2.1.

Experimental Setup

To perform polarization sensitive measurements, we set up a custom swept source OCT system (Fig. 1) with single-mode fibers and a bulk optics scanner head, which is mainly based on a concept initially proposed by Hee et al.²¹ A swept source laser (Axsun Technologies Inc., Billerica, Massachusetts) with a sweep rate of 50 kHz, a center wavelength of ${\lambda }_0=1310\mathrm{nm}$, and a spectral bandwidth of $\mathrm{\Delta }\lambda =110\mathrm{nm}$ (used for image processing) is connected via fiber couplers (FC) to a fiber Bragg grating (FBG), to create a phase stable sweep trigger signal, and to a booster optical amplifier to compensate later coupling losses in the interferometer setup. Polarization controllers (PCs) allow the alignment of linearly polarized light incident into the polarization-dependent booster optical amplifier (BOA) and the bulk optics setup, which is connected via an optical circulator (OC). An initially passed polarizing beam splitter (PBS) operates in forward direction as a polarizer, before a nonpolarizing beam splitter (BS) equally separates the light into reference and sample arm. The polarization rotation of the reference light results in a diagonal polarization, as the quarter wave plate (QWP) in the reference arm has an orientation of 22.5 deg with respect to the optical axis. Contrarily, the incident light on the sample is circularly polarized due to a 45-deg-oriented QWP in the sample arm. Therefore, the returning sample light obtains an arbitrary elliptical polarization state depending on the sample’s birefringence. The superposed light from reference and sample arm is then split by two PBS into both orthogonal polarization states, which finally results via collimating optics and single-mode fibers in a dual balanced detection of the co- and cross-polarization interference spectra. To acquire the data linear in $k$-space, the clock signal of the swept laser is utilized as a sampling trigger of the high-speed digitizer (Alazar Technologies Inc., Pointe-Claire, Canada).

Fig. 1

PS-OCT system with swept laser (${\lambda }_0=1310\mathrm{nm}$, $\mathrm{\Delta }\lambda =110\mathrm{nm}$). FC, fiber couplers, Det, detectors; FBG, fiber Bragg grating; PC, polarization controllers; BOA, booster optical amplifier; OC, optical circulator; PBS, polarization beam splitters; LP, linear polarizers; BS, polarization independent beam splitter; QWP, quarter wave plates oriented at 22.5 deg and 45 deg; RM, reference mirror; GS, galvanometer scanners; BD, balanced detectors; and DA, data acquisition card.

For this study, volumes of $1280\times 1280$ A-scans with a step size of $8\mu \mathrm{m}$ in both lateral directions and a total imaging depth of 4.96 mm, corresponding to 1024 pixels or an axial pixel size of $4.8\mu \mathrm{m}$ in air, were recorded. The lateral and the axial resolutions in air were measured to be 15.6 and $15.1\mu \mathrm{m}$, respectively. All data acquisition and image processing were performed by customized LabVIEW (National Instruments Inc., Austin, Texas) and Fiji²² software.

2.2.

Image Calculation and Representation

As the underlying concept of polarization, Jones and Stokes formalisms, and image formation in conventional as well as PS-OCT with circularly polarized incident light on the sample and the presented detection scheme is widely described and was recently summarized by de Boer et al.,⁹ the image formation from the spectra will be outlined here in brief.

The inverse Fourier transform of the balanced and linearly in $k$-space detected interference spectra for both cross- and co-polarization channel results in complex, depth-resolved A-scans with amplitudes $A_x(z)$, $A_y(z)$, and phases ${\varphi }_x(z)$, ${\varphi }_y(z)$, and phase differences $\mathrm{\Delta }\phi (z)={\phi }_y(z)-{\phi }_x(z)$, respectively. Hence, the reflectivity $R(z)$, the retardation $\delta (z)$, and the fast axis orientation $\theta (z)$ can be calculated as

From the calculus’ symmetry derive unambiguous measurement ranges of $[0;\pi /2]$ for $\delta (z)$ and $[-\pi /2;\pi /2]$ for $\theta (z)$. For visualization, we chose a color gradient of blue, cyan, green, yellow, and red for $\delta (z)$ (usually known as “jet” scale) and a transition from purple over blue, white and red to purple for $\theta (z)$, as $-\pi /2$ and $\pi /2$ represent the same orientation.

Additionally, the Stokes vector elements $I$, $Q$, $U$, and $V$ can be calculated for each depth pixel

Applying the conventional degree of polarization calculus $\mathrm{DOP}=(Q_{\mathrm{norm}}^2+U_{\mathrm{norm}}^2+V_{\mathrm{norm}}^2{)}^{1/2}$ pixel by pixel on the thus derived Stokes components would result in a $\mathrm{DOP}=1$ (fully polarized) for the entire image, so that an averaging of $U$, $Q$, and $V$ for adjacent pixel in a certain evaluation kernel is introduced,¹⁶ which leads to the DOPU

As the resulting DOPU is highly dependent on the number of speckles that are taken into account for averaging, and the speckle size itself depends on the axial and lateral resolutions,²³ we decided to evaluate the kernel size as a multiple of axial and lateral resolution. Consequently, the chosen kernel size of $3\times 3$ corresponds to an averaging of 9 (axial) $\times$ 6 (lateral) pixels. To maintain image sizes and enable real-time processing, a recursive two-dimensional moving average algorithm, which avoids redundant calculation steps, was implemented. The chosen color transition for representing fully depolarized (0) up to completely polarized (1) light comprises red, yellow, and green, whereas yellow matches for a better contrast not the center (0.5) but a DOPU of about 0.7 in this dimensionless quantity.

Furthermore, a gray mask was applied on retardation, orientation, and DOPU images, which is based on a 16-dB threshold of the reflectivity data and overlays image regions with noisy or without sample information. Since the ratio between axial and lateral pixel sizes was not corrected for a superior depiction of depth information, all scale bars correspond to $500\mu \mathrm{m}$, whereby axial depths are consistently adjusted on the refractive index of enamel in the 1300-nm range of 1.631.²⁴

2.3.

Tooth Samples

Based on German regulations for this type of research, no ethical approval was mandatory for this study.²⁵ Three extracted human molar teeth with proximal lesions were used for PS-OCT imaging. The teeth were provided by enretec GmbH (Velten, Germany) and were stored in a distilled water–thymol solution to prevent dehydration. The selected teeth were visually examined by an experienced dentist and showed the following characteristics:

3.1.

Polarization Sensitive Imaging

To demonstrate the capability of the PS-OCT system for measuring birefringence in dental hard tissue and likewise comparing the effect of an early carious lesion on the different representation modalities, Fig. 2 shows the intensities measured by co- and cross-polarization channels as well as the resulting reflectivity. Furthermore, retardation and optical axis orientation are shown next to the DOPU for a $3\times 3$ (multiples of resolution) evaluation kernel according to Eqs. (1) and (3), respectively. The presented B-scan of the proximal side of an extracted human molar tooth corresponds to the same region as presented in Fig. 5 for “white spot.” Enamel (E), dentin (D), and the dentin–enamel junction (DEJ) are labeled in the images as well as the region that has been identified as a white spot (W). In addition to the visible dental structures, imaging artifacts such as the mirrored surface reflex, which is especially discoverable in the lower half of the co-polarization image, appear due a coherence revival in the swept laser and should not be confused with actual sample structures.

Fig. 2

OCT B-scan of the co-, cross-polarization channels and the determined reflectivity image showing enamel (E), the dentin–enamel junction (DEJ), dentin (D), and white spot (W) of an extracted human molar tooth. For polarization contrast imaging, the retardation, the fast axis orientation, and the DOPU ($3\times 3$ kernel) are displayed. This B-scan is an adjacent of the B-scan as shown in Fig. 5 for “white spot.” Scale bars correspond to $500\mu \mathrm{m}$.

As it can be clearly seen in the retardation as well as co- and cross-polarization images, the high birefringence of sound enamel becomes visible for an incident beam perpendicular to the enamel rods or prisms, which are oriented approximately perpendicular to the surface.²⁶ While this is the case in the left third, the enamel rods in the center third are commonly parallel oriented to the incident beam and the retardation remains constant over the depth. Reversely, the orientation image allows an estimation of the rod structure in this center image region, but further investigations of the polarization sensitive image formation with regards to the precise spatial distribution²⁷ are necessary for a conclusive interpretation. For dentin, less birefringence related to its substructure²⁶ and a decreased DOPU, which has been previously observed²⁸ and occurs due to multiple scattering,²⁹ allow a delimitation from the surrounding enamel, as well as the in the intensity images visible DEJ.

Additionally, a white spot, an early stage of caries, and a case of demineralization in the outer enamel are present here. Due to a reduced penetration depth, a differentiation of the white spot from the nearby sound tissue is possible in this case for all modalities. However, while the comparison of co- and cross-polarization images with altered intensity ratios as well as the particular textures in the retardation and orientation images might enable a trained expert to recognize this feature, the DOPU offers an unambiguous contrast for carious lesions and demineralization.

Moreover, a decreased DOPU can be observed in the right image third near the enamel–cementum intersection, which is assumed as an artificial deformation, possibly by the mechanical impact during the extraction of the molar tooth.

3.2.

DOPU Evaluation Kernel

We compared different symmetric sizes of the evaluation kernel that is used for averaging the Stokes components $Q$, $U$, and $V$ [Eq. (2)] in a certain window before the DOPU is calculated [Eq. (3)]. As this refers to multiples of the axial and lateral resolution, a kernel size of $1\times 1$ corresponds to $3\times 2\text{pixels}$ (axial $\times$ lateral dimension) and a kernel size of $6\times 6$ to $19\times 12\mathrm{pixels}$. The resulting images in Fig. 3 show an increasing contrast with increasing kernel size, whereby the resolution suffers from the applied averaging. Additionally, the mean DOPU value for both, the sound enamel and the white spot, decreases for increasing kernel size, as shown in the evaluation (Fig. 4) for the marked regions of interest (ROI, $40\times 40\text{pixels}$) in Fig. 3. However, the ratio between both values as an achievable contrast increases. Therefore, the visual impression in Fig. 3 is confirmed by the plotted values in Fig. 4.

Fig. 3

OCT B-scan with different DOPU evulation kernel sizes as multiples of axial by lateral resolution. Two ROIs for sound enamel and white spot are marked. Case $3\times 3$ equals the DOPU depiction in Fig. 2. Scale bars correspond to $500\mu \mathrm{m}$.

Fig. 4

Mean DOPU values with SD for two different ROI, dependent on the DOPU evulation kernel size. The related ROIs are marked in Fig. 3.

Fig. 5

Comparison of reflectivity and DOPU for B-scans of three molar teeth with different proximal lesions: white spot, brown spot, and cavity. Photographs of the examined teeth with a marking of the corresponding B-scan region are presented. Scale bars correspond to $500\mu \mathrm{m}$.

Following both the visual and the measured results, we decided to use a kernel size of $3\times 3$ for all subsequent analyses, as it offers a high contrast, which does not considerably increase for larger kernel sizes, and at the same time, maintains a suitable resolution. Moreover, the lower standard deviation (SD) for larger kernel sizes derives from a convergence of ROI and kernel size. It should be noted that for certain cases or questions an asymmetric kernel might be more convenient, as it preserves the resolution in one over the other dimension, and the particular choice should adapt to the particular issue.

3.3.

Imaging Different Caries Stages with DOPU

To prove the suitability of depolarization imaging with DOPU as an indicative contrast for both early and advanced stages of proximal carious lesions, we selected three exemplary molar teeth for PS-OCT imaging. Teeth 1 and 2 show a noncavitated enamel lesion, which appears as a result of an ongoing demineralization and remineralization process that can finally lead to a collapse of the enamel surface and a cavity (tooth 3). As it can be seen in Fig. 5 by means of the presented photographs, the enamel of the white spot has lost its translucency without an additional staining, whereas both the brown spot and the cavity show a considerable discoloration. For all three cases, significant changes of the DOPU appear in those regions that can be identified and assigned as lesions from the photographs. Although it is even possible to visually distinguish areas with differing scattering behavior through the reflectivity images, especially for border areas a clear differentiation seems to be difficult in comparison with the DOPU. Furthermore, the significant DOPU contrast appears to enable a better delimitation of the undermining carious progression, as it happens in case of the cavity. On the other hand, particularly for the direct surface regions, an interpretation of the demineralization progress might depend on the influence of the bright surface reflex, which has to be further investigated. In addition to the enhanced processing algorithms, the application of an index matching substance should be taken into account to solve this issue.

Compilations with all representations, equally shown as in Fig. 2, can be found for all three samples in the appendix.