Open Access
Add to BibSonomyAbstract
We report a novel technique for polarimetric characterization of samples through a flexible fiber endoscope, with a single shot measurement per pixel. The sample is simultaneously probed with a large diversity of polarization states, and both degree of polarization and linear retardance are determined thanks to specific processing of data. The probe polarization states are spectrally encoded on the 10 nm bandwidth of the source. The key component of the endoscope is a 3 m long specially designed optical fiber which consists of the optimized concatenation of highly birefringent fiber pieces. For a proof of principle, different calibrated or manufactured samples were successfully characterized. The proposed technique is attractive in view of reducing the measurement time of polarimetric images, in endoscopic applications.
© 2015 Optical Society of America
1. Introduction
In the recent past, optical polarization imaging has been demonstrated to be a very attractive technique for early detection of diseases in biological tissues such as melanoma, fibrosis, cervical cancer or colon cancer, as it can reveal contrasts that do not appear in standard intensity images [1–4]. In fibrillar tissues such as type I collagen, healthy and pathological regions can be discriminated considering the structural anisotropy and the disorganization degree of the fibers arrangement, which respectively result in linear birefringence and depolarization capability of the tissue. These two polarimetric characteristics can be measured by probing the tissue (sample) with known polarization states and by analyzing the polarization states of the backscattered beam: the linear birefringence and depolarization effect of the sample are then respectively deduced from the linear retardance and from the degree of polarization (DOP) of this backscattered beam [1].
For in vivo in situ characterization of internal tissues, light from the source cannot directly illuminate the sample. It must be guided towards the sample by means of a flexible optical fiber-based endoscope. The same fiber is also used to collect part of the light backscattered by the sample and to deliver it to the detection device. At this point, it is important to note that, due to the intrinsic and induced birefringence of the fiber, the polarization states of the guided fields are modified both in the forward and in the backward path, in an unpredictable, uncontrolled and time dependent manner. Therefore, the polarization state of the wave which is launched into the optical fiber is different from that of the probe. Likewise, the polarization state delivered by the fiber in feedback from the sample under test is different from that of the backscattered radiation. For that reason, polarization characterizations of samples through a fiber endoscope cannot be achieved by means of usual polarimetric measurements techniques.
Few methods only, allowing polarimetric characterization of samples through an optical waveguide, have been reported in the literature. Some of them give access to depolarization parameter only [5, 6]. Some other techniques need a reference arm, like in polarization-sensitive optical coherence tomography [7]. Mueller polarimetry has also been demonstrated through an optical waveguide, but it requires the use of a straight and rigid laparoscope, strongly limiting the applications to some easily reachable regions [8]. For in vivo applications, the measurement time is also a crucial issue to be addressed. To avoid blurred or distorted images due to unavoidable movements of the sample during its characterization, one shot measurement is highly preferable.
In this paper, we report a polarimetric measurement technique allowing precise determinations of both linear retardance and depolarization induced by a sample, through a flexible optical fiber, in one shot. The sample is assumed to be free of diattenuation and circular birefringence, as it is generally the case for fibrillar tissues. The paper is organized as follows: the measurement principle is first presented and then the experimental setup designed to implement the technique is described. Special attention is paid to the design and the optimization of a spectrally encoded polarization states generator (SEPSG) used in this setup, as it is a key component for achieving accurate one shot measurement. Finally, we report and comment preliminary experimental results obtained with this setup.
2. Measurement of polarization changes induced by a sample using spectrally encoded polarization states as a probe
The technique reported in this paper is based on a measurement principle reported in a previous work, in which (i) a real time self-compensation of the fiber birefringence over a round trip of light is achieved, (ii) the sample is probed by a diversity of polarization states (PPS), (iii) and a specific polarization analysis of the guided feedback is carried out [9]. The key steps of the measurement principle are schematically depicted on Fig. 1.
Fig. 1 Block diagram describing the principle of the method (PIBS = Polarization Insensitive Beam Splitter).
A linearly polarized beam from a light source is launched in a piece of single mode optical fiber at its so-called “proximal end”, after crossing a polarization insensitive beam splitter (PIBS). The coupled light is delivered at the opposite end of the fiber (distal end) with an unknown polarization state because of the fiber birefringence. The emerging beam passes through a miniaturized Faraday rotator which rotates its polarization state by a 45° angle, before being focused on the sample. In the following, the polarization state of the light illuminating the sample is called probe polarization state (PPS). As a result of the interaction of light with the sample, the polarization state of the field backscattered by the sample is modified. After a second pass through the Faraday rotator, a part of the backscattered radiation is coupled back into the fiber for transmission to the proximal end. The double 45° rotation of the incoming polarization states achieved by the Faraday rotator results in a self-compensation of the fiber birefringence. The light exiting the fiber at the proximal end is finally sent to a polarization analysing system by means of the PIBS. This analysing system consists of a polarization beam splitter (PBS) and two detectors which respectively measure the intensities of the components parallel (I//) and perpendicular (I⊥) to the input polarization, both intensities depending on the unknown PPS. The part of the detected light which is polarized parallel to the input beam, is denoted by K after normalization:
For an elementary region of the sample probed by the beam (pixel), one can determine the DOP of the reflected beam, and the phase retardance θ induced by this elementary region, from the following relationships:AndWithwhere Kmin stands for the minimum value of K and where K'max is the maximum value of K' when the PPS is varied over the Poincaré sphere.Derivation of the above mentioned equalities can be found in [9]. For a non-depolarizing sample, Kmin = 0, DOP = 1 and K' = K. In the particular case of a non-depolarizing non-birefringent sample, the assembly “Faraday rotator + sample” behaves as a standard Faraday mirror. Thus, I// = 0 and accordingly K' = 0, whatever the PPS and whatever the polarization effects in the fiber. Consequently, θ is found to be zero, as expected.
To be properly characterized, each pixel of the sample must be probed by a sufficiently large number of PPS covering as much as possible the Poincaré sphere. In [10], Desroches et al. demonstrated that, as can be expected, the higher the number of acquisition the higher the accuracy on the measured DOP and retardance. 50 measurements with varied PPS are required in order to get both Kmin and K'max with a precision better than 1%. Calculations show that, in this case, the resulting precision on the DOP is 2%. Concerning the retardance, the uncertainty remains lower than 3% for any K'max < 0.99.
In the case of PPS sequentially generated, for example by means of a polarization scrambler at the input of the optical fiber, this somewhat large number of required acquisitions results in a long measurement time. This is one of the reasons why we propose here a modified version of our technique in which the required PPS are spectrally encoded. Polarization states encoding in the spectral domain was already used in polarimetric instrumentation, in particular for channeled spectropolarimetry [11,12]. In the present case, the encoding occurs along the forward path of light in a specially conceived and optimized fiber-based endoscope. A broadband source is used and the detection device consists in two spectrometers as shown in Fig. 2. This arrangement allows one shot measurements of I//(λ) and I⊥(λ). Quantities K(λ) and K'(λ) can then be calculated from Eq. (1) and Eq. (4), which respective minimum and maximum values are used to deduce both DOP and retardance θ, as stated in Eq. (2) and Eq. (3).
Fig. 2 One shot per pixel endoscopic polarization imaging system: PBS, polarization beam splitter; PIBS, polarization insensitive beam splitter; SEPSG, spectrally encoded polarization states generator.
In the proposed setup, the fiber section of the endoscope, serving for light delivery and back transmission, also works as a spectrally encoded polarization states generator (SEPSG). It must be designed to provide the required variety of PPS over the source bandwidth. This SEPSG consists of the concatenation of two pieces of a highly birefringent (HiBi) fiber spliced with their fast axis set at 45° (Fig. 3). A similar combination is known as a fiber Lyot depolarizer in the context of fiber-optic gyroscope [13,14], and in another example it served in a polarization state analyzer [15].
Fig. 3 Representation of the spectrally encoded polarization states generator; SAP: stress applying parts inducing high birefringence in the fibers, with eigenaxes in the x and y directions; λa and λb are two wavelengths both linearly polarized at the input and providing two different polarization states at the output
Each piece of fiber behaves as a pure non-depolarizing retarder [16]. Linearly polarized light from the broadband source is launched at 45° to the eigenaxis of the input fiber (Fiber 1), which directions are respectively noted x and y. The direction of the launched polarization, defined in the reference frame of x and y, is denoted v. The launched light can be expanded in two orthogonal eigenmodes with their electric fields respectively parallel to x and y. They have identical amplitudes, and their relative phase shift φ(z,λ) evolves linearly along the fiber:
where z is the propagation distance in Fiber 1 and bφ(λ) is the phase birefringence of this fiber at the wavelength λ.The polarization states at the output of Fiber 1 thus progressively change versus wavelength, varying from linear in the v-direction to circular (right handed or left handed), then linear perpendicularly to the v-direction, then again circular (resp. left handed or right handed), and finally again linear in the v-direction. Their trace on the Poincaré sphere corresponds to a meridian crossing the equator at the point representing the linear polarization in the v-direction, completed by the opposite meridian. The spectral bandwidth δλ1 around a central wavelength λ0 which is required for providing a variety of output polarization states covering an entire meridian circle on the Poincaré sphere is given by:
where L1 is the length of Fiber 1, and BG is the group birefringence of the fiber around λ0.These polarization states are then launched in the second piece of HiBi fiber (Fiber 2, length L2) which eigenaxes are set at 45° to those of Fiber 1, as depicted in Fig. 3. In order to determine the polarization states exiting from Fiber 2, we achieved simulations by means of the Jones formalism [17]. As one can expect, the exiting polarization states can be much more varied than at the output of Fiber 1. Their trace on the Poincaré sphere depends on the ratio L1/L2 as shown on the examples of simulation results displayed in Fig. 4. The traces consist of a series of chained loops with variable diameter.
Fig. 4 Distribution of the PPS exiting the SEPSG represented on the Poincaré sphere for 3 different ratios L1/L2.
The spectral range over which the polarization states exiting from Fiber 2 are different from each other is governed by the ratio L1/L2. It is approximately given by the least common multiple of δλ1 and δλ2 with δλ2 = λ02/(L2.BG). It must be noticed that the source bandwidth will be limited in practice to the range for which the Faraday rotator properly achieves π/4 rotation of the polarization.
3. Practical implementation of the method and experimental results
For a proof of principle, we experimentally implemented the setup schematically depicted in Fig. 2. The operating wavelength was chosen in the near infrared (λ0 = 830 nm) for being compatible with those used for the characterization of biological tissues [18]. The chosen Faraday rotator (OFR IO-D-830) correctly achieved π/4 rotation of the polarization on a Δλ = 10 nm wavelength range around λ0. The optical source was a 30 mW superluminescent emitting diode (Superlum SLD-38-HP3, peak wavelength: 830 nm, spectral width: 14 nm). In the experiments, the two compact spectrometers (Ocean Optics HR 2000) had 0.1 nm resolution. Therefore 100 independent measurements can be achieved over Δλ, i.e. twice the number of measurements theoretically required for an accuracy of 1% in the determination of Kmin and K'max.
The fiber used to fabricate the SEPSG was a commercial HiBi fiber (Thorlabs PM630-HP) with a beat length LB = 2.3 mm and a group birefringence BG = 2.5 10−4 at 830 nm. This SEPSG must be sized in order to find a tradeoff between the number of different polarization states (to keep large) and the polarization changes over the 0.1 nm integration range of the spectrum analyzer (to keep small to avoid depolarization artefact). This means that the PPS path over Δλ must explore as much as possible the Poincaré sphere surface while remaining as short as possible. To fix the design we started by considering that the ratio L1/L2 should be of 10 at least to sufficiently cover the Poincaré sphere with a source of Δλ = 10 nm bandwidth (see Fig. 4). Keeping the fibers as short as possible leads to δλ2 = Δλ. Therefore δλ1 = δλ2/10 giving L1 = 2.76 m and L2 = 0.28 m, by use of Eq. (6). Consequently the PPS path on the sphere represents approximately 1/10 of a loop for a scan of 0.1 nm (spectrometer resolution) which is compatible with the second request. Fiber 1 and Fiber 2 were cut with these lengths and prepared for splicing. The main axes at the output of Fiber 1 and at the input of Fiber 2 were carefully aligned in a fusion splicer (Fujikura FSM-20PMII specialty splicer) and then rotated by 45° before being spliced, resulting in a SEPSG with an overall length of about 3 m.
We experimentally evaluated the operation of this SEPSG by observing changes of the output PPS by means of a polarimeter (Meadowlark Optics). However, to avoid tedious careful calibrations required at each working wavelength, we kept the wavelength fixed (λ0 = 830 nm) and we experimentally simulated the effects of spectral changes of the source on the SEPSG by varying the fiber temperature. To this aim, we used two superimposed temperature-controlled heating carpets sandwiching fibers to be heated. For calibration, we launched light at 45° to a main axis of a 40 cm long piece of HiBi fiber and we measured the output polarization states versus temperature. We observed that the path of the output polarization state on the Poincaré sphere described exactly one loop along a meridian, corresponding to a phase shift (retardance) of 2π, for a temperature rise of 4 °C. The phase shift in the fiber was then determined to be 3.925x10−2 rad/°C/cm. On another hand, we know that the change of retardance with a variation in wavelength around λ0 is given by 2πBG/ λ02 = 2.279x10−2 rad/nm/cm. Thus, for a given length of fiber the polarization state evolution on a 10 nm bandwidth at fixed temperature should be similar to the one observed with a temperature change of 5.7 °C whilst keeping the excitation at 830 nm. For practical reasons, instead of heating the entire SEPSG, we chose to reduce the fiber length to be heated (reduction factor = 7) and to increase accordingly the temperature variation range to 40 °C (from 20 °C to 60 °C). So, two HiBi fibers, Fiber 1' and Fiber 2' respectively, were spliced with their fast axis set at 45°. Lengths L'1 = 10L2π = 40 cm of Fiber 1'and L'2 = L2π = 4 cm of Fiber 2', on both sides of the splice, were sandwiched between the two heating carpets, as depicted in Fig. 5.
Fig. 5 Experimental device designed for measuring the diversity of the polarization states provided by the optimized SEPSG.
The path of the output polarization states on the Poincaré sphere, measured when heating the fibers, is plotted in Fig. 6b. They are in fair agreement with those expected at the output of the SEPSG from computations when the wavelength is swept from 825 nm to 835 nm (Fig. 6a). Weak discrepancy can be attributed to the temperature gradient on the fiber sections close to the carpet limits. These preliminary experiments and calculations show that the required diversity of polarizations states for the probe should be obtained with this SEPSG.
Fig. 6 Trajectory on the Poincaré sphere of the polarizations states exiting the polarization states generator a) calculated for λ varying from 825 nm to 835 nm, at fixed temperature; b) measured at λ0 = 830 nm, for a temperature varied from 20 °C to 60 °C.
The SEPSG was installed in the polarimetric characterization setup depicted in Fig. 2 where it was used as the flexible optical waveguide of the endoscope. The ability of this setup to precisely measure the phase retardance of a birefringent sample was first tested with a tunable calibrated target consisting of a Babinet-Soleil compensator (BSC) followed by a mirror. First, we found Kmin < 10−2 whatever the settings of the BSC. The result is in agreement with the predictions since the assembly BSC-mirror behaves as a non-depolarizing target. In Fig. 7, the retardance measured with the setup is plotted versus the value expected from the compensator setting, from 0° to 180°. In most of the cases, the experimental results are in very good agreement with the expected ones. However, some discrepancies can be noticed near 0° and 180°, i.e. for values of K'max very close to 0 and close to 1. More precisely, measured K'max was found to be slightly higher (resp. lower) than expected values when the later are close to 0 (resp.1). This discrepancy is attributed to the contribution of weak spurious signal in both I// and I⊥. The crosstalk of the polarization beam splitter being negligible (< 10−3), this undesirable signal mainly came from residual Fresnel reflections on optical components of the setup, prior to the Faraday rotator, which could be reduced by using components with antireflection coatings. Other potential Fresnel reflections from the fiber faces have been removed from the optical path with careful angle cleaving.
Fig. 7 Retardance measured by a one shot measurement for each point, with the setup of Fig. 2 including the 3 m optimized SEPSG, versus retardance θ set on the sample. The sample was a tunable calibrated retarder consisting in a Babinet-Soleil compensator followed by a mirror (solid line is a guide to the eye).
A more complex sample (11 mm X 7.5 mm) was then prepared based on partially superimposed layers of transparent birefringent films stuck on a mirror. A standard intensity image of this sample is shown in Fig. 8a. The left (resp. right) vertical layer was set so that its fast (resp. slow) axis was parallel to the fast axis of the horizontal layer. A complete polarization image (220 X 150 pixels, 50 µm resolution) was further realized by moving the sample in the focal plane of the probe beam in the setup described in Fig. 2, and by performing a one shot measurement for each pixel. Kmin was found to be lower than 10−2 over the entire sample, indicating that there was no significant depolarization. The retardance image, deduced from K'max, is displayed in Fig. 8b. Slight distortions which can be observed at the boundaries of the different areas are due to mechanical imperfections of our 2D scanning system. As expected, the retardance measured in the empty areas noted “①” is very close to 0°. In the regions with only one birefringent layer, noted “②”, uniform retardance of ~55° was measured whatever the orientation of the sample eigenaxes. Twice this retardance (~110°) was measured in region “③” where two layers with parallel fast axis were superimposed. In region “④”, the two superimposed layers had their fast axis perpendicular, resulting in a compensation of the retardance. Zero retardance was indeed measured in this region, in agreement with predictions.
Fig. 8 Sample made of superimposed layers of transparent birefringent films: a) intensity image; b) retardance measured with the setup of Fig. 2.
4. Conclusion
In this paper we reported a technique allowing simultaneous measurements of both the DOP and the linear retardance of a sample, through an optical fiber, in one shot per pixel. The sample is probed with a large variety of polarization states generated over the bandwidth of the source in a specially designed optical fiber serving both as a flexible light guide and as a spectrally encoded polarization states generator (SEPSG) for the endoscope. This component is particularly simple, as it merely consists of the optimized concatenation of two lengths of HiBi single mode fibers spliced with their main axes set at 45°. The 3 m overall length of this fiber is fully compatible with practical needs of endoscopic imaging systems. For a proof of principle, we obtained polarization characterization and polarimetric images of different calibrated or manufactured samples. The reported technique, in combination with an appropriate scanning device, is attractive in view of achieving polarimetric imaging at high speed, this feature being a major issue for in vivo endoscopic applications.
Based on the use of the SEPSG, high speed sequential acquisition scheme could also be investigated, using high speed tunable laser as light source and standard fast photodiodes instead of spectrometers for the detection system. For example, a tunable source based on Fourier domain mode locking (FDML) has already been demonstrated to be able to operate at up to 290 kHz effective sweep rates over more than 100 nm full width [19]. By reducing the swept bandwidth to 10 nm as required in the reported setup, sweep rates should be further increased, making this source attractive in view of a sequential implementation of the method.
References
1. S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7(3), 329–340 (2002). [CrossRef] [PubMed]
2. 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(6), 1061–1063 (2012). [CrossRef] [PubMed]
3. M. Anastasiadou, A. De Martino, D. Clement, F. Liège, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi 5(5), 1423–1426 (2008). [CrossRef]
4. 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(2), 1582–1593 (2011). [CrossRef] [PubMed]
5. 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(3), 388–397 (2002). [CrossRef] [PubMed]
6. J. Fade and M. Alouini, “Depolarization Remote Sensing by Orthogonality Breaking,” Phys. Rev. Lett. 109(4), 043901 (2012). [CrossRef] [PubMed]
7. S. Jiao, W. Yu, G. Stoica, and L. V. Wang, “Optical-fiber-based Mueller optical coherence tomography,” Opt. Lett. 28(14), 1206–1208 (2003). [CrossRef] [PubMed]
8. J. Qi, M. Ye, M. Singh, N. T. Clancy, and D. S. Elson, “Narrow band 3 × 3 Mueller polarimetric endoscopy,” Biomed. Opt. Express 4(11), 2433–2449 (2013). [CrossRef] [PubMed]
9. J. Desroches, D. Pagnoux, F. Louradour, and A. Barthélémy, “Fiber-optic device for endoscopic polarization imaging,” Opt. Lett. 34(21), 3409–3411 (2009). [CrossRef] [PubMed]
10. J. Desroches, D. Pagnoux, A. Barthélémy, and F. Louradour, “Polarization measurements through a standard single mode fiber for imaging and remote characterization,” Eur. Phys. J. 5, 06007 (2010).
11. H. Okabe, M. Hayakawa, H. Naito, A. Taniguchi, and K. Oka, “Spectroscopic polarimetry using channeled spectroscopic polarization state generator (CSPSG),” Opt. Express 15(6), 3093–3109 (2007). [CrossRef] [PubMed]
12. 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(6), 1061–1063 (2012). [CrossRef] [PubMed]
13. K. Bohm, K. Petermann, and E. Weidel, “Performance of Lyot depolarizers with birefringent single-mode fibers,” J. Lightwave Technol. 1(1), 71–74 (1983). [CrossRef]
14. W. Burns, “Degree of polarization in the Lyot depolarizer,” J. Lightwave Technol. 1(3), 475–479 (1983). [CrossRef]
15. E. Kim, D. Dave, and T. E. Milner, “Fiber-optic spectral polarimeter using a broadband swept laser source,” Opt. Commun. 249(1-3), 351–356 (2005). [CrossRef]
16. T. Chartier, A. Hideur, C. Ozkul, F. O. Sanchez, and G. M. Stéphan, “Measurement of the elliptical birefringence of single-mode optical fibers,” Appl. Opt. 40(30), 5343–5353 (2001). [CrossRef] [PubMed]
17. D. Goldstein, Polarized Light, Revised and Expanded (Taylor & Francis, 2003).
18. S. L. Jacques, “Optical properties of biological tissues: a review,” Phys. Med. Biol. 58(11), R37–R61 (2013). [CrossRef] [PubMed]
19. R. Huber, M. Wojtkowski, and J. G. Fujimoto, “Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography,” Opt. Express 14(8), 3225–3237 (2006). [CrossRef] [PubMed]
