an optical fiber endoscope is difficult. In spite of this, a few techniques for achieving polarimetry through a fiber endoscope have been proposed until now [11–13]. However, all of these techniques provide only part of the polarimetric parameters of interest. Recently, implementation of 3 × 3 Mueller matrix imaging in a laparoscope was reported [6]. With such a straight and rigid endoscope, applications to regions only reachable via bent natural ways like bronchi or colon are not possible. In order to reach these regions of interest, a flexible endoscope incorporating an optical fiber is needed. In this communication, we report the first measurements of the full 4 × 4 Mueller matrices of different samples, performed through an optical fiber. The technique is based on a differential polarimetric characterization of (i) the fiber only, (ii) and the assembly fiber + sample. The paper is organized as follows: first, the experimental setup built to implement this differential technique is described. Then, a mathematical treatement used to decouple the fiber contribution from the measurement of fiber + sample and to extract sample Mueller matrix is #226669 - $15.00 USD (C) 2015 OSA

Received 12 Nov 2014; revised 8 Jan 2015; accepted 12 Jan 2015; published 2 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003047 | OPTICS EXPRESS 3048

presented. Finally, experimental results on different calibrated, manufactured and biological samples are shown and discussed. 2.

Experimental setup and measurement principle

A schematic of the experimental setup is depicted in Fig. 1.

Fig. 1. Schematic of the experimental setup. PIBS : Polarization Insensitive Beam Splitter ; MSM : Micro-Switchable Mirror ; PSG : Polarization States Generator ; PSA : Polarization States Analyzer.

The beam from a monochromatic laser source (Oxxius LBX660, λ = 660 nm, 100 mW) was coupled into a 2 m long single-mode optical fiber (Corning RGB-400, λc = 400 nm) at the proximal side, after passing through a Polarization States Generator (PSG) and a Polarization Insensitive Beam Splitter (PIBS, Thorlabs BS010). A Miniaturized Switchable Mirror (MSM) was set in the optical path between the fiber output (distal side) and the sample. The light reflected by either the mirror (MSM on) or the sample (MSM off) was back coupled into the fiber and reflected towards a photodiode (Hamamatsu S8745-01), after being analyzed by a Polarization States Analyzer (PSA). PSG is made of an assembly of a linear polarizer, followed by two tunable ferroelectric liquid crystal cells, sandwiching a quarter waveplate [14]. PSA is built with the same components in the reverse order. For one Mueller matrix determination, 16 discrete measurements are achieved, each based on 6 averaged acquisitions. To calibrate our polarimeter, we used the eigenvalue calibration method (ECM) [15]. This calibration determines the matrices describing the PSG and the PSA by performing a set of intensities measurements. The reference samples used in the calibration are a linear polarizer and a quarter waveplate. Any imperfection in optical components is automatically taken into account by the calibration procedure, like possible linear retardance of the PIBS. The details of PSG and PSA operation, calibration, and Mueller matrix determination was explained in other communications [14, 15]. Experiments were done at a constant temperature, therefore no significant drift of the PSG and PSA characteristics has been observed after calibration over 24 hours [16]. It is worth mentioning here that because of the calibration procedure the Mueller matrix of a mirror is an identity matrix. Consequently, with the MSM on, the first measurement provides a Mueller matrix M1 = MFB MFF , where MFF and MFB are the Mueller matrix of the fiber in forward and backward directions respectively. The second measurement with the MSM off provides a new Mueller matrix M2 = MFB MS MFF , where MS is the Mueller matrix of the sample. The sought Mueller matrix MS is determined from M1 and M2 , both measured within 70 ms. For transparent samples, a mirror was used to couple light back into the fiber. Therefore, in this case, MS is the Mueller matrix of the sample in double pass. It has already been stated in another study that a single-mode optical fiber can be considered as a concatenation of a large number n of thin linear birefringent plates with some arbitrary orientations [17], without depolarization and diattenuation. Therefore, the Mueller matrix of

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Received 12 Nov 2014; revised 8 Jan 2015; accepted 12 Jan 2015; published 2 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003047 | OPTICS EXPRESS 3049

the fiber MFF can be written as : MFF = MEn · . . . · ME2 · ME1

(1)

where MEi = R(θi )D(δi )R(−θi ). θi and δi are the orientation angle and the linear retardance of the ith birefringent plate respectively. The rotation matrix R(θi ) and Mueller matrix of a linear retarder D(δi ) are expressed as :   1 0 0 0 0 cos θi − sin θi 0  (2) R(θi ) =  0 sin θi cos θi 0 0 0 0 1   1 0 0 0 0 1 0 0   (3) D(δi ) =  0 0 cos δi sin δi  0 0 − sin δi cos δi Repeated application of the pull-through lemma [18] shows that for any choice of θi and δi , there exist angles θa , θb and linear retardance δ such that the matrix MFF can be factorized as : MFF = R(θb )D(δ )R(−θa )

(4)

This theoretical result was experimentally validated by analyzing several single-mode fibers in different conditions. Typical example of measured Mueller matrix MFFexp of a single-mode fiber in forward direction is shown in Table 1. MFFexp was multiplied by R(θ ) and R(θ 0 ) as shown in Eq. (5).  M¯ θ , θ 0 = R(−θ )MFFexp R(θ 0 ) (5) 0 where qθ and θ are scanned over the span [0, π] in order to numerically minimize the quantity 2 2 2 2 A = M¯ (2,3) . M¯ (u,v) refers to the element in row u and column v of + M¯ (2,4) + M¯ (3,2) + M¯ (4,2) ¯ The values of θ and θ 0 at which A is minimum correspond to θa and θb respectively. matrix M. The resulting matrix M¯ (θa , θb ) has the form similar to D(δ ), as shown in Table 1. Computed values of θa , θb , and δ are 69◦ , 3◦ and 69.8◦ respectively.

Table 1. Measured Mueller matrix MFFexp and Mueller matrix M¯ after minimizing the quantity A (θ = θa and θ 0 = θb ).

 1 0 0.001 0.004  0.007 −0.712 0.696 −0.093  MFFexp =   0.003 −0.289 −0.173 0.925  −0.003 0.632 0.691 0.337   1 0.001 −0.001 0.004  0.007 1.000 −0.007 0.004  M¯ (θa , θb ) =   0.002 −0.006 0.324 0.930 −0.003 −0.007 −0.936 0.337 

Therefore, by using Eq. (4), the Mueller matrix M1 can be written as : M1 = MFB MFF = R(θa )D(δ )R(−θb )R(θb )D(δ )R(−θa ) = R(θa )D(2δ )R(−θa )

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(6a) (6b) (6c)

Received 12 Nov 2014; revised 8 Jan 2015; accepted 12 Jan 2015; published 2 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003047 | OPTICS EXPRESS 3050

The measurement of M1 allows to deduce θa and δ [19]. Considering the fact that acquisition time for both M1 and M2 is very small, variation of δ and θa can be neglected. We verified this assumption by vibrating the fiber over its whole length (both ends being kept fixed), with a vibration amplitude of about ± 5 mm, the vibration frequency being varied from 1 to 8 Hz. In these severe conditions, maximum changes of δ and θa between two measurements of the fiber alone remain respectively lower than 1.2◦ (mean value = 0.46◦ , standard deviation = 0.26◦ ) and 1.5◦ (mean value = 0.55◦ , standard deviation = 0.38◦ ) over 1000 successive measurements. Therefore, M2 can be written as : M2 = R(θa )D(δ )R(−θb )MS R(θb )D(δ )R(−θa )

(7)

Separating known and unknown quantities, Eq. (7) becomes R(−θb )MS R(θb ) = D-1 (δ )R(−θa )M2 R(θa )D-1 (δ )

(8)

Since right-hand side of Eq. (8) is known, thus left hand side can be computed. This provides the Mueller matrix of the sample but with some orientation, whose value is not equal to the actual orientation axis of the sample. In the following, the former is called false orientation. However, this does not affect absolute values of polarimetric parameters of the sample, except its absolute orientation axis values. Furthermore, any change in the latter can be quantified. 3.

Results and discussion

In order to experimentally validate this approach, Mueller matrices of a waveplate (λ /8 at 632.8 nm) at different orientation angles were recorded at 660 nm (linear retardance ≈ 86.32◦ in double pass). The computed values of linear retardance and rotation angles of this waveplate are shown in Fig. 2. When the waveplate is at 0◦ in lab frame, as stated earlier we observed

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some false orientation value, and this value was substracted from the all measured rotation

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Received 12 Nov 2014; revised 8 Jan 2015; accepted 12 Jan 2015; published 2 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003047 | OPTICS EXPRESS 3051

values. As expected, a constant value of linear retardance was observed, independently of the rotation angle. Measured rotation and linear retardance values are in very good agreement with the expected ones. Next, measurements of Mueller matrices were done on combination of a Babinet-Soleil compensator (tunable linear retarder with fast axis oriented at 45◦ ) and a tilted glass plate which acts as a linear diattenuator with eigenaxis of diattenuation at 0◦ (linear diattenuation ≈ 0.35). The Babinet-Soleil compensator is followed by the glass plate. This combination generates both linear and circular diattenuation depending on the value of linear retardance. Mueller matrices of the assembly were also simulated. To retrieve the polarimetric parameters from Mueller matrices, polar decomposition was used [19], with the diattenuator set first. As shown in the Fig. 3, the measured parameters are in good accordance with the simulated ones. After obtaining satisfactory results from the calibrated samples, experiments were done LR : LD : CD :

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Babinet-Soleil compensator LR (degrees) Fig. 3. Retrieved polarimetric parameters from measured and simulated Mueller matrices of the assembly Babinet-Soleil compensator with variable linear retardance and tilted glass plate. LR : Linear Retardance ; LD : Linear Diattenuation ; CD : Circular Diattenuation.

on manufactured and biological samples. For this, a microscope objective (10x, 0.25 N.A., Olympus) was set after the MSM to focus and collect light from the sample. We separately measured the Mueller matrix of this microscope objective, and verified that it corresponds to an identity matrix with a precision better than 3 %. In very first implementation, complete images were built by moving the sample in the focal plane of the probing beam with the help of motorized XY stages (Thorlabs MT3-Z8). Let us note that due to the very low dynamics of these stages, characterizations of only 6 (respectively 3) pixels can be achieved per second for a 10 µm (respectively 50 µm) resolution, significantly increasing the time required for a complete image acquisition. A sample was manufactured by fixing on a mirror a sheet polarizer and different layers of transparent adhesive tape (cellophane tape) which is known to have linear birefringence property. In Fig. 4(a) (raw image), regions 2 and 4 correspond to two superimposed tape layers with fast axes oriented parallel and perpendicular to each other respectively, whereas rest of the tape regions correspond to a single layer (regions 3). #226669 - $15.00 USD (C) 2015 OSA

Received 12 Nov 2014; revised 8 Jan 2015; accepted 12 Jan 2015; published 2 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003047 | OPTICS EXPRESS 3052

Fig. 4. Sample raw image (a), corresponding measured Mueller matrix (b), retrieved linear diattenuation (c), and linear retardance (d) from measured Mueller matrix.

The linear polarizer is set in region 1. The scanned image size is 9.5 mm × 6 mm with resolution of 50 µm. Images of measured Mueller matrix along with retrieved polarimetric parameters are shown in Figs. 4(b)-4(d). Due to the presence of the polarizer in region 1, very high linear diattenuation was observed, as shown in Fig. 4(c). In Fig. 4(d), as expected the value of linear retardance (average value ≈ 95◦ ) is almost double where fast axes of the tape layers are aligned parallel to each other (region 2), compared to the retardance value (average value ≈ 50◦ ) in single layer (region 3). On the contrary, linear retardance diminished (average value ≈ 8◦ ) where layers fast axes are aligned perpendicular to each other (region 4). Little difference between observed values and expected ones (for region 2 ≈ 100◦ and region 4 ≈ 0◦ ) may be due to non-uniformity of the sample or little misalignement of the layers eigenaxes. To test our system performance on biological samples, we imaged a 50 µm thick sample of type I collagen extracted from rat tail tendon. The scanned image size is 1.35 mm × 1.7 mm with resolution of 10 µm. The raw image and measured polarimetric images are shown in Fig. 5. Collagen which is highly birefringent material [20] exhibits high linear retardance in the

Fig. 5. Raw image of type I collagen sample (a), retrieved linear retardance (b) and eigenaxis orientation of linear retardance (c) from measured Mueller matrix.

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Received 12 Nov 2014; revised 8 Jan 2015; accepted 12 Jan 2015; published 2 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003047 | OPTICS EXPRESS 3053

corresponding areas encircled by red lines as shown in the Fig. 5(b). This can be attributed to the well oriented structure of collagen fibers in these areas which is further supported by presence of the well-defined orientation pattern of collagen fibers as shown in Fig. 5(c). On the other hand, areas outside the red line show low even no linear retardance, that is mainly due to presence of non-birefringent ground substance of connective tissue. Consequently, in Fig. 5(c), no evident orientation pattern was observed in the corresponding areas. No depolarization was observed over the whole sample. 4.

Conclusion

For the first time, to our knowledge, we have proposed and demonstrated a technique making remote full Mueller polarimetric imaging possible through an optical fiber. This can be considered as a first step towards realization of Mueller endoscopy that can further be used for biomedical diagnosis. For the feasibility demonstration of the approach, differential measurements were done : first for characterizing the fiber only and second for characterizing the assembly of fiber and sample. Then, a suitable mathematical treatment allows to extract the sample Mueller matrix. Proof of principle was demonstrated by achieving experiments on calibrated samples like retarders and diattenuators. Preliminary demonstrations on manufactured and biological tissues (rat tail tendon) were also successfully carried out. At this stage of the study, the demonstrated technique is not yet applicable to real in vivo endoscopic applications, because of the very long measurement time of each image pixel (70 ms), due to electronics and low modulation frequency of the liquid crystals cells in our polarimeter. However, there exist applications requiring relaxed time constraints such as analysis of cells cultures at the bottom of culture wells which are not reachable by classical microscope. To decrease the measurement time, photo-elastic modulators can be used instead of ferroelectric liquid crystal cells. Another way to reduce the measurement time is to implement snapshot Mueller measurement technique [21]. Further work will be devoted to address this crucial issue of acquisition time. Acknowledgments The authors are grateful to the French ANR for its financial support through the IMULE project.

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Received 12 Nov 2014; revised 8 Jan 2015; accepted 12 Jan 2015; published 2 Feb 2015 9 Feb 2015 | Vol. 23, No. 3 | DOI:10.1364/OE.23.003047 | OPTICS EXPRESS 3054

Demonstration of full 4×4 Mueller polarimetry through an optical fiber for endoscopic applications.

A novel technique to measure the full 4 × 4 Mueller matrix of a sample through an optical fiber is proposed, opening the way for endoscopic applicatio...
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