2.1.

Experiments

The optical polarimetry system was constructed with a polarization analyzer (Thorlabs PAX 5710IR1). A near-infrared laser diode (LD), 780 nm, was employed as a light source. The Stokes parameters were determined by utilizing a polarization state analyzer (PSA) PAX 5710IR1. Figure 1 shows the experimental setup for the optical polarization measurements. The polarization state of the incident light was controlled by half- and quarter-waveplates (WPs). The measurement data were collected and analyzed using computer software (Thorlabs TXP5000). The tooth sample and light source were put on moving stages for optical scanning and calibration. For one-dimensional optical scanning, the stage was moved at 0.5 mm per step from the left of the sample, and the Stokes components were measured as Stokes 0, Stokes 1, Stokes 2, and Stokes 3. The scanning path was 15 mm as shown in Fig. 2. All the Stokes parameters were spatially plotted as the experimental results. The institutional review board (IRB) at National Yang-Ming University (IRB no. 100104) approved this research.

Fig. 1

Experimental setup. $\lambda /2\mathrm{WP}$ and $\lambda /4\mathrm{WP}$ represent half- and quarter-waveplates. LD is a laser diode, and the header is an optical detector.

Fig. 2

Tooth slice sample. The boundary between enamel and dentin indicates the DEZ. Dashed arrow indicates the optical one-dimensional scanning path of the sample tooth in the experiment.

2.2.

System Calibration

Before optical measurement of the tooth sample, the quarter- and half-WPs were experimentally calibrated and the Stokes elements were recorded after rotating the waveplates 10 deg. The optical attenuation from the WPs was $<0.2\mathrm{dB}$. The error with regard to sample thickness was controlled to $<10\mathit{\mu }\mathrm{m}$. Figure 3 shows the spatial distribution of Stokes 0 in the horizontal plane, $+45\mathrm{deg}$ and righthand circular polarization inputs. Because Stokes 0 indicates the measured optical power, the result implies the thickness distribution of each tooth layer of the sample.

Fig. 3

Spatial distributions of Stokes 0 in the horizontal plane, $+45\mathrm{deg}$, and righthand circular polarization inputs. G: glass, E: enamel, Z: DEZ, D: dentin.

3.1.

DEZ Evidence

The change from enamel to dentin is illustrated in Figs. 4Fig. 5–6. Unlike the traditional concept of a junction interface between dentin and enamel, the DEZ description offers more objective and accurate information. This technique, DEZ optical properties determined by birefringence, can be used for diagnosing dentin hypersensitivity. This technique can also be applied to diagnose and treat other abnormalities of the tooth. For example, this measurement can be used for monitoring the enamel and/or dentin damage after bleaching teeth; the composition of the changes of chemical materials, noted in the birefringence, can be determined.¹⁴

Fig. 4

Stokes 1 of three input states (horizontal, $+45\mathrm{deg}$, right circular polarization).

Fig. 5

Stokes 2 of three input states (horizontal, $+45\mathrm{deg}$, right circular polarization).

Fig. 6

Stokes 3 of three input states (horizontal, $+45\mathrm{deg}$, right circular polarization).

Clinicians can assess the pathogenic risk of dentin hypersensitivity and efficacy of surgery by comparing polarization states. Previous studies used AFM and SEM^8–10 to determine the characteristics of the DEZ. Although they demonstrate the scallop structure of the DEZ, these tools are difficult to use clinically because of physical limitations. Optical polarization probing is a convenient and portable optical scanning technique for the characterization of tooth structure.

3.2.

Polarization Probing of Tooth Structure

The Mueller matrix is a method used to calculate the optical properties of transmitted material for manipulating Stokes vectors, which represent the polarization of incoherent light. By analyzing the Mueller matrix, the optical properties of transmission such as diattenuation and retardance can be determined mathematically.¹⁵ According to classic optical theory, every optical element can be treated as a linear matrix.¹⁵ If the incident Stokes parameter is $S$, the output result after transmitted through a sample is $S^{\prime }$, the relationship between $S$ and $S^{\prime }$ is:

Direct comparison of the histological structure was performed by measuring the tooth sample with transmittance mode probing. In the experiment, the horizontal plane, $+45\mathrm{deg}$, and right circular polarized light were used to illuminate the tooth sample. Figures 4Fig. 5–6 show the Stokes 1–3 spatial distributions via input polarization states, using 0.5-mm step scanning. In a previous study,¹¹ enamel and dentin showed different retardance that originated from their different microstructure direction. A gradient change of birefringent properties was observed between 6.5 and 8.5 mm via different input polarization. The Mueller matrix of glass was nearly transparent without diattenuation or retardance according to the measurements [Eq. (4)]. Equations (5)–(7) show the measured Mueller matrices of enamel, dentin and DEZ.

Fig. 7

Transmittance (a) and back-reflection (b) experiment modes. $M_T$: transmission Mueller matrices, $M_R$: reflection Mueller matrices, $M_{\text{initial}}$: Mueller matrices of input light, $M_{\text{sample}}$: Mueller matrices of sample, $\theta$: incident angle.

Mueller matrix of glass:

Fig. 8

Characterization of tooth structure. The structural directions of enamel and dentin are plotted based on the Stokes–Mueller calculation. The DEZ is indicated by characterization of the enamel-dentin structure.

Table 1

Retardance of each tooth layer.

The gradient retardance angle change in the DEZ of a healthy tooth is illustrated in Fig. 8. In this paper, the minimum spatial resolution of the polarimater was around 500 μm. When a patient has a critical fracture, it destroys the DEZ structure and changes the retardance angle. Although the spatial resolution is limited, the fractured tooth DEZ can still be assessed because it usually occurs within several millimeters. This additional information can help dentists evaluate the risk of tooth fracture at the region where the retardance angle is noted to be changing. With high-spatial-resolution (around 20 μm) polarization optical coherence tomography (PS-OCT), it is possible to meticulously define the DEZ working width with in vivo optical testing.

Furthermore, the odontoblast process, as noted in Fig. 8, affects the estimation of the DEZ retardance angle; this illustrated the odontoblast process of dentin. The odontoblast process is an extension of a cell called an odontoblast, which forms the dentin in a tooth. It also extends into the enamel of a healthy tooth.¹¹ The odontoblast process can be observed in Fig. 8 changing from dentin to enamel. It resides in the dentinal tubules, is approximately 1 μm in diameter, is embedded in a collagen matrix–apatite reinforced composite.^1,12,13 Because the tubular structure is oriented from dentin to enamel, the odontoblast process effects the final polarization calculation. Moreover, a copious thickness is observed around these tubular structures. The transmittance is affected, as are the measurements of accumulated polarizing effects, which can lead to the retardance angle being overestimated. Correction of this deviation, to obtain uniform thickness of samples, can be obtained.

Such results can be used to establish a dental clinical application database. A complete database of a patient’s DEZ retardance can be used by clinics to compare the variation of the DEZ. A comparison can help clinics to clarify and distinguish dentin hypersensitivity from other oral problems because of the confirmation of a relationship between the DEZ and this common problem.¹¹ Moreover, an early, more accurate diagnosis will benefit patients.