*in vitro*and

*in vivo*.

## 1.

## Introduction

Since the first implementation of optical coherence tomography (OCT), it has proven to be a useful medical diagnostic technique.^{1} Three OCT methods have been developed so far: time-domain OCT (TD-OCT),^{1} spectral-domain OCT (SD-OCT),^{2} and optical frequency domain reflectometry OCT (OFDR-OCT).^{3} Several groups of investigators have studied of dental tissue by using TD-OCT^{4, 5} and SD-OCT,^{6} and have shown that a depth range greater than
$5\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$
is needed for *in vivo* diagnosis of multiple teeth simultaneously. For sufficiently deep penetration into dental tissues, high sensitivity is also required. Both SD-OCT and OFDR-OCT are Fourier-domain OCT (FD-OCT), and the sensitivity of FD-OCT has been demonstrated to be 20 to
$30\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$
better than that of TD-OCT.^{7, 8} FD-OCT is also faster than TD-OCT. Aberration of the lens in the spectrometer used in the SD-OCT configuration limits the depth range of SD-OCT to less than about
$2.5\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$
,^{9} and greater depth ranges have been obtained by using OFDR-OCT.^{10, 11} Another reason that OFDR-OCT is better for dentistry is that the SD-OCT configuration, having a spectrometer and a charge-coupled device, is more complex than the OFDR-OCT configuration. We have been developing an OFDR-OCT system, using as a discretely swept source the superstructure-grating distributed Bragg reflector (SSG-DBR) lasers^{12, 13, 14} originally developed for telecommunications applications. The OCT images of an extracted tooth that we could obtain *in vitro* with that source, at a scanning speed
$10\phantom{\rule{0.3em}{0ex}}\mathrm{\mu}\mathrm{s}$
per step, had a depth range of
$6\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$
.^{10, 15}

In the work presented here, OCT imaging of both hard and soft dental tissues with the system, we have not only extended the depth range to $12\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$ by using a SSG-DBR laser with a longer wavelength to reduce scattering by tissues, but have also reduced motion artifacts by increasing the scanning speed to $0.5\phantom{\rule{0.3em}{0ex}}\mathrm{\mu}\mathrm{s}$ per step.

## 2.

## Theory

Figure 1
shows the fiber optic Mach-Zehnder interferometer configuration of the OFDR-OCT system with a SSG-DBR laser as the light source. The principles and theory of the system have already been reported,^{3, 10} so we describe them only briefly. The light from the source is split into the sample and reference arms by coupler 1. In the sample arm, light illuminates the sample and the light reflected from the sample is received. In the reference arm, light is reflected by the reference mirror. Both lights are combined by coupler 2, which outputs the interference signal. It is detected by the balanced photoreceiver.

The SSG-DBR laser emits light at $N$ discrete wavenumbers ${k}_{i}={k}_{0}+i\delta {k}_{i},(i=1,2\dots N)$ . The photoreceiver current ${I}_{d,i}$ at the wave number ${k}_{i}$ is described as

## 1

$${I}_{d,i}=\frac{\eta q}{h\nu}\{{p}_{r}+{p}_{0}\int {r}^{2}\left(z\right)dz\pm 2\sqrt{{p}_{r}{p}_{0}}\int r\left(z\right)\Gamma \left(z\right)\mathrm{cos}[2{k}_{i}z+\varphi \left(z\right)]dz\},$$## 2

$${I}_{d,i}=\frac{\eta q}{h\nu}\{2\sqrt{{p}_{r}{p}_{0}}\int r\delta (z-{z}_{0})\mathrm{cos}\left[2{k}_{i}z\right]dz\}=\frac{\eta q}{h\nu}2\sqrt{{p}_{r}{p}_{0}}r\phantom{\rule{0.2em}{0ex}}\mathrm{cos}\left(2{k}_{i}{z}_{0}\right)=\frac{\eta q}{h\nu}2\sqrt{{p}_{r}{p}_{s}}\phantom{\rule{0.2em}{0ex}}\mathrm{cos}\left(2{k}_{i}{z}_{0}\right),$$## 3

$${F}_{c}\left(z\right)=\frac{\eta q}{h\nu}2\sqrt{{p}_{r}{p}_{s}}\sum _{i=1}^{N}\mathrm{cos}\left(2{k}_{i}{z}_{0}\right)\mathrm{cos}\left(2{k}_{i}z\right),$$## 4

$$Fs\left(z\right)=\frac{\eta q}{h\nu}2\sqrt{{p}_{r}{p}_{s}}\sum _{i=1}^{N}\mathrm{cos}\left(2{k}_{i}{z}_{0}\right)\mathrm{sin}\left(2{k}_{i}z\right).$$## 6

$${F}_{t}{\left(z\right)}^{2}={r}^{2}{\left(\frac{\eta q}{h\nu}\right)}^{2}{p}_{r}{p}_{0}({\left\{\frac{\mathrm{sin}\left[\mathrm{\Delta}k(z-{z}_{0})\right]}{\mathrm{sin}\left[\delta k(z-{z}_{0})\right]}\right\}}^{2}+{\left\{\frac{\mathrm{sin}\left[\mathrm{\Delta}k(z+{z}_{0})\right]}{\mathrm{sin}\left[\delta k(z+{z}_{0})\right]}\right\}}^{2}+B\left(z\right)),$$## 7

$$B\left(z\right)=2\phantom{\rule{0.2em}{0ex}}\mathrm{cos}\left\{[4{k}_{0}+2(N+1)\delta k]{z}_{0}\right\}\times \frac{\mathrm{sin}\left[\mathrm{\Delta}k(z-{z}_{0})\right]}{\mathrm{sin}\left[\delta k(z-{z}_{0})\right]}\frac{\mathrm{sin}\left[\mathrm{\Delta}k(z+{z}_{0})\right]}{\mathrm{sin}\left[\delta k(z+{z}_{0})\right]}.$$^{10}For $\delta k=2.62\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{-1}$ and $\delta k=1.31\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{-1}$ , the depth ranges are respectively 6 and $12\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$ . The full width at half maximum (FWHM) of the peaks in Eq. 6 defines the resolution of the axial distance measurement. By numerical calculation, we can obtain the axial resolution

^{10}$\delta z$ (FWHM) asfor $\mathrm{\Delta}k=N\delta k$ , $N=769$ , and $\delta k=1.31\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{-1}$ , the resolution $\delta z$ will be $28\phantom{\rule{0.3em}{0ex}}\mathrm{\mu}\mathrm{m}$ in air. In a tissue with a refractive index of $n$ , the resolution increases by a factor of $1\u2215n$ .

## 3.

## Experimental Setup

The experimental setup is shown in Fig. 1. In this research we used two different SSG-DBR lasers: a C-band laser (wavelength $\lambda =1529$ to $1568\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ ) and an L-band laser ( $\lambda =1560$ to $1600\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ ). Our newly developed L-band laser emits light at approximately 0.05-nm wavelength steps. In frequency values, the sweep range is from 187 to $192\phantom{\rule{0.3em}{0ex}}\mathrm{THz}$ with steps of $6.25\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ , corresponding to a wavenumber interval of $1.31\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{-1}$ .

The total number
$N$
of wavelengths emitted by the source is 769. At the 500-ns/step wavelength scanning speed used in this experiment, the A-scan time is
$0.3845\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$
. This corresponds to a 2.6-kHz A-line rate. The C-band source we used in our previous works scanned at
$10\phantom{\rule{0.3em}{0ex}}\mathrm{\mu}\mathrm{s}$
per step.^{10, 15} The C-band source used in the work reported here was able to scan at
$500\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$
per step. The specifications of the newly developed C-band and L-band lasers are listed in Table 1
.

## Table 1

Specification of the SSG-DBR lasers.

Wavelength λ (nm) | Tunable range (nm) | Frequency interval δν (GHz) | Wavenumber interval δk(cm−1) | Scanning speed (μs) | A-line rate (kHz) | |
---|---|---|---|---|---|---|

C-band | 1529.46 to 1567.86 | 38.40 | 6.25 | 1.31 | 10 or 0.5 | 0.13 or 2.6 |

L-band | 1559.99 to 1599.96 | 39.97 | 6.25 | 1.31 | 0.5 | 2.6 |

The light was split into the sample arm and reference arm at the first coupler (coupler 1) with a splitting ratio of 90:10. Light in the sample arm was fed to the input port of circulator 1. Light out of the output/input port of circulator 1 illuminated the sample via the collimator lens, galvanometer mirror, and objective lens with a focal length of $60\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$ . Back-reflected light (including back-scattered light) from the sample was gathered with the illuminating optics. Output light from the output port of circulator 1 was fed to coupler 2, with the splitting ratio being 50:50. Light that passed through the reference arm was also fed to coupler 2, from which the interference signal was obtained. Polarization controllers PC 1 and PC 2 adjusted the polarization dispersion in both arms to maximize the interference signal.

Figures 2 and 3
show the setups for *in vitro* and *in vivo* imaging. We did not use a special dentistry probe but instead used a commercially available OCT probe for the anterior segment of the eye. The targeted teeth could be seen with the stereoscopic microscope. For *in vivo* imaging (Fig. 3), we rested the head on a chin rest of the probe and lifted the upper lip to expose the teeth. In this situation, we could not access molars or premolars because the lips were in the way. In the *in vitro* imaging, however, we could access the phantom at any angle and view multiple teeth.

## 4.

## Results and Discussion

Images of an extracted lower lateral incisor that were obtained with the C-band source at scanning speeds of 10 and $0.5\phantom{\rule{0.3em}{0ex}}\mathrm{\mu}\mathrm{s}$ per step are shown in Figs. 4 and 5 . Comparing the obtained two OCT images, one sees that the 20-fold increase in scanning speed did not cause any deterioration of the image quality. In air, the estimated depth range and resolution were respectively $12\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$ and $28\phantom{\rule{0.3em}{0ex}}\mathrm{\mu}\mathrm{m}$ . As seen in those figures, the depth of the images extends over an optical length greater than $5\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$ , which indicates need for an imaging depth range greater than $5\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$ .

Images of an extracted upper canine that were obtained with the L-band source are shown in Figs. 6 and 7 . Because we found no difference of OCT image quality between the L-band source and with the C-band source, we carried out all the following OCT imaging with the L-band source. The blue lines in the photographs in Figs. 6a, 7a, 8a indicate the scanning direction.

To verify the capability of obtaining 12-mm OCT images, we imaged the teeth of a phantom. Figure 8a shows a picture in which three teeth of the phantom are numbered 1, 2, and 3. The scale in Fig. 8b is an aid to indicate the physical length of the gather of the three teeth. As the scale shows, the length is about $12\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$ . The result of OCT imaging of the three teeth is shown in Fig. 8c. The vertical length of the OCT image is $12\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$ , verifying the capability of imaging a 12-mm-depth range.

We extended our work to *in vivo* imaging of teeth, and Fig. 9a
is a photograph of the target teeth. The lines labeled X and Y are the horizontal and vertical directions in which OCT imaging was performed, and Figs. 9b and 9c are OCT images obtained in those directions. The enamel-dentin junction is clearly seen all over the OCT images. Soft and hard tissues (gingiva, enamel, and dentin) are distinguished clearly, but the image of the hard tissue under the soft tissue was indistinct. Unfortunately, because of the lip barrier and the restrictions due to using an OCT probe designed for the anterior segment of the eye, we did not have access to the occlusal pits and fissures areas in which most dental caries are found. We therefore need to develop a specifically designed dental probe.

## 5.

## Conclusion

We perform *in vitro* OCT imaging of an extracted canine by using a newly developed C-band SSG-DBR source, and find that the image quality obtained at a scanning speed of
$0.5\phantom{\rule{0.3em}{0ex}}\mathrm{\mu}\mathrm{s}$
/step does not differ from that obtained at
$10\phantom{\rule{0.3em}{0ex}}\mathrm{\mu}\mathrm{s}$
/step. Our newly developed SSG-DBR sources enable scanning at a wavenumber step of
$1.31\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{-1}$
, corresponding to a 12-mm-depth range. This depth range was confirmed by obtaining OCT images of a tooth phantom. We can clearly see the enamel-dentin junction in *in vitro* OCT images of an extracted canine that are obtained with the newly developed L-band SSG-DBR source. We can also see the enamel-dentine junction in OCT images obtained *in vivo*. This OCT system can be used for early detection of dental caries if we develop a dental probe providing access to occlusal pits and fissures.

## Acknowledgments

We thank T. Amano, D. Choi, H. Furukawa, and H. Hiro-Oka at Kitasato University for helpful comments and suggestions. This research was partly supported by the System Development Program for Advanced Measurement and Analysis of Japan Science and Technology Agency (JST).