1. Introduction

Optical coherence tomography (OCT) [1], as a non-invasive cross-sectional imaging method, has been applied in many fields such as ophthalmology [2,3], cardiology [4,5] and dermatology [6]. Although OCT can provide histomorphometric images of a sample by detecting the refractive index inhomogeneities, it could not discriminate tissues of different properties. To enable functional imaging, polarization-sensitive OCT has been developed to reveal depth-resolved birefringence information of tissue [7]. The polarization state of light changes while propagating in birefringent tissue, such as the aorta, cornea, airway muscle, retinal nerve fiber layer, and retinal pigment epithelium (RPE) [8]. In a simplified model neglecting depolarization, polarized light is decomposed into orthogonally vibrating components traveling at different group velocities after entering a birefringent sample. One component is thus retarded with respect to the other one depending on the magnitude of birefringence of the medium. Another phenomenon in some materials is diattenuation which seems to be negligible in biological tissue studied so far [9,10]. Polarization properties including retardation [7,11], optic axis orientation [12,13] and depolarization [14] can be extracted by analyzing the backscattered light from the sample by PS-OCT.

Single input polarization state PS-OCT has been favored due to the simplicity in comparison with its two inputs counterpart. It illuminates the sample with circularly polarized light and detects the back-scattered light with polarization diverse detection [7,15–17] Assuming the optic axis was constant, the accumulative birefringence could be extracted by one-shot measurement. Afterward, ultra-high-resolution OCT has demonstrated its great potential in revealing more details [2,5], compared to the conventional OCT. Single input PS-OCT with high resolution has been widely used in ophthalmology [3,18–21], dermatology [22–24], brain micro-tractography [25], etc. Meanwhile, there are a lot of technical publications dealing with dispersion compensation essential for ultra-high resolution [26–28], spectrometers alignment for birefringence artifacts removal [18,29,30], ghost images elimination in polarization-maintaining fiber-based system [15,31]. There are a few publications discussing the polarization distortions in two input PS-OCT (or PS-OFDI). Zhang et al. compensated polarization mode dispersion (PMD) caused by circulator and optical fiber with three calibration signals [32]. Braaf et al. modeled the whole system using the Jones calculus and compensated polarization distortion with two calibration signals from the sample data [33]. Yamanari et al. compensated the distortion with the signal from the surface of the sample using k-dependence correction [34]. Villiger et al. conceived the spectral binning method to mitigate the PMD effect [35] and obtained reliable optical axis orientation through Jones matrix symmetrization and catheter modeling [36]. Yet few discuss the polarization distortion caused by the polarizing components in the system operating under a broad bandwidth.

In the current single input polarization state PS-OCT systems, the polarization state manipulation of the illumination light is achieved by quarter-wave plates (QWPs) or single-mode fiber (SMF) [7,15,16,37]. Ideally, a QWP oriented at 45° in the sample arm provides circularly polarized illumination, and a QWP oriented at 22.5° in the reference arm provides 45° linearly polarized reference light after double pass. This mechanism works well when the operating spectral bandwidth is not so broad that the retardance induced by the QWP is uniform over the whole spectrum. However, if the operating spectral bandwidth becomes so broad that the chromatic variations in the retardation induced by the QWP or SMF are no longer negligible. Take a commercially available achromatic QWP (AQWP10M-980, Thorlabs Inc.) as an example, the mean value and standard deviation of the induced retardance within the spectral band of 760-920 nm for single pass are 93° and 0.25°, respectively, making the illumination light deviated from the circular polarization state, and the double pass through the QWP amplifies the defects in the current setup configuration [38]. Moreover, in the spectrometer-based polarization diverse detection, the mismatch in the sensitivity roll-off between the two spectrometers also leads to polarization distortions. These polarization distortions become salient when the sample birefringence is weak.

In this work, we introduced a Jones matrix model of a single input PS-OCT system, considering the polarization distortions induced by the wavelength-dependent retardance of QWP and the sensitivity roll-off mismatch between the two spectrometers over a broad bandwidth. Based on the model, a correction method has been developed to tackle these distortions. Numerically, we investigated the impact of the polarization distortion caused by the QWP on scattering samples at different birefringence scale and validated the correction method. Furthermore, a sample with known birefringence was imaged to demonstrate the performance of the correction. Lastly, we imaged animal tissues such as swine retina and rat esophagus ex vivo to demonstrate potential clinical applications.

2. System description and calibration

2.1. System description

The modeling and correction were based on a spectral domain PS-OCT system. The output of a super-continuum light source (SCL: SC-5OEM, YSL Photonics) was clipped by a dichroic mirror (DMSP950 Thorlabs Inc., not shown in Fig. 1) and collimated into the fiber coupler (90/10, TW850R2A2, Thorlabs Inc.). The input light was transformed into a circularly polarized light using a linear polarizer (P1: LPNIRE100-B, Thorlabs Inc.) and a QWP (AQWP10M-980, Thorlabs Inc.) before being split into the sample and reference arms by a non-polarizing beam splitter (50/50, BS014, Thorlabs Inc.). Another linear polarizer (P2) in the reference arm was used to produce reference light with identical amplitude and phase on the two spectrometers. The dispersion caused by polarizer P2 was balanced by a compensator (DC) made of polarization independent BK7 glass in the sample arm. In the detection arm, a half-wave plate (HWP: AHWP10M-980, Thorlabs Inc.) was employed to align the polarization coordinates of the free-space interference light to match the polarization axes of the polarization-maintaining fiber (PMF: P3-780PM-FC-2, Thorlabs Inc.). The polarization diverse detection unit consists of a polarizing beam splitter and two identical spectrometers, each of which was made up of a transmission grating (Wasatch TG: 1200 line/mm), a camera lens (L9: Nikon AF Nikkor 85mm f/1.8D), and a line scan CCD (E2V, EV71YEM4CL2010-BA9). The operating bandwidth was ~160 nm centered at 840 nm. The software for image acquisition and reconstruction was implemented with LabVIEW 2015 (National Instrument Inc.) and MATLAB 2016b (MathWorks Inc.), respectively.

 

Fig. 1 (a) Schematic of single input polarization state PS-OCT system. BS, beam splitter; DC, dispersion compensator; HWP, half-wave plate; L1-9, lenses; LS, linear stage; M1-2, mirrors; P1-2, polarizers; PBS, polarizing beam splitter; PM, power meter; PMF, polarization-maintaining fiber; QWP, quarter-wave plate; SCL, supercontinuum laser; SMF, single-mode fiber; SP, spectrometer, TG, transmission grating. (b)-(e) Process of k-space linearization. (b) the mapping function $k=\Phi \left(n\right)$ from CCD pixel index n to the k-space. (c) Raw interferogram. (d) Remapped interferogram in linear k-space. (e) Normalized point spread function (PSF) with a full width at half maximum (FWHM) of 2.3 μm in air after dispersion calibration. (f)-(h) Spectral alignment process after k-space resampling. Normalized profiles of the horizontal channel (red line) and vertical channel (blue line) with reflector optical path length difference of $\Delta z_1$ (dashed line), $\Delta z_2$ (solid line) before (f) and after (g) the spectral alignment, respectively. The spectrum rescaling factor a was determined by the ratio of the distances between the signal peaks’ positions of each channel. After spectrum rescaling, the peak positions of reflection surfaces of both channels were aligned together. (h) Determination of k-space pixel shift by drawing the functions of cross-correlation between interferograms of two channels against the amount of k-space shift at different path length differences.

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2.2. Polarizing component alignment

With a power meter located at the PM port of the input fiber coupler, we were able to precisely adjust the angular position of each polarization-changing element (polarizers, QWP, HWP) following the steps below:

2.3. K-space linearization and spectral alignment

To remap the fringe into evenly sampled k-space [29], took the advantage of the perfect sinusoidal modulation in the fringe resulting from additional reference reflectors. In our experiment, we used a similar method that used a reflector as the sample and numerically calibrate the system, without using additional reflection signals (the linearization process is illustrated in Fig. 1) [27]. Briefly speaking, the compensation is based on the fact that the interference fringes generated with a specular sample are ideally sinusoidal. Note that we added a polarizer between the beamsplitter and HWP to make sure the interference fringes captured by the two spectrometers were in-phase, which was removed after the calibration was completed. These interference fringes recorded for dispersion compensation were also used in the next step, namely the spectral alignment.

After the interference fringes were linearly resampled in k-space respectively, we aligned the index of wavenumber between spectra of the two spectrometers. We modeled the relationship of the wavenumber indices between the spectra from the two spectrometers as a linear function $k_2=a\cdot k_1+b$, where $k_1$, $k_2$ stands for wavenumber indices of the two spectra, respectively, $a$ and $b$ are the stretching coefficient and the k-space shift, respectively. If the two fringes are well aligned, the stretching factor a should be equal to 1, corresponding to the aligned peaks position in the depth $z$ domain. According to scaling properties of Fourier transform, the effects of stretching coefficient a on the wavenumber domain and the Fourier transformed depth domain can be revealed by Eq. (1) where $I$ is the spectrum, $k$ is the wavenumber, FT stands for the Fourier transform, $\Gamma$ is the depth profile, and $z$ is the depth in the sample.

Figures 1(f)-1(h) shows the procedures to determine coefficients $a$ and b for spectral alignment. The stretching coefficient $a$ could be determined via the linear regression on the peaks’ position of the PSFs of the two channels. (shown in Figs. 1(f)-1(g)). In the plot of cross-correlation between the interference fringes of the two channels against k-space shift b, the point at which all cross-correlation functions from different optical path-length differences (OPD) reach their maximum simultaneously reveals the optimal amount of pixel shift b (shown in Figs. 1(h)).

3. Jones matrix model of polarization distortion calibration

3.1. Jones matrix modeling of the detected signals

Following the model Braaf et al. used in [33], we modeled the system transmission and detected signal using the Jones calculus. In single input PS-OCT, the signal intensity $\stackrel{\rightharpoonup }{I}\left(k\right)={\left[I_{\perp }\left(k\right),I_{\parallel }\left(k\right)\right]}^{\text{T}}$ of a single scattering sample detected by two orthogonal polarization channels can be expressed as a function in terms of wavenumber $k$.

In practice, the DC term ${\left[\begin{array}{cc}{E}_{\text{ref}\perp }{E}_{\text{ref}\perp }^{*}& E_{\text{ref}\parallel }{E}_{\text{ref}\parallel }^{*}\end{array}\right]}^{\text{T}}$ and ${\left[\begin{array}{cc}{E}_{\text{sam}\perp }{E}_{\text{sam}\perp }^{*}& E_{\text{sam}\parallel }{E}_{\text{sam}\parallel }^{*}\end{array}\right]}^{\text{T}}$ are subtracted as the background. The complex electrical field interference vector could be obtained by Hilbert transform ($H$) as follows.

Usually, the polarization dependent attenuation can be ignored, so the attenuation factors regarding the optical loss and sample reflectivity can be simply described as scalars $c_{\text{ref}}(k)$ and $c_{\text{sam}}(k)$. The optical path length traveled from the reference reflector and the sample back to the spectrometer were $z_{\text{ref}}$, $z_{\text{sam}}$, respectively. The reference signal detected on the spectrometer can be expressed as:

Combining Eq. (2)-(5), the complex electrical field $\overrightarrow{\text{E}}(k)$ could be described in Eq. (6) as the product of the input electrical field, a diagonal matrix which depicts the overall effects of the reference and the spectrometers’ efficiency, and a Jones transmission matrix of the sample which is the objective of measurement. Note that $\Delta z=\Delta z_{\text{sam}}-\Delta z_{\text{ref}}$ is the OPD between the sample arm and reference arm. For simplicity, $R_{\perp }(k)$ and $R_{\parallel }(k)$ represent the combined effects of quantum efficiency ${\eta }_{\perp }(k)$, ${\eta }_{\parallel }(k)$, and orientation of polarizer on the orthogonal polarization channels. To simplify the analysis, we omit the power spectral density S(k).

In practice, the OPD dependent roll-offs of the two custom-made spectrometers might be different due to slight mismatch in the collimation or focal length of the camera lens. Therefore, the actual electrical field $\overrightarrow{\text{E}}(k)$ should consider another diagonal matrix for the roll-off effect. In summary, for the single input state PS-OCT, the detected complex electrical field is shown in Eq. (7) where $\beta (\Delta z)$ is the spectrometer roll-off coefficient.

3.2. Polarization distortion calibration

Following the above modeling, the polarization distortion consists of two parts: the phase distortion mainly caused by the imperfection of QWP, and the roll-off difference between two orthogonal polarization channels. In this section, we calibrated the detected phase Ψ(k) to be π/2 independent of k with a static mirror as the sample. The unbalanced roll-off coefficient ${\beta }_{\perp }(\Delta z)$, ${\beta }_{\parallel }(\Delta z)$ which depended on $\Delta z$ was compensated using the interferograms obtained with different OPD. The electrical field detected from a specular surface can be expressed by Eq. (8), in which we assume that the k-dependent $R_{\perp }$ and $R_{\parallel }$ can be negligible because the spectral responses of the two cameras generally are the same. Therefore, the overall response difference was compensated by a vector factor indexed in the depth domain.

The detected phase was compensated to the theoretical value by adding the offset point to point (Fig. 2(a)). At the same time, the amplitude roll-off ratio curve was fitted at a series of the reference mirror positions within 0.8 mm from the DC (Fig. 2(b)). Hence, the amplitude response of the two detection channels can be calibrated to be identical. To validate the polarization distortion calibration, we transformed the detected Jones vectors recorded with a specular sample and different reference mirror positions into Stokes vectors and plotted them on the Poincare sphere. The reference mirror was moved by a step of 100 µm over a series OPDs to 1200 µm. After polarization distortion correction, all the polarization states gathered around ${\left[\begin{array}{ccc}0& 0& 1\end{array}\right]}^{\text{T}}$, while the uncorrected spread out into an irregular line and deviates from ${\left[\begin{array}{ccc}0& 0& 1\end{array}\right]}^{\text{T}}$ (Fig. 2(c)), which demonstrates that the illumination polarization states were calibrated to be circular polarization at all depths.

 

Fig. 2 Polarization distortion compensation process and measurement of a polarizer and a QWP. (a). Measured phase difference versus the k-space index, the compensated values were obtained by point to point subtraction between the measured values and theoretical values. (b). PSF peak ratios between two spectrometers at different imaging depths. (c). Measured polarization states from the sample mirror with a series of OPDs, with (red points) and without (blue points) distortion correction. (d). The measured orientation of linear polarizer. The asterisk points are the measured data, the blue line is the linear-least-square fit of the measurements, and the red dashed line is the theoretical relation. (e). Measured phase retardation of QWP when placed at different orientations.

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We further validated our system performance by measuring the transmission axis of a linear polarizer (LPNIRE100-B, Thorlabs Inc.), and the retardation of a QWP (AQWP10M-980, Thorlabs Inc.). The retardation and optic axis reasoning are introduced in the next section. First, a linear polarizer was inserted in the sample arm and rotated by 10 degrees for each measurement. The measured transmission axis orientation of the linear polarizer is shown in Fig. 2(d). Then, the polarizer was replaced by a QWP, and the above rotation steps were repeated. The method to retrieve the retardation of the QWP is explicitly explained in section 4. The double-pass cumulative retardance of the QWP with different optic axis orientations is shown in Fig. 2(e). The average and standard deviation of the measured cumulative retardation of the QWP were 171.48° and 5.48°, respectively. These results agreed well with the theoretical expectations, indicating the high reliability of the calibrated system.

4. Extraction of sample polarization parameters

4.1. Jones matrix modeling of accumulative birefringence measurement

For non-depolarizing tissues, the Jones matrix of the sample $\text{J}$ can be decomposed as $\text{J=}{\text{R}}^{-1}\cdot \text{D}\cdot \text{P}\cdot \text{R}$, where $\text{R}$ is a rotation matrix defining the optic axis orientation $\theta$ of the sample with $\text{R=}{\left[\left[\begin{array}{cc}\cos \theta & -\sin \theta \end{array}\right],\left[\begin{array}{cc}\sin \theta & -\cos \theta \end{array}\right]\right]}^{\text{T}}$, and $\text{D}$, $\text{P}$ are diattenuation matrix and retardation matrix, respectively [10]. Diattenuation in biological tissue is usually negligible, and retardation matrix can be expressed as $\text{P=}{\left[\left[\begin{array}{cc}{e}^{i\delta }& 0\end{array}\right],\left[\begin{array}{cc}0& e^{-i\delta }\end{array}\right]\right]}^{\text{T}}$ where $\delta$ could be considered to be linearly dependent on $k$ considering the wavelength-dependent retardance of QWP so that the sample Jones matrix can be written as Eq. (9) [38].

When the system is well calibrated following the procedures described above, measured complex field (Eq. (8)) can be rewritten as

After the Fourier transform, depth information could be the convolution of the transformed sample Jones matrix with a delta function which defines the depth-displacement. The depth-resolved information is shown in Eq. (11), where $\delta (z)=\Delta n\cdot k_0\cdot z$ is the retardance between ordinary and extraordinary beams, and $k_0$ is the center wavenumber of the light source).

Furthermore, after we convert the Jones vector into the Stokes vector, a more simplified version of the depth-resolved information is shown as Eq. (12), where $\Delta \Phi$ is the phase difference between the two orthogonal polarization channels.

The intensity depth profile, retardation, optic axis, and DOPU could be calculated by Eq. (13). Of note, we used full Stokes averaging to reject speckle noise [8,35,39]. Compared with other complex averaging methods [40,41], Stokes averaging is more intuitive and coincidently makes retardation and optic axis calculation in the designed model more concise. In this paper, a 3D Gaussian kernel including pixels within 40 µm is defined for the Stokes averaging. Namely, the resolution of accumulative retardation and optic axis measurement in this paper is 40 µm.

5. Results

5.1. Simulations

To evaluate the influence of QWP’s wavelength-dependent retardance (AQWP10M-980, Thorlabs Inc.) on the measurement of retardation and optic axis, we simulated a phantom with two scattering layers. Meanwhile, we demonstrated the performance of the correction method for correcting the imperfection of QWP. The first layer has homogeneous retardation and optic axis orientation, while the second layer is a non-birefringent scattering sample. The thickness of each layer is 280 μm. To compare the performance of the correction method under different amount of birefringence, we performed the simulation twice and set the retardance of the first layer to be 0.15 rad and 1.5 rad, respectively. Gaussian noise corresponding to average signal-to-noise ratio (SNR) of 20 dB was added to the interferogram. The simulated bandwidth was set to be consistent with the actual system (760-920 nm). In the simulation, the wavelength-dependent birefringence properties of the QWP was set based on the data provided by the manufacturer (Thorlabs Inc.) and other optical elements were assumed ideal. The retardation and optic axis reasoning were performed according to the description in section 3. The area chosen for analysis was the second non-birefringent layer. The width of lateral and axial averaging kernel with Gaussian shape were 10 A-lines and 16 μm, respectively. The area of interest (AOI) was chosen from the second non-birefringent layer, from depth 350 μm to 380 μm. For a comprehensive evaluation, each sample was imaged six times at different orientation. For each sample orientation angle, 5000 points within the AOI were evaluated.

Figures 3(a) and 3(c) show the measured retardance value within the AOI without (blue boxes) and with (red boxes) the distortion correction where the first layer exhibits two different levels of birefringence and Figs. 3(b)-3(d) show the corresponding optic axis orientation measurement. To make the comparison better visualized, we present the optic axis measurements as the difference between the reconstructed values and corresponding ground truths. When the retardance of the first layer was set to be 0.15 rad, the mean value and the standard deviation of the measured accumulative retardation without the polarization distortion correction on different sample orientations were 0.1541 rad and 0.0383 rad, respectively, which became 0.1497 rad and 0.0072 rad, respectively, when polarization distortion correction was applied. The mean and the standard deviation of the optic axis error was 0.070° and 7.88° without the correction and becomes −0.13° and 1.24° with the correction, respectively. The polarization distortion caused by the QWP imperfection made the measurement noisy, while the corrected one yielded estimation close to the ground truth. When the accumulative retardation was set to be 1.5 rad, the difference in retardation measurements between the uncorrected and corrected method was almost negligible, while the corrected method still showed some improvement in the optic axis results. In general, the impact of the distortion on the measurement decreases as the sample birefringence increases, and the optic axis measurement is more susceptive to the polarization distortion than accumulative retardation.

 

Fig. 3 Simulation of the accumulative retardation and optic axis measurement without (blue box plot) and with (red box plot) calibration when imaging a two-layer phantom positioned at different orientation angles. (a-b). Demonstration of the effect of polarization distortion correction on accumulative retardation (a) and optic axis (b) measurement when the accumulative retardation of the first layer is set to be 0.15 rad; (c-d) Demonstration of the effect of polarization distortion correction on accumulative retardation and optic axis measurement when the accumulative retardation of the first layer is set to be 1.5 rad.

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5.2. Imaging results

We developed a polarization-corrected single input PS-OCT system and validated its performance. The axial resolution was ~2.3 µm in air, and the 6-dB roll-off depth was 500 µm in air. First, we imaged a phantom which consisted of two layers. The first non-birefringent layer was made by 1.0% polystyrene microspheres (Polysciences Inc., 300 nm in diameter) solution. The second layer was a tissue-like birefringent phantom which was fabricated following the procedures described in [42]. From the intensity image (Fig. 4(a)), the two layers can be distinguished by a bright boundary. Figure 4(b) shows the accumulative retardation image without the polarization distortion correction, where the first non-birefringent layer shows some amount of accumulative retardation. In contrast, the corrected image is shown in Fig. 4(c), where the upper layer (microspheres solution) exhibits zero accumulative retardation and the second layer presents gradually increasing accumulative retardation along the depth. We obtained differential retardance [43] image (Fig. 4(d)), by axially differentiating the accumulative retardation (Fig. 4(c)) with an interval set to be the kernel size of the averaging of Stokes vectors. In the differential retardance image (d), the boundary delineated by the distinct retardation difference accords well with the boundary seen in the intensity image (Fig. 4(a)).

 

Fig. 4 A demonstration of polarization distortion removal on a designed phantom. (a). Intensity image, scale bar 100 µm; MS: microsphere solution (non-birefringent sample); AP: ABS phantom (birefringent sample made of acrylonitrile butadiene styrene (ABS)). (b) Accumulative retardation image without the polarization distortion correction; (c). Accumulative retardation image with polarization distortion correction; (d) Differential retardance image, which was obtained by point-to-point differentiation of the accumulative retardation presented in image (c).

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Then, we imaged swine retina ex vivo. The swine eye ball was collected from a slaughterhouse within one hour after harvesting. We removed the cornea and vitreous body of the eye, thus exposing the retina directly to the air. The scanned area centered at the optic nerve head and spanned to the macular area. Note that swine retina does not have fovea shape at the center of the macular area, which is different from that of human [44]. Figure 5(a) shows the cross-sectional intensity image of the retinal structure, where layer structures such as the retinal nerve fiber layer (RNFL) and the retinal pigment epithelium (RPE) can be clearly visualized. Figure 5(e) shows the DOPU contrast of retina. The low DOPU value at the RPE indicates strong depolarizing effects and can be used to differentiate RPE and choroid for the diagnosis of drusen [21,45]. Figure 5(b) shows that the accumulative retardation increases gradually along depth within the RNFL, especially on the right side of the image. The birefringence distribution in the retina is better visualized in Fig. 5(c) after differentiation on accumulative retardation image Fig. 5(b), from where highly birefringent RNFL can be easily distinguished. In contrast, in the uncorrected retardation images Fig. 5(g), the birefringence distribution does not accord well with the RNFL, especially in the area indicated by the white arrows. While in the uncorrected optic axis image, the change of the measured optic axis is more toneless than the corrected one, the difference will be more evident in the en face image shown in Fig. 6.

 

Fig. 5 A comparison of birefringence imaging of swine retina near the macular with and without the polarization distortion correction. (a). Intensity image, scale bar: vertical 100 µm, horizontal 500 µm. RNFL: retinal nerve fiber layer, RPE; retinal pigment epithelium. (b) Accumulative retardation with polarization distortion correction. (c) Differential retardance with polarization distortion correction. (d) Accumulative optic axis image. (e) DOPU image. (f)-(h) Accumulative retardation, differential retardance, accumulative optic axis image without polarization distortion correction, respectively. The white arrows indicate the area where RNFL is not highlighted as high birefringence area.

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Fig. 6 Birefringence imaging of swine retina near the optical nerve head. (a) Intensity image, scale bar: vertical 100 µm, horizontal 500 µm. (b) Accumulative retardation with polarization distortion correction. (c). Differential retardance with polarization distortion correction. (d) Accumulative optic axis image. (e) DOPU image. (f). Intensity projection, scale bar 400 um. (g) The en face projection accumulative retardation at the bottom of the retinal nerve fiber layer. (h). En face projection of optic axis without polarization distortion correction. (i). En face image of optic axis after polarization distortion correction

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Figure 6 shows a set of cross-sectional images and en face projections of the optic nerve head area of the swine retina, where the RNFL is much thicker than the macular area. The en face projections were obtained by averaging the corresponding results along depth within the RNFL. Fiber structures are clearly seen in the en face intensity projection in Fig. 6(f). The accumulative retardation at the lower boundary of RNFL is mapped as an en face image illustrated in Fig. 6(g). Figures 6(h)-6(i) demonstrate en face projections of optic axis with and without the polarization distortion calibration: the calibrated optic axis image (Fig. 6(i)) reveals the radial pattern of the nerve fiber orientation, while the uncorrected one (Fig. 6(h)) shows an indistinct pattern.

Figure 7 shows cross-sectional images of rat esophageal tissue scanned along the circular direction. To mitigate surface reflection, we placed a cover glass gently on the tissue surface to keep in contact with it, meanwhile inserted an identical cover glass in the reference arm to balance the dispersion. In the intensity image (Fig. 7(a)), layered structures are clearly visualized with high resolution. In accumulative retardation image (Fig. 7(c)), the top five layers (keratinized layer to submucosa layer) do not present significant birefringence, while the muscularis propria (MP) layer shows a rapid cumulation of phase retardation. The amount of birefringence in each layer can be better visualized in the differential local retardation image (Fig. 7(d)). In Fig. 7(b), the distinct optic axis orientation difference between the internal circular layer (ICL) and outer longitudinal layer (OLL) of muscularis propria agrees well with the orientation of the muscle fibers shown in the histology image (Fig. 7(e)).

 

Fig. 7 Birefringence imaging of rat esophagus. (a) Intensity image; (b) Optic axis orientation image; (c) Accumulative retardation image. (d) Differential retardance image. (e). Histology of rat esophagus (transverse section). KL: keratinized layer; EP: epithelium; LP; lamina propria; MM: muscularis mucosa; SM: submucosa; MP: muscularis propria; ICL; internal circular layer; OLL: outer longitudinal layer; AD: adventitia. Scale bar: vertical 100 µm, horizontal 200 µm.

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6. Discussion and conclusion

Based on the Jones matrix modeling of the system, we corrected the illumination polarization state to be circularly polarized across all depth. According to the simulation, the calibration is crucial for the determination of the accumulative optic axis of the sample when the sample birefringence is weak. This might be why the optic axis contrast of the retina was obscure without this polarization distortion correction. Moreover, the retardation was also deviated from its ground truth when the initial polarization state is not circular polarization. Due to the inherent limitation of single input state PS-OCT, we could not reliably obtain the quantitative birefringence information of deeper layers featuring different optical axis orientations from the first layer [46]. The non-ideal circular polarization illumination could be considered as residual birefringence before the sample surface. In our case, comparing Fig. 5(c) to Fig. 5(g), the uncorrected differential retardance of the RNFL displayed varying measurement errors corresponding to the varying optic axis across different lateral locations. We can also notice biases resulted from the same reason in the simulation of retardation measurement in Fig. 3, where the measurement error varied with the rotation of the optic axis of the sample. In contrast, the measurement of strong retarder (such as muscularis propria in Fig. 7) seems far less affected by the polarization distortion. This implies a negative correlation between the impact of the polarization distortion and strength of the retarder. Thereby, it is crucial for the measurement of low birefringence tissue such as retina to correct this polarization distortion.

It’s worth mentioning that the system configuration of our single input PS-OCT setup also provides some convenience for the polarization distortion correction over the existing ones. The light beam is manipulated to be circularly polarized before entering the beamsplitter, thus precluding the back-reflected and back-scattered light from passing QWP again, which provides a convenience for the calibration of the imperfection of QWP. In the reference arm, the QWP at 22.5° is replaced by a more economical linear polarizer at 45°. The requirement on the orientation of the linear polarizer is less strict than a QWP since a polarizer ensures identical phase inherently for the horizontal and vertical components of the reference light so that only the amplitude responses of the two detection channels needs compensation. Compared with the traditional single-input PS-OCT system, our customized system theoretically has lower polarization distortion caused by polarizing components. In the sample arm, the double pass through the imperfect QWP exacerbates the defect of wavelength-dependent characterization. In the reference arm, double pass through the imperfect QWP cannot ensure identical reference light beam for the orthogonal polarization detections, especially the phase. These modifications also provide convenience in the correction of the polarization distortion induced by the roll-off difference of the two spectrometers.

In conclusion, we introduced a single input PS-OCT system with high resolution and presented self-consistent fabrication and detailed calibration procedures. We investigated the effect of polarization distortion induced by the imperfection of QWP on the measurement of birefringence. And we developed a polarization distortion correction method based on the Jones matrix modeling of the PS-OCT system. Correspondingly, an algorithm for retardation, optic axis, and DOPU reasoning was formed. To demonstrate the performance of the polarization distortion correction method, we performed a numerical simulation. Moreover, images of the swine retina and rat esophagus demonstrated the capability of resolving the birefringence property of real tissues.