1.

Introduction

Optical coherence tomography (OCT) is a novel biological imaging technology that has been developed rapidly in the last decade. Since Huang obtained the first OCT image of the tiny structure of the human retina in 1991,¹ many research groups have achieved clear OCT images of both normal and decayed dental tissues and have proven that OCT can be applied to oral medical diagnosis.^{2, 3, 4}

The refractive index is an important optical parameter of biological tissues, especially for teeth. It has been found that early demineralization caused by caries will alter a tooth’s refractive index; therefore, the accurate measurement of the changes in a tooth’s refractive index can help the early diagnosis of dental caries.⁵ Presently, a relatively successful method for measuring a tooth’s refractive index is the OCT-based focus-tracing method.^{6, 7, 8} However, such a measurement is difficult to perform in practice because it requires at least two adjustments of the focal point during each measurement and the precise calibration of the numerical aperture of the lens, making the measurement slow and more susceptible to measurement errors. A method to record spatial variations of the refractive index of the porcine renal artery using differential-phase optical coherence microscopy was reported in Ref. 9. However, the calculation of the tissue refractive index requires a priori knowledge of the section thickness and the refractive index of the surrounding medium. Another limitation of this method is that the thickness of the calcite prism pair should be carefully adjusted to introduce the same amount of equivalent phase retardation introduced by the tissue.

This paper describes a simple method based on optical path-length (OPL) matching during an OCT scan for measuring the refractive index of the in vitro teeth. This OCT path-length matching method has the advantages of easy operation, fast measurement, and high accuracy, especially compared with the OCT focus-tracing method. As a result, the index distribution profile across a tooth also can be readily obtained. In this paper, we first present the basic structure of our all-fiber polarization-insensitive OCT system, and then describe the principle of the path-length matching method. Finally, we show the measurement results of the refractive indices of different parts of in vitro human teeth and the corresponding refractive index profiles.

2.

All-Fiber OCT System

The OCT system utilizes the principle of low-coherence interferometry with a broadband light source to obtain high spatial resolution. To overcome the polarization sensitivity commonly found in all-fiber OCT systems, we developed a polarization-insensitive scheme. Figure 1 is the schematic of our all-fiber polarization-insensitive OCT system.

Fig. 1

Schematic of the all-fiber OCT system. SLD: superluminescent diode; OC: optical circulator; Glens: GRIN lens; S: sample, DP: displacement plate; C: coupler; D: detector; VDL: variable delay line; FS: fiber stretcher; FRM: Faraday rotator mirror; CF: compensation fibers; VOA: variable optical attenuation; DAQ card: data acquisition card; PC: personal computer.

The system uses a super luminescent diode (SLD) with a $50\text{-}\mathrm{nm}$ FWHM bandwidth and a $1310\text{-}\mathrm{nm}$ center wavelength as a light source, resulting in a free-space coherence length of $15\mu \mathrm{m}$ . We choose $1310\mathrm{nm}$ because teeth are a highly scattering tissue with their maximum penetration at $1310\mathrm{nm}$ . Near-infrared light at $1310\mathrm{nm}$ is well suited for the detection and imaging of interproximal caries lesions.¹⁰ Light is delivered to the sample by a gradient index (GRIN) lens with a $3\text{-}\mathrm{mm}$ focal length. The reflected light from the exit surface of the GRIN lens is used as the reference light. One arm of the interferometer consists of a fiber stretcher-based scanning optical delay line to scan the optical path delay and a variable delay line (VDL) to match the optical length between the two interferometer arms. A Faraday rotator mirror is placed at each end of both interferometer arms to eliminate polarization fluctuations in the single-mode fiber. Such an arrangement completely eliminates polarization sensitivity, even when the sample arm and the interferometer arms are perturbed. The balanced detector receives the interference signal, and the data acquisition (DAQ) card collects the data and transmits them to the computer. A 1-D translation stage driven by a stepper motor is used for transverse scanning of the sample.

3.

Description and Validation of the Path-Length Matching Method

Since the time-domain OCT described in Fig. 1 is based on broadband interferometry, it directly measures the group delay of the sample. If the thickness of the sample is known, the group refractive index can be calculated from the group delay. The actual group refractive index $n_g$ and phase refractive index $n_p$ have the following relationship:

To measure the refractive index of a sample, we first place the sample on a metal (unpolished aluminum) plate and then acquire the OCT images. Figure 2 shows a schematic diagram of the sample on the metal plate, where the vertical position of the metal plate’s reflection surface is $z_0$ , the vertical position of the sample surface is $z_1$ , the thickness of the sample is $d$ , and the refractive index of the sample is $n_S$ .

Fig. 2

Schematic diagram of the sample on a metal plate.

Figure 3a is a 2-D OCT image (B-scan) of a glass slide on the metal plate that shows the change in the metal plate’s vertical position caused by the glass slide. The left portion of the image shows the position of the metal plate without the glass slide present, while the right portion shows its position with the glass slide. The upper surface position of the glass also can be seen clearly. As expected, the depth of the metal plate increases when the glass slide is on top (the position of the metal plate surface changes from $z_0$ to $z_0^{\prime }$ ), which results from the optical path-length increase caused by the relatively large refractive index of the glass (compared with the air). Assuming that the increase in the optical path-length induced by the glass plate (sample) is $z_0-z_0^{\prime }$ and the actual thickness of the sample is $z_1-z_0$ , we can obtain the relationship between the thickness and the refractive index of the glass slide (sample):

Fig. 3

OCT image of the glass slide: (a) 2-D OCT image of the metal substrate and the glass slide; (b) 1-D OCT image of the metal substrate and the glass slide.

Note that at $1310\mathrm{nm}$ , the attenuation of light inside teeth is primarily from scattering, and the absorption is negligible.^{10, 13} Consequently, the imaginary part of the index of refraction can be ignored. In addition, our method is based on the phase measurement of interfering beams, and there are no apparent attenuation variations within the bandwidth of the SLD source used in the experiment¹⁴; therefore, any absorption or imaginary part of the index will have little impact on the measurement results.

4.

Results of Teeth Measurement

We measured the enamel, dentin, and cementum of in vitro human teeth. In the experiment we first cut and polished freshly removed teeth into thin slices with a slice thickness of $300\text{to}400\mu \mathrm{m}$ , and then placed each tooth slice onto the metal plate to replace the glass slide in Fig. 2. When not in use, these tooth slices were kept in distilled water. Finally, we took B-scan OCT images of the tooth slices placed on the metal plate. The results are shown in Fig. 4 . Figures 4a, 4b, 4c are the OCT images of an enamel slice, a dentin slice, and a cementum slice, respectively.

Fig. 4

OCT image of in vitro human teeth slices: (a) OCT image of the enamel slice; (b) OCT image of the dentin slice; (c) OCT image of the cementum slice.

We measured 20 samples of the in vitro human tooth slices separately, and the resulting refractive indices of the enamel, the dentin, and the cementum were $1.631\pm 0.007$ , $1.540\pm 0.013$ , and $1.582\pm 0.010$ , respectively. In Refs. 15, 16, the refractive indices of enamel and dentin were 1.60 to 1.65 and 1.50 to 1.55, respectively. Thus our measurement results were consistent with those of Refs. 15, 16, but with much better accuracy. As reported in Ref. 5, the ranges of refractive index of noncarious and carious enamels are $1.623\pm 0.005$ and $1.628\pm 0.004$ respectively at the wavelength of 577 nm. We expect the index difference between the noncarious and carious enamels to be similar at 1310 nm and that the resolution of our measurement method is sufficient to detect the changes in refractive index caused by caries. We are currently performing further experiments to measure the indices of noncarious and carious enamels at 1310 nm and will publish the results elsewhere. We performed an analysis of variance (ANOVA) using the 20 sets of refractive index data of dentin and cementum to ensure the refractive indices of dentin and cementum had statistically significant differences. We found that the mean within-group variance of dentin and cementum was 0.000039297 and the variance of the group means was 0.017736731. The corresponding F-test (the ratio of variance of the group means and mean within-group variance) was 451.35, well above the required F-test of 7.35 from the ANOVA look-up table. Therefore, we are certain that the measured indices of dentin and cementum were statistically different.

We did not take the polarization effect into account in the measurements so the resulting data are the average of ordinary and extraordinary indices. Further polarization-sensitive OCT measurements are under way to separately measure both indices.

Figure 5a is a photographic image of an in vitro tooth slice subject to refractive index measurement. We took a B-scan along the direction marked with a white line in Fig. 5a and obtained the 2-D OCT image shown in Fig. 5b. Using the path-length matching method described above, we obtained the refractive index distribution profile shown in Fig. 5c along the scan direction by taking each axial scan (A-scan) information [vertical position information in Fig. 5b]. One can clearly see from Fig. 5c the changes in the refractive index along the scan direction: from the air (with a refractive index of 1) to the cementum (refractive index around 1.58), to the dentin (refractive index around 1.54), and then to the cavum of a pulp cavity (refractive index of 1), and finally to the cementum of the lower side.

Fig. 5

Refractive index profile of a tooth slide: (a) image of the tooth slice; (b) 2-D OCT image of the tooth slice; (c) refractive index distribution of a tooth slice in (a). A: air; C: cementum; D: dentin.

5.

Summary

We developed a path-length matching method for accurately and quickly measuring the refractive index and index profile across a tooth with a single OCT B-scan. With this method, we obtained the refractive indices of the enamel, the dentin, and the cementum of in vitro teeth using 20 different tooth slice samples. We also obtained the refractive index distribution profile of the in vitro human teeth. Such an accurate determination of a tooth’s refractive indices at different locations is important for the early diagnosis of dental caries that may cause local changes in the refractive index. Equipped with this tool, we can quantitatively study the changes in the refractive index induced by caries and dental decay in detail and relate the data to the early diagnosis of dental caries.