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Abstract
The incorporation of polarization sensitivity into optical coherence tomography (PS-OCT) imaging can greatly enhance utility by allowing differentiation via intrinsic contrast of many types of tissue. In fiber-based OCT systems such as those employing endoscopic imaging probes, however, polarization mode dispersion (PMD) can significantly impact the ability to obtain accurate polarization data unless valuable axial resolution is sacrificed. In this work we present a new technique for compensating for PMD in endoscopic PS-OCT with minimal impact on axial resolution and without requiring mutually coherent polarization inputs, needing only a birefringent structure with known orientation in view (such as the catheter sheath). We then demonstrate the advantages of this technique by comparing it against the current state of the art approach.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Polarization sensitive optical coherence tomography (PS-OCT) [1–4] enhances the potential contrast of OCT [5] by enabling sensitivity to birefringent media. In biological tissue this includes tissue types such as collagen and muscle. For in vivo investigation of luminal organ systems such as the pulmonary, cardiovascular, and gastrointenstinal systems, a fiber-based OCT system is employed typically with a side-viewing fiber-based imaging probe that can easily be incorporated into an endoscopic procedure [6]. This approach allows for rapid, minimally-invasive volumetric scanning of the luminal system. Potential applications of endoscopic PS-OCT that have been investigated thus far include assessing the likelihood of atherosclerotic plaque rupture [7], identifying lung tumor margins for tissue biopsy [8], and investigating airway smooth muscle in asthma [9].
Unfortunately, some added technological complications arise when dealing with endoscopic PS-OCT imaging. Chief amongst these are the issues that arise in measuring the polarization state of light that has been transmitted through non-ideal single mode fibers and optical components of the OCT system. The first of these issues is the arbitrary change in the polarization state of light as it travels from source to sample and from sample to detector. This change occurs due to both birefringence in the system fiber and imaging probe motion, if present. Calibration techniques have recently been proposed to address this particular issue [10,11] with successful results. The second, more challenging issue, commonly referred to as polarization mode dispersion (PMD) [12] in the OCT field, but more accurately characterized by the general behavior of birefringence chromatic dispersion. Wavelength dependence in the birefringence of an optical component (such as a circulator) or a given length of optical fiber can contribute substantially to polarization noise in fiber-based OCT systems [13,14].
It has previously been shown that the addition of calibration signals to the PS-OCT system can be used to calculate and compensate for PMD [15]. This work also established much of the theory behind PMD and its compensation in PS-OCT imaging. Techniques for addressing PMD in PS-OCT systems without additional hardware modifications can be separated based on whether or not they require mutually coherent polarization measurements. In mutually coherent PS-OCT systems as in those where the polarization measurements are depth-multiplexed [16,17], it has been demonstrated that PMD can be corrected for with minimal compromise [18,19]. Such procedures, however, cannot be implemented in systems that acquire incoherent polarization measurements: for instance, in systems where the input polarization state is modulated among adjacent A-lines [20], the illumination and detection beam modes represent physically distinct tissue regions, which exhibit decorrelated speckle realizations at sufficiently fast beam scanning speed [21]. This is the case in most endoscopic PS-OCT systems, in which the necessary frame rate due to motion artifacts during imaging in vivo impose a high rotational speed of the probe [22,23]. A technique for addressing PMD under these circumstances is called spectral binning [24]. In this approach, the acquired fringes are divided into overlapping bins, the spectral width of each ideally being commensurate with the magnitude of the system PMD. PS processing is then performed separately on each bin before being recombined at the final step. While this technique is very successful at mitigating the impact of PMD, it suffers from the drawback of reduced axial resolution.
In this work we present a novel technique for mitigating PMD without sacrificing axial resolution that does not require mutually coherent polarization measurements. In order to demonstrate the flexibility of this technique we present results from endoscopic PS-OCT data obtained from airways both in vivo and ex vivo and compare them against data processed using no PMD calibration as well as data processed using spectral binning. Comparison between PS-OCT images and histology demonstrates how this technique allows us to accurately measure birefringent features approaching the axial resolution of our system.
2. Materials and methods
2.1 OCT system
All data presented here was obtained using a wavelength-swept PS-OCT system [25] with an electro-optic modulator for input polarization diversity. Our system was custom built in our lab and had 120 nm bandwidth centered at 1310 nm. The axial resolution of the system was approximately 10 $\mu$m in air, and the ranging depth approximately 10 mm. The fiber optic imaging catheter used a monolithic side-viewing ball lens design with a beam spot size of approximately 30 $\mu$m at the focal distance (1.5 mm from catheter sheath). Optical circulators, known to induce moderate PMD, were employed in the reference and sample arms, and a fiber-based imaging probe attached to a rotary junction was used to acquire sample data. Polarization sensitivity was accomplished by using a polarization diverse detection scheme. An acousto-optic modulator was used to remove depth degeneracy and yielded complex fringes after the data was reshifted in post-processing [26]. This is a standard system configuration which we have previously described in detail [9]. Standard post-processing including linear k-mapping and dispersion compensation [27] were performed prior to further processing described below.
2.2 Differential birefringence measurements
Measured Stokes vectors were filtered in the transverse direction using a Gaussian filter with a 12 pixel (corresponding to approximately 4.2$^{\circ }$ of angular separation in our endoscopic data) FWHM for all data. Axial filtering was also performed using a Gaussian filter, although with a kernel size that varied depending on the comparison being made and which will be specified at the appropriate points in the manuscript. All differential birefringence measurements were then obtained from the filtered Stokes vectors using a depth offset of a single pixel to simplify comparisons. OA calibration was performed on all of the data in order to correct for measurement distortion as previously described [10]. This calibration was performed prior to and separately from the PMD calibration, with neither being affected by the other.
2.3 PMD calibration technique
2.3.1 Overview
The technique described in this work can be viewed as an extension of a PMD compensation technique for PS-OCT developed by Villiger et. al. [24], and is specifically intended to address PMD in PS-OCT systems in which the polarization states are not mutually coherent. As described in Section 1, in that work PS-OCT fringes were spectrally binned and Stokes formalism PS-OCT processing was performed individually on each bin. Two consequences resulted from the fact that all of this processing was done in the Fourier domain: first, the system input channel PMD could be eliminated from the calculations and therefore ignored; and second, the axial resolution of the data was irreversibly impacted.
In contrast with that work, here we demonstrate an approach in which both the output and input channel PMDs are measured and compensated for. Corrections that are performed in the Fourier domain are converted back to the k domain, mitigating the loss of axial resolution. Much of what is novel about our work has to do with compensating for the input channel PMD specifically: mathematically, it is not at all straightforward to eliminate the effects of the input channel PMD in the k domain due to the fact that its effects on the input states are incurred prior to interaction with the sample. Our approach attempts to overcome this problem by using measurements made in the Stokes formalism to essentially redefine the polarization properties of the original fringes, recasting them in a form in which they are simply the product of a purely birefringent sample with input states that are orthogonal on the Poincaré sphere but otherwise arbitrarily defined. An overview of the steps involved in this process are depicted in Fig. 1.
The remainder of this section is divided into three parts: first, we specify the system inputs and the assumptions we are making for performing this technique. Next we describe how to determine the PMD compensation matrices. This section in particular involves much of what is already outlined in Ref. [24], somewhat refined and extended to both PMD channels. The last section primarily deals with the technique we have developed for compensating for the input channel PMD, as compensating for the output channel PMD is straightforward once the matrices have been determined.
2.3.2 Inputs and assumptions
The inputs to the calibration algorithm are a total of four complex interference fringes obtained from using two polarization inputs and two detection channels, corresponding to a pair of A-lines, and the calibration itself is performed on every A-line pair in the data. For our approach to determining $J_B$ and $J_A$ two such A-line pairs are used, corresponding to two different angular positions of the rotating endoscopic probe. In the description of the calibration technique that follows, we refer to a single A-line pair only (with the understanding that it is to be performed on every pair). In the case of the two measurement channels being coherent, these measurements represent a Jones matrix that can be expressed as
In all of the following derivations we make the assumption that excluding PMD all elements can be represented as simple retarders; i.e., neither diattenuation nor any additional manifestation of k-dependence is present either in the system elements or in the sample itself. We note that these assumptions may lead to the accumulation of some residual error in our results; the absence of diattenuation is based on the assumption of lossless propagation in optical fiber and has been previously addressed [23], while the assumption of the absence of additional k-dependence neglects the k-dependence in the splitting ratio of $2x2$ fiber splitters (as addressed in the PMD compensation approach developed by Braaf et. al. [18]). Treating these assumptions as nevertheless valid to a reasonable approximation, the Stokes representation, Eq. (1) is then given by
Combining the contributions from the sample and catheter fiber.
2.3.3 Determination of PMD matrices
In order to compensate for input and output channel PMD we must first have some method for measuring them. To accomplish this we start by dividing the interference fringes into a series of overlapping Gaussian windows, each narrow enough so that we can assume the PMD within any given bin to be negligible. This approach, known as spectral binning, was demonstrated in one of the first PMD compensation papers for OCT [24] and has proven to be very effective. We then take the Fourier transform of each bin and convert to Stokes to yield
2.3.3.1 Determination of $J_B$ compensation matrices
Differential birefringence measurements in PS-OCT [23] can be made by comparing Stokes vectors at each depth in the sample with those at some previous depth (typically a fixed pixel offset). Mathematically this approach is equivalent to solving for the following equation:
Equation (6) describes a similarity transformation of the true sample birefringence matrices in which the eigenvalues (retardances) are preserved while the eigenvectors (OAs) are rotated by $S_B(\Delta k_i)$. In a previous work we demonstrated that the linear birefringence of the catheter fiber itself could be isolated under the assumption that its intrinsic birefringence doesn’t change as the catheter rotates by taking measurements at the inner surface of the catheter sheath using two different angular positions rather than two depth positions [10]:
Because the reflection from the sheath is well-defined, consistent, and uncorrupted (or minimally corrupted) by speckle, we choose Eq. (7) as our reference for making our PMD measurements. We select the central bin as our reference bin from which the relative rotation of all other bins will be calculated. Solving Eq. (7) for each bin, we then compute this relative rotation in a least-squares sense [24]:
where $\Delta k_c$ denotes the central bin. This gives us discrete values for the relative rotation in each bin. Next we linearly interpolate these rotations across all k-samples in order to go from $S_B(\Delta k_c)S_B^{-1}(\Delta k_i)$ to $S_B(k_c) S_B^{-1}(k)$, where $k_c$ is the central k-sample. Finally, we employ the following relationship for converting from a rotation on the Poincaré sphere to a Jones matrix: where $\hat {r}$ is the Stokes OA, $\varphi$ the Stokes retardance, and $\vec {\sigma }$ the vectorized Pauli matrices [12]. Using Eq. (9), we convert our array of PMD compensation matrices from the Stokes formalism to the Jones formalism, yielding:With the k compensation matrices corresponding to the number of samples originally acquired in each fringe.
2.3.3.2 Determination of $J_A$ compensation matrices
Solving for $J_{A,\textrm {comp}}$ is accomplished in a similar fashion, but with a few additional (initial) steps. Starting again from Eq. (5), we solve for:
Which is accomplished by calculating the total rotation relative to the input Stokes vectors. While these are only fixed in terms of their relative orientations ($\pi /2$ separation on the Poincaré sphere), we can arbitrarily select any two such vectors we wish so long as we remain consistent throughout all of our calculations. For simplicity we opt to use $+Q$ and $+U$ as our inputs in these calculations and in all that follow. We then invert Eq. (11) to obtain:
Equation (13) is then analogous to Eq. (5), and as a result all of the equations outlined in the description for the determination of the $J_B$ compensation matrices above apply [Eqs. (5–9)], except that the final result must again be inverted [to account for the inversion in Eq. (13)]:
Figure 2 demonstrates the results of this approach for a sample experimental dataset. In all data presented in this work, 50 bins were used to measure the PMD prior to k-sample interpolation.
Fig. 2. Retardance (a,b) and axis (c,d) as a function of sample number of the PMD matrices obtained from an experimental dataset. The left column corresponds to the output matrix $J_{B}$ and the right column the input matrix $J_{A}$. These results were obtained according to the procedure outlined in Section 2.3.3.
2.3.4 PMD Compensation
In a PS-OCT configuration in which the two inputs are coherent, Eq. (10) and Eq. (14) can be applied directly to Eq. (1) in order to fully compensate for system PMD. Unfortunately, phase instability and/or a spatial offset between the two inputs, common in many if not most PS-OCT systems, renders the measurements incoherent. The effect of this is that $J_{A,\textrm {comp}}$ cannot be applied to Eq. (1) without coherently mixing incoherent measurements and therefore corrupting the results. To correct for this we have developed a novel method for compensating for input PMD with incoherent measurements. Briefly, this is accomplished by applying corrections on Fourier-transformed data in the Stokes formalism in such a way that full spectrum fringes can still be recovered. This method allows both output and input PMD to be compensated for without a significant impact on resolution. A step-by-step description of the method is as follows:
- 1. Compensate for output PMD directly. Output PMD can immediately be compensated for by pre-multiplying the acquired matrix specified in Eq. (3) by the output PMD compensation matrix specified in Eq. (10), yielding:
This result can be simplified for future derivations by rewriting $\mathbf {J_{out}^{'}}(k)=J_{B,\textrm {comp}}(k)\mathbf {J_{out}}(k)$ and $J_B=J_B(k_c)$:
The effect of this compensation is to eliminate the k-dependence from the output channel, reducing its effect to a single rotation corresponding to the initial birefringence of the central sample point $k_c$.
- 2. Spectrally bin fringes, convert them to Stokes vectors, and apply transverse filtering. The next steps are to spectrally bin and Fourier transform Eq. (16):
In the text preceding Eq. (1), however, we noted that the result is truly only valid for coherent measurements; i.e, measurements acquired using mutually coherent inputs developing the same speckle realizations (by probing the same depth location) within the sample. Since our original data does not meet these criteria, Eq. (17) is more accurately represented as the following pair of equations:
$$\mathbf{out_1^{'}}(\Delta k_i, \theta, z)={J_B}{J_{1SC}(\Delta k_i, \theta, z)}{J_A}(\Delta k_i){\mathbf{in_1}}$$$$\mathbf{out_2^{'}}(\Delta k_i, \theta, z)={J_B}{J_{2SC}(\Delta k_i, \theta, z)}{J_A}(\Delta k_i){\mathbf{in_2}}$$where the input and output matrices have been separated into individual vectors due to the presence of two distinct sample matrices arising from two distinct lateral positions along the sample. The first goal, then, is to eliminate this discrepancy. This is ultimately accomplished through the use of lateral filtering. Employing many of the same techniques of the previous section, Eqs. (18) and (19) are converted to the Stokes formalism, yielding$$\mathbf{s_{1out}^{'}}(\Delta k_i, \theta, z)={S_B}{S_{1SC}(\Delta k_i, \theta, z)}{S_A}(\Delta k_i){\mathbf{s_{1in}}}$$$$\mathbf{s_{2out}^{'}}(\Delta k_i, \theta, z)={S_B}{S_{2SC}(\Delta k_i, \theta, z)}{S_A}(\Delta k_i){\mathbf{s_{2in}}}$$Next, lateral filtering of the pair of measurements is performed at every image pixel for every bin. Since the purpose of this step is to reduce the effects of different speckle realizations between the two inputs, the size of the filtering kernel should be selected in consideration of the spatial offset between the inputs. Assuming sufficient filtering we can then approximate our measurements at each pixel as being the product of the same sample birefringence and combine Eqs. (20) and (21) into
$$\mathbf{S_{out}^{'}}(\Delta k_i, \theta, z)={S_B}{S_{SC,\delta x}(\Delta k_i, \theta, z)}{S_A}(\Delta k_i){\mathbf{S_{in}}}$$With $S_{SC,\delta x}$ indicating the filtered result.
- 3. Measure the total rotation mapping the input matrix onto the output matrix. The combination of spectral binning and lateral filtering (along with the assumption of only birefringence being present) permits the interpretation that Eq. (22) represents a single rotation (per bin, per pixel) mapping the input matrix onto the output matrix. Analogous to Eq. (11), we can compute this rotation using our same supposed (orthogonal, but otherwise arbitrary) input vectors of $+Q$ and $+U$. This rotation is given by:
And is calculated individually for every pixel in every bin of our data.
- 4. Convert to Jones matrix. The Stokes rotation $S_R(\Delta {{k}_{i}}, \theta, z)$ obtained in the previous step is converted to a Jones rotation $J_R(\Delta {{k}_{i}}, \theta, z)$ using Eq. (9), yielding:
It is important to note that because Eq. (24) was derived from Eq. (23) the original absolute phase information is not present in ${J}_{SC,\delta x}$- rather it is simply the Jones representation of the sample birefringence.
- 5. Solve for the input PMD-compensated measurements. Our approach for compensating for the $J_A$ PMD from our measurements begins by taking the product of $J_R^{-1}(\Delta k_i,z)$ with Eqs. (18) and (19). Using Eq. (18) this reduces to
With a similar result obtained for Eq. (19). The effectiveness of this approach at mitigating $J_A$ then depends upon how well the products ${{J}_{SC,\delta x}^{-1}}(\Delta {{k}_{i}}, \theta, z){J_{1SC}(\Delta k_i, \theta, z)}$ and ${{J}_{SC,\delta x}^{-1}}(\Delta {{k}_{i}}, \theta, z){J_{2SC}(\Delta k_i, \theta, z)}$ reduce to complex scalar multiples of the identity matrix, as otherwise the matrices will in general be non-commutative. This criteria is met given the assumptions outlined in Section 2.3.2 if an additional assumption holds: the sample birefringence encapsulated in $J_{SC,\delta x}$ matches the underlying birefringence contained in $J_{1SC}$ and $J_{2SC}$. If these assumptions are not adequately fulfilled the effectiveness of this approach at compensating for $J_A$ will be reduced by a factor generally dependent upon the deviation of these products from a scalar matrix.
If these assumptions hold, Eq. (25) reduces to
$${J}_{R}^{{-}1}(\Delta {{k}_{i}},\theta, z)\mathbf{out_1^{'}}(\Delta k_i, \theta, z)={\Lambda_{1SC}(\Delta k_i, \theta, z)}{\mathbf{in_1}}$$where $\Lambda _{1SC}$ indicates a scalar sample matrix that contains the absolute phase (speckle) information of the original data without any polarization properties. The sample birefringence can be mapped back onto Eq. (26) via the product$$\begin{aligned} J_R(\Delta {{k}_{i}},\theta, z){{J}_{A,\textrm{comp}}^{{-}1}}(\Delta k_i) & {\Lambda_{1SC}(\Delta k_i, \theta, z)}{\mathbf{in_1}}=\\ & {{J}_{B}}({{k}_{c}}){J}_{SC,\delta x}(\Delta {{k}_{i}}, \theta, z){\Lambda_{1SC}(\Delta k_i, \theta, z)}{{J}_{A}}({{k}_{c}}){\mathbf{in_1}} \end{aligned}$$And the same steps can be performed for Eq. (19) to obtain
$$\begin{aligned} J_R(\Delta {{k}_{i}},\theta, z){{J}_{A,\textrm{comp}}^{{-}1}}(\Delta k_i) & {\Lambda_{2SC}(\Delta k_i, \theta, z)}{\mathbf{in_2}}=\\ & {{J}_{B}}({{k}_{c}}){J}_{SC, \delta x}(\Delta {{k}_{i}}, \theta, z){\Lambda_{2SC}(\Delta k_i, \theta, z)}{{J}_{A}}({{k}_{c}}){\mathbf{in_2}} \end{aligned}$$Ending with Eqs. (27) and (28) we have now aligned the rotation of each bin to the coordinate system of the central bin.
After recovering the PMD-compensated fringes in step 6, PS processing can be performed using established techniques [9,10,20]. Polarimetry noise and loss of resolution that may be incurred by the compensation procedure can be minimized by taking care with the binning that is performed. In determining the PMD matrices as well as in performing the compensation, we used a Hanning-windowed bin at $20\%$ of the full spectrum bandwidth, shifted along the spectrum at $2\%$ intervals. This yielded a total of 50 bins.
3. Results
We assessed the efficacy of our technique using real-world data obtained by imaging airway segments both ex vivo and in vivo. Airway smooth muscle (ASM) bands are comprised of birefringent muscle tissue and are ubiquitous at shallow depths within the walls of airways. In addition to being clinically relevant to airway diseases such as asthma and COPD [29], they are useful in evaluating the performance of PMD compensation techniques due to the fact that they possess a distinct birefringent signature compared to the surrounding tissue, being consistently oriented with an OA that is approximately circumferential [9]. They also have varying axial thickness that, at the lower end in healthy human and large-animal airways, approach typical OCT resolutions ($\sim 10 \:\mu m$) [30].
Figures 3–5 depict data acquired in vivo during endobronchial imaging of a human airway, performed in the course of an ongoing asthma study we have been conducting. Figure 3 depicts intermediate results obtained from a depth location within the birefringent ASM band of our airway data. The ASM band is indicated with arrows in the tomogram of Fig. 3(a). Panels (b-e) plot the normalized Stokes vectors for one of the measured Stokes vectors across 18 bins (interpolated for plotting) spanning the full spectral range. Figure 3(b) depicts the broad range of Stokes vectors measured across bins, resulting from the PMD in the input and output channels of our system. Figure 3(c) shows the intermediate result of compensating for the output PMD $J_B$ only, while Fig. 3(d) depicts the full ($J_B$ and $J_A$) compensation. We observed in analyzing our techniques that the results become less reliable at the edges of our fringes due to the low SNR of those bins, but this outcome minimally impacts the final results as the contribution from those bins are correspondingly reduced relative the rest of the spectrum.
Fig. 3. Normalized Stokes vector measurements across spectrally binned data from a location in the birefringent ASM band of airway data acquired in vivo. (a) The tomogram corresponding to where the data was obtained with the ASM band indicated. (b) Stokes vector measurements with no PMD compensation applied. (c) Stokes vector measurements with only output channel PMD compensated. (d) Stokes vector measurements with input and output PMD compensated. Measurements were obtained using 18 spectral bins spanning the full spectrum and interpolated for plotting. Scale bar, 1 mm.
As mentioned in Section 2.2, we employed both a fixed Gaussian filter for transverse filtering (12 pixel FWHM) and a fixed birefringence calculation depth differential (1 pixel) in all of our retardance and OA data. The transverse filtering kernel was selected based on the fact that this is what we have previously found to provide the best results in the analysis of our airway data, while the single-pixel differential offset was selected to mitigate its impact on the interpretation of our results. Figure 4 depicts the PMD-calibrated retardance and OA of an airway cross-section calculated using these parameters as well as various axial filtering: no axial filter [Fig. 4(a,b)], a smaller Gaussian filter kernel (5 pixel FWHM) [Fig. 4(c,d)], and a larger Gaussian filter kernel (9 pixel FWHM) [Fig. 4(e,f)]. The OA data is presented as an angle in the plane specified by the circumferential (0 / $\pi$ radians) and longitudinal ($\pi /2$ radians) axes [10]. These results demonstrate that while some degree of axial filtering will likely be necessary to obtain useful results, flexibility is available in selecting the kernel size and it can be tailored according to the scale of the features of interest in the data. In imaging ASM in particular we have found that a 9 pixel FWHM kernel offers the best compromise of resolution and image interpretability.
Fig. 4. PS-OCT OA and retardance images from a human airway obtained using our PMD calibration technique and demonstrating varying axial filtering. (a) OA and (b) retardance using no axial filter. (c) OA and (d) retardance using a 5 pixel FWHM axial Gaussian filter. (e) OA and (f) retardance using a 9 pixel FWHM axial Gaussian filter. The arrows indicate the birefringent feature corresponding to the ASM band. Scale bar, 1 mm.
Figure 5 compares the PMD-calibrated, 9 pixel FWHM filtered OA and retardance images of the previous figure [fig. 4(e,f)] against two other approaches: basic PS processing without any additional handling of PMD [Fig. 5(a,b)], and the current state of the art approach for mitigating PMD, spectral binning [Fig. 5(c,d)]. All data in Fig. 5 was axially filtered using the same 9 pixel FWHM Gaussian filter, though it should be noted that the effect of this kernel on spectrally binned data is minimal up to a point due to the inherent axial filtering of the spectral binning technique. A total of 9 overlapping bins were used in the spectral binning approach, as we have previously found this number to produce the best results with our PS-OCT system [9]. Care was also taken to ensure that the other internal parameters of the spectral binning mechanism were optimized to produce the best available results.
Fig. 5. PS-OCT OA and retardance images from a human airway comparing different approaches for handling PMD. (a) OA and (b) retardance using no PMD mitigation or correction. (c) OA and (d) retardance using spectral binning. (e) OA and (f) retardance using our PMD calibration technique. No correction (a,b) suffers from inaccurate and inconsistent birefringence measurements while spectral binning’s (c,d) drawback is in decreased axial resolution. Scale bar, 1 mm.
While the previous data shows promising results for our PMD calibration technique compared to alternatives, the best way to validate the technique is by comparing measurements of meaningful birefringent features made using it against known values. In order to accomplish this we also imaged a canine airway in vivo and compared the results of our imaging against histology stained with alpha smooth muscle actin for identifying the ASM band (Fig. 6). The matching of the histology to OCT data was done by an independent observer using only the structural OCT data. A 9 pixel FWHM axial filter was again used for the spectral binning technique [Fig. 6(b,c)], and a 9 pixel FWHM filter for our technique [Fig. 6(d,e)]. The ASM band thickness was subjectively measured at five different locations in both the histology and OA images, and the results for each measurement are provided in the figure along with tick marks indicating the length and location of each measurement. Although spectral binning has been used extensively with great success, including in our own work [9], the narrowness of the airway wall layers in this airway sample highlights the inherent limitations in the spectral binning technique: as the layers of the sample become increasingly narrow, the mixing of measurements across layers increases proportionately (within the limits of the system resolution). This is the reason the OA measurements in the vicinity of the ASM band are here shown to tend towards $3\pi /4$ radians; the circumferentially oriented ASM band measurements are mixing with those of the longitudinally oriented connective tissue surrounding it. This effect is also evident in the retardance images of Fig. 6, with the retardance corresponding to the location of the ASM band in our approach [Fig. 6(e)] being much more sharper and clearly defined compared to that of spectral binning [Fig. 6(c)]. As a result, our approach has the capacity to greatly enhance the accuracy of both manual and automated segmentation of tissue features such as ASM bands.
Fig. 6. Histology and PS-OCT images for a section of canine airway. (a) Histology stained with alpha smooth muscle actin. (b) OA and (c) retardance PS-OCT images when spectral binning is used. (d) OA and (e) retardance PS-OCT images when our PMD calibration technique is used. The tick marks and adjoining numbers (in $\mu$m) indicate where manual subjective measurements of ASM thickness were obtained. Arrows are used to indicate the ASM band in the retardance image (e). Scale bars, $100 \mu$m.
4. Conclusion
In this work we have demonstrated a novel method for compensating for PMD in PS-OCT systems that have incoherent input states. This method was designed to be used primarily with endoscopic PS-OCT imaging, but can be applied to bench-top imaging equally as effectively so long as a sufficient reference signal is available for the estimation of the PMD matrices. We have validated our approach by comparison against histology, demonstrating a clear advantage over spectral binning in cases where increased axial resolution is desired. We believe this approach has the potential to offer a significant increase in the accuracy of birefringence measurements obtained with common implementations of fiber-based PS-OCT systems.
Funding
National Institutes of Health (K25HL145120, R01CA255326, R01HL133664).
Acknowledgments
The authors would like to thank Dr. Néstor Uribe-Patarroyo for his valuable participation in discussions related to the development of the PMD calibration algorithm, as well as his feedback in the preparation of the manuscript.
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. M. R. Hee, D. Huang, E. A. Swanson, and J. G. Fujimoto, “Polarization-sensitive low-coherence reflectometer for birefringence characterization and ranging,” J. Opt. Soc. Am. B 9(6), 903–908 (1992). [CrossRef]
2. J. F. de Boer, T. E. Milner, M. J. C. van Gemert, and J. S. Nelson, “Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography,” Opt. Lett. 22(12), 934–936 (1997). Publisher: Optica Publishing Group. [CrossRef]
3. C. Hitzenberger, E. Goetzinger, M. Sticker, M. Pircher, and A. Fercher, “Measurement and imaging of birefringence and optic axis orientation by phase resolved polarization sensitive optical coherence tomography,” Opt. Express 9(13), 780–790 (2001). [CrossRef]
4. B. Park, M. Pierce, B. Cense, and J. de Boer, “Real-time multi-functional optical coherence tomography,” Opt. Express 11(7), 782–793 (2003). [CrossRef]
5. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and A. Et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef]
6. G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276(5321), 2037–2039 (1997). [CrossRef]
7. S. K. Nadkarni, M. C. Pierce, B. H. Park, J. F. de Boer, P. Whittaker, B. E. Bouma, J. E. Bressner, E. Halpern, S. L. Houser, and G. J. Tearney, “Measurement of collagen and smooth muscle cell content in atherosclerotic plaques using polarization-sensitive optical coherence tomography,” J. Am. Coll. Cardiol. 49(13), 1474–1481 (2007). [CrossRef]
8. L. P. Hariri, M. Villiger, M. B. Applegate, M. Mino-Kenudson, E. J. Mark, B. E. Bouma, and M. J. Suter, “Seeing beyond the bronchoscope to increase the diagnostic yield of bronchoscopic biopsy,” Am. J. Respir. Crit. Care Med. 187(2), 125–129 (2013). [CrossRef]
9. D. C. Adams, L. P. Hariri, A. J. Miller, Y. Wang, J. L. Cho, M. Villiger, J. A. Holz, M. V. Szabari, D. L. Hamilos, R. S. Harris, J. W. Griffith, B. E. Bouma, A. D. Luster, B. D. Medoff, and M. J. Suter, “Birefringence microscopy platform for assessing airway smooth muscle structure and function in vivo,” Sci. Transl. Med. 8(359), 359ra131 (2016). [CrossRef]
10. D. C. Adams and M. J. Suter, “Processing-based approach for resolving the sample optic axis in endoscopic polarization-sensitive optical coherence tomography,” Opt. Express 26(19), 24917–24927 (2018). [CrossRef]
11. M. Villiger, B. Braaf, N. Lippok, K. Otsuka, S. K. Nadkarni, and B. E. Bouma, “Optic axis mapping with catheter-based polarization-sensitive optical coherence tomography,” Optica 5(10), 1329–1337 (2018). [CrossRef]
12. J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. 97(9), 4541–4550 (2000). [CrossRef]
13. E. Z. Zhang and B. J. Vakoc, “Polarimetry noise in fiber-based optical coherence tomography instrumentation,” Opt. Express 19(18), 16830–16842 (2011). [CrossRef]
14. M. Villiger, E. Z. Zhang, S. Nadkarni, W.-Y. Oh, B. E. Bouma, and B. J. Vakoc, “Artifacts in polarization sensitive OCT caused by polarization mode dispersion,” Opt. Lett. 38(6), 923–925 (2013). [CrossRef]
15. E. Z. Zhang, W.-Y. Oh, M. L. Villiger, L. Chen, B. E. Bouma, and B. J. Vakoc, “Numerical compensation of system polarization mode dispersion in polarization-sensitive optical coherence tomography,” Opt. Express 21(1), 1163–1180 (2013). [CrossRef]
16. Y. Lim, Y.-J. Hong, L. Duan, M. Yamanari, and Y. Yasuno, “Passive component based multifunctional Jones matrix swept source optical coherence tomography for Doppler and polarization imaging,” Opt. Lett. 37(11), 1958–1960 (2012). [CrossRef]
17. B. Baumann, W. Choi, B. Potsaid, D. Huang, J. S. Duker, and J. G. Fujimoto, “Swept source / Fourier domain polarization sensitive optical coherence tomography with a passive polarization delay unit,” Opt. Express 20(9), 10229–10241 (2012). [CrossRef]
18. B. Braaf, K. A. Vermeer, M. de Groot, K. V. Vienola, and J. F. de Boer, “Fiber-based polarization-sensitive OCT of the human retina with correction of system polarization distortions,” Biomed. Opt. Express 5(8), 2736–2758 (2014). [CrossRef]
19. Q. Li, K. Karnowski, P. B. Noble, A. Cairncross, A. James, M. Villiger, and D. D. Sampson, “Robust reconstruction of local optic axis orientation with fiber-based polarization-sensitive optical coherence tomography,” Biomed. Opt. Express 9(11), 5437–5455 (2018). [CrossRef]
20. C. E. Saxer, J. F. de Boer, B. H. Park, Y. Zhao, Z. Chen, and J. S. Nelson, “High-speed fiber–based polarization-sensitive optical coherence tomography of in vivo human skin,” Opt. Lett. 25(18), 1355–1357 (2000). [CrossRef]
21. Q. Li, K. Karnowski, G. Untracht, P. B. Noble, B. Cense, M. Villiger, and D. D. Sampson, “Vectorial birefringence imaging by optical coherence microscopy for assessing fibrillar microstructures in the cornea and limbus,” Biomed. Opt. Express 11(2), 1122–1138 (2020). [CrossRef]
22. J. Zhang, W. Jung, J. S. Nelson, and Z. Chen, “Full range polarization-sensitive Fourier domain optical coherence tomography,” Opt. Express 12(24), 6033–6039 (2004). [CrossRef]
23. B. H. Park, M. C. Pierce, B. Cense, and J. F. de Boer, “Jones matrix analysis for a polarization-sensitive optical coherence tomography system using fiber-optic components,” Opt. Lett. 29(21), 2512–2514 (2004). [CrossRef]
24. M. Villiger, E. Z. Zhang, S. K. Nadkarni, W.-Y. Oh, B. J. Vakoc, and B. E. Bouma, “Spectral binning for mitigation of polarization mode dispersion artifacts in catheter-based optical frequency domain imaging,” Opt. Express 21(14), 16353–16369 (2013). [CrossRef]
25. S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, “High-speed optical frequency-domain imaging,” Opt. Express 11(22), 2953–2963 (2003). [CrossRef]
26. S. H. Yun, G. J. Tearney, J. F. de Boer, and B. E. Bouma, “Removing the depth-degeneracy in optical frequency domain imaging with frequency shifting,” Opt. Express 12(20), 4822–4828 (2004). [CrossRef]
27. N. Uribe-Patarroyo, S. H. Kassani, M. Villiger, and B. E. Bouma, “Robust wavenumber and dispersion calibration for Fourier-domain optical coherence tomography,” Opt. Express 26(7), 9081–9094 (2018). [CrossRef]
28. 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). Publisher: Optica Publishing Group. [CrossRef]
29. R. K. Lambert, B. R. Wiggs, K. Kuwano, J. C. Hogg, and P. D. Paré, “Functional significance of increased airway smooth muscle in asthma and COPD,” J. Appl. Physiol. 74(6), 2771–2781 (1993). [CrossRef]
30. C. Y. Seow, R. R. Schellenberg, and P. D. Paré, “Structural and functional changes in the airway smooth muscle of asthmatic subjects,” Am. J. Respir. Crit. Care Med. 158(supplement_2), S179–S186 (1998). [CrossRef]
