Optical coherence tomography (OCT) is a non-invasive imaging technique that provides volumetric structural information by measuring the light intensity backscattered from a sample [1]. The directionality of scattering strongly depends on the tissue composition [2]. Conventional OCT devices, however, only provide information about the directly backscattered light. Various OCT approaches such as dark-field configurations [3,4], multi-channel OCT [5], or angular compounding [6–8] have been developed to overcome this limitation. These approaches, however, involve complex designs or require multiple acquisitions. We recently developed a bright- and dark-field (BRAD) OCT system that separates the backscattered light into the modes of a few-mode fiber (FMF) depending on the angle of incidence [9]. Since the guided modes of a FMF have different excitation profiles and different effective refractive indices, the fiber itself performs a decomposition of the backscattered light and encodes the angular information at different depths of the OCT image. We demonstrated BRAD-OCT in ex vivo brain samples for visualizing neuritic plaques in Alzheimer’s disease and differentiating tumorous tissue. As in most of the intensity-based OCT systems, only a single unknown polarization state was acquired with our system. However, according to the Mie theory, the scattering directionality profile of a particle often has a strong polarization dependence and a different distribution for each polarization state [10]. Thus, in order to assess the scattering properties more completely, we have integrated a polarization-sensitive (PS) extension into our previous BRAD-OCT system.

A swept-source laser operating at 1310 nm with a tuning range of 140 nm was used as the light source. The sample arm of the Mach–Zehnder interferometer was designed to provide a single-mode Gaussian illumination on the sample [9]. While in our previous system a polarizing beam splitter (PBS) and a quarter-wave plate were used to redirect the backscattered light into our FMF and maximize collection efficiency for co-polarized light, a non-PBS cube was now used in order to be sensitive to any polarization state scattered from the sample, as shown in Fig. 1. Two PBS cubes were placed after interfering with the signal from the reference arm with the output of the FMF coming from the sample arm to separate the vertical and the horizontal polarization components. A pair of balanced detectors was used for simultaneously acquiring the orthogonal polarization states from which the Stokes vectors were computed [11]. A polarization control paddle (PC2) located on the reference arm was used to set a linear polarization state (45°) at the PBS and, thus, provide equal reference power to both detectors. A fixed polarization state at 45° could be ensured by placing a polarizer between fiber collimators (FCs) and beam splitters (BSs). The polarization state incident in the sample was set to left-handed circularly polarized light by PC1.

 

Fig. 1. BRAD-OCT setup with PS extension. AOC, analog output card; BD, balanced photodetector; BS, beam splitter; DAQ, data acquisition; FC, fiber collimator; FMF, few-mode fiber; L, lens; MEMS, scanner; PBS, polarizing beam splitter; PC, polarization control paddles; RR, retroreflector; S, sample; SMF, single-mode fiber.

Download Full Size | PDF

For the purpose of extracting the polarization properties of a sample, a calibration step needs to be performed in advance, since the optics in the system, in particular the FMF, also influence the polarization state of the signal. The detected polarization state not only represents the sample properties, but also its combination with the birefringence induced by the FMF. Thus, we need to compensate for the effects of the fiber to extract the sample polarization properties. The birefringence behavior of an optical fiber can be approximated by an elliptical retarder that rotates the measured polarization state on the Poincaré sphere [12,13]. Since the fiber birefringence remains constant for each mode, the angle between the measured Stokes vectors remains constant (assuming no polarization mode dispersion), although they are rotated on the Poincaré sphere. To determine the FMF birefringence to be compensated for, we performed two consecutive measurements using a circular ($S_c$) and a vertical ($S_v$) input polarization state (set with PC1 and a polarimeter) to image a mirror [14]. The measured Stokes vectors $S_c^{\prime }$ and $S_v^{\prime }$ are rotated by the FMF, although their orthogonality is maintained as indicated in Fig. 2(a). Since an elliptical retarder can be described by a combination of a linear and a circular retarder, two consecutive rotations are needed to align the measured $S_c^{\prime }$ and $S_v^{\prime }$ with the original $S_c$ and $S_v$ and, therefore, compensate for FMF birefringence. First, a rotation matrix $R1({\theta }_1)$ around the normal $S_c^{\prime }\times S_c$ will rotate the measured Stokes vectors after being normalized to match the position of $S_c^{\prime }$ to $S_c$, as illustrated in Fig. 2(b). The resulting $S_v^{\prime }$ after this first rotation will be located in the $QU$ plane due to the orthogonality of the Stokes vectors in the Poincaré sphere. Thus, a second rotation $R2({\theta }_2)$ around the $V$ axis will align $S_v^{\prime }$ to its original location $S_v$, while maintaining the previously aligned $S_c^{\prime }$ at its respective orientation, as shown in Fig. 2(c). To verify that our calibration is stable and constant for every measurement, we carried out six acquisitions of 512 repeated scans over a duration of 30 min. The averaged polarization state in the sample remained constant with respect to the initial measurement [$(\mathrm{\Delta }Q,\mathrm{\Delta }U,\mathrm{\Delta }V)=(2°,2°,4°)$] during the first 20 min until the laser output polarization state exhibited some variability [$(\mathrm{\Delta }Q,\mathrm{\Delta }U,\mathrm{\Delta }V)=(17°,19°,13°)$]. For illustrating the calibration result, a birefringent foil was imaged. The normalized Stokes vectors $S=(Q,U,V)$ were calculated and displayed in an RGB image. The (signed) Stokes values for each pixel were normalized for visualization purposes by $S_n(Q,U,V)=[S(Q,U,V)+1]/2$. Figure 3 illustrates the measured Stokes vectors without (a) and with (c) the calibration procedure. When plotting a depth profile of the birefringent foil, the Stokes vector distribution rotates around the Poincaré sphere when going deeper in the sample, as represented by the yellow dots in Figs. 3(b) and 3(d). For the Stokes vector of a unique pixel taken from the surface indicated by the red arrow in (a) and (c), a rotation of the pointer of the Stokes vectors around the Poincaré sphere to the $-V$ axis can be observed. The input left-handed polarization state used for illuminating the sample is recovered after applying the FMF calibration, as shown in Fig. 3(d).

 

Fig. 2. Illustration of the FMF birefringence compensation procedure. (a) Measured Stokes vectors $S_c^{\prime }$ and $S_v^{\prime }$ are transformed from the input vectors $S_c$ and $S_v$ due to the FMF birefringence which changes the orientation in the Poincaré sphere. (b) First rotation $R1({\theta }_1)$ around the normal $S_c^{\prime }\times S_c$ to align $S_c^{\prime }$ with $S_c$. (c) Second rotation $R2({\theta }_2)$ around the $V$ axis to match the input Stokes vectors orientation.

Download Full Size | PDF

 

Fig. 3. (a) Stokes vector image of a birefringent foil for ${\mathrm{LP}}_{01}$ without calibration. The pixels with low intensity are masked in gray. (b) Poincaré sphere showing the Stokes vectors as a function of depth indicated in yellow and the pixel indicated in red in (a). (c) Stokes vector image after the calibration procedure. (d) Poincaré sphere plotting the cross section in yellow and the pixel in red indicated in (c).

Download Full Size | PDF

Phase retardation is one of the characteristic birefringent properties that can be retrieved from biological tissues [11,15]. Given our imaging scheme, retardation values caused by linear birefringence can be calculated from the corrected Stokes vectors after applying the FMF calibration. The polarization state $S_{\mathrm{surf}}$ at the sample surface is expected to be oriented along $-V$ after FMF correction. As illustrated in Fig. 4, for each pixel with a respective normalized Stokes vector $S^{\prime }=(Q,U,V)$ after fiber correction, the cumulative phase retardation $\delta$ in linearly birefringent tissue can be calculated as

 

Fig. 4. Illustration of phase retardation calculation from the corrected Stokes vectors $S^{\prime }$ using the surface Stokes vector $S_{\mathrm{surf}}$ as reference.

Download Full Size | PDF

 

Fig. 5. Stokes parameter distributions for phantoms containing (a) 5 μm microspheres reconstructed by ${\mathrm{LP}}_{01}$, (b) 7 μm microspheres reconstructed by ${\mathrm{LP}}_{01}$, (c) 5 μm microspheres reconstructed by ${\mathrm{LP}}_{21}$, and (d) 7 μm microspheres reconstructed by ${\mathrm{LP}}_{21}$.

Download Full Size | PDF

The modified BRAD-OCT system with a PS extension was used for imaging an ex-vivo formalin fixed sample of a human brainstem retrieved from the Neurobiobank of the Medical University of Vienna (ethics approval number 396-2011). The fiber tracts in the brainstem are known to be highly birefringent [17]. In the B-scan image displaying backscattered intensity of ${\mathrm{LP}}_{01}$ [Fig. 6(a)], the tissue morphology appears as largely homogeneous and only shows slightly shallower light penetration in regions corresponding to the location of fiber tracts. Nevertheless, a clear differentiation from the surrounding gray matter tissue is difficult based solely on their appearance in the intensity image. In the corresponding retardation B-scan, two areas with different characteristics can be easily differentiated: birefringent fiber tracts with strongly increasing retardation and polarization preserving gray matter tissue. Intensity and retardation en-face projection images were averaged over five pixels (around 30 μm) beneath the tissue surface. While the fiber tracts were clearly visible in the ${\mathrm{LP}}_{01}$ mode of the co-polarized channel [Fig. 6(c)], some fiber structures provided a hyperintense signal in the cross-polarized channel [Fig. 6(d)]. A similar characteristic of the co- and cross-polarized channels can be observed in the ${\mathrm{LP}}_{21}$ images showing dark-field scattering information in Figs. 6(e) and 6(f). In order to visualize angular scattering differences, we computed the BRAD ratio between the intensity of ${\mathrm{LP}}_{01}$ corresponding to the bright field and the intensity of ${\mathrm{LP}}_{21}$ representing the dark-field scattering [Fig. 6(g)] [9]. A high BRAD ratio indicates more direct backscattering and was observed in some fiber tracts. Several strands of these fiber tracts also appeared to be hyperscattering in the cross-polarized channels and provided a strong birefringence signal in the retardation image calculated from ${\mathrm{LP}}_{01}$ [Fig. 6(h)].

 

Fig. 6. PS BRAD-OCT images of a human brainstem. (a) Intensity B-scan of the ${\mathrm{LP}}_{01}$ co-polarized channel. (b) Corresponding ${\mathrm{LP}}_{01}$ retardation B-scan. Gray matter tissue appears as polarization preserving (yellow arrow), while the white matter appears as birefringent (increasing retardation, red arrow). (c) En-face projection image of the co-polarized intensity collected by ${\mathrm{LP}}_{01}$. (d) En-face projection image of the cross-polarized intensity collected by ${\mathrm{LP}}_{01}$. The hyperscattering fiber tracts are indicated by the yellow arrows. (e) En-face projection image of the co-polarized intensity collected by ${\mathrm{LP}}_{21}$. (f) En-face projection image of the cross-polarized intensity collected by ${\mathrm{LP}}_{21}$. (g) BRAD ratio image of ${\mathrm{LP}}_{01}$ and ${\mathrm{LP}}_{21}$ reflectivity signals reveal strong direct backscattering for the indicated fiber tracts. The granular yellow spots correspond to locations where the wet tissue surface created specular reflection artifacts. (h) Corresponding ${\mathrm{LP}}_{01}$ retardation map where high retardation values reveal birefringent white matter tracts. The scale bars correspond to 150 μm.

Download Full Size | PDF

The possibility of analyzing the polarization properties, in combination with the angular scattering properties, provides an interesting route for optical tissue investigation. In this Letter, the combination of BRAD-OCT and PS imaging has been demonstrated. Without extensive modifications of the optical layout, we have expanded our FMF-based system [9] with a PS detection. Different approaches have been proposed to compensate for the fiber-induced birefringence in PS-OCT systems such as probing with two sequential polarization states [11,14] or multiplexing two polarization states in a single shot [15,18]. In the approach presented here, fiber birefringence was compensated for based on two calibration measurements prior to the imaging session which then enabled the retrieval of the tissue polarization properties using only a single circular input state. Similar to other single input state PS-OCT approaches [19,20], polarization stability is crucial for this method to be accurate. The scattering characteristics of two different phantoms were tested with our system, and the BRAD imaging extension revealed distinct Stokes vector distributions for each particle size (Fig. 5). The polarization properties measured by the dark-field method also might be affected by coherent backscattering [21] and the fact that optical reversibility is not held, unlike bright field configurations [22]. Since it has been shown that angle-dependent PS measurements may improve the detection of tissue irregularities such as cellular hypertrophy [23], PS BRAD-OCT could be an interesting candidate for non-destructively interrogating cell proliferation in pre-cancerous tissue. In the image data from the brain tissue (Fig. 6), PS BRAD-OCT revealed directional scattering differences, as well as spatially diverse birefringence characteristics of white matter tracts. Given the fact that BRAD contrast relies on microstructural parameters such as the size and orientation of scatterers and that the observed retardation relies on the composition and packing of white matter fibers [17], our approach might be an interesting tool for neuroimaging applications.