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Abstract
We construct a terahertz swept source optical coherence tomography system using a continuous-wave diode multiplier source in the 600-GHz band for defect inspection in multilayer objects and evaluate its performance. Using this system, we image a multilayer plastic sample to demonstrate the effectiveness of nondestructive three-dimensional imaging. To enhance the depth resolution, we apply an annihilating filter to the analysis and confirm that two surfaces of a 1-mm-thick plastic plate can be resolved. In addition, the repeatability of measured thicknesses is 0.22 mm. These values are approximately one-half and one-tenth of the resolution achievable by conventional Fourier analysis, respectively.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Corrections
28 April 2020: A typographical correction was made to the author affiliations.
1. Introduction
In recent years, the deterioration of infrastructure constructed in the 1970s—a period considered to be the age of high-speed economic growth in Japan—has become a serious social concern. Several accidents caused by the exfoliation of wall surfaces have occurred with severities ranging from injurious to fatal. To detect possible wall exfoliation, various inspection techniques such as visual inspection and hammering tests are performed regularly. However, the effectiveness of these inspections is constrained by two issues: the manual and subjective performances by individual experts, and the insufficient number of available experts for building and infrastructure inspection. Thus, the development of a novel inspection technique for contactless and nondestructive measurement of three-dimensional (3D) internal structures is imperative. Further, for inspecting a large structure, a reflection type measurement method is advantageous because it may not be easy to apply a transmission type measurement. Moreover, a compact measuring system that can be mounted on moving bodies such as drones, robots, and vehicles is required for fast and easy inspection [1–3].
Existing contactless and nondestructive inspection methods include passive thermography which utilizes infrared light, and microwave radars such as ground-penetrating radars and reinforced concrete radars. Thermography is a method that enables two-dimensional (2D) imaging with a wide range during a short duration. However, it is significantly influenced by the measurement environment, and expert knowledge may be required to correctly judge the defects from the images [4]. Electromagnetic waves with frequencies ranging from several hundred MHz to several GHz are used in microwave radars. Although the penetration depth is on the order of tens of centimeters, the 3D spatial resolution is several centimeters to several tens of centimeters, which is insufficient for measuring surface layers.
Next-generation inspection methods include 2D imaging using X-ray backscattering [5] and laser hammering [6]. Backscatter X-ray imaging is a high-potential measurement method that can realize both enough spatial resolution and deep penetration. However, in practical applications, the considerable device size and strict legal regulations are problematic. Laser hammering using high-power laser pulses has been applied for high-speed remote sensing, but it has not yet been utilized for acquiring 3D information.
In view of the above, this study examines imaging using terahertz (THz) waves which holds great potential for application in various fields such as medicine [7], agriculture [8], security [9], and wireless communication [10]. As a result of the frequencies being as high as 0.1–10 THz, and although the penetration depth is shallower, the 3D spatial resolution can be expected to be higher than that of microwave radars. Moreover, various 3D imaging methods have been proposed to utilize the characteristics of THz waves [11–19]. In particular, the 3D imaging method using THz swept source optical coherence tomography (THz-SS-OCT) may be useful for inspection applications. Time-domain THz tomography employs a mechanical time-delay stage or electronically controlled optical sampling system to measure the intensity profile in the depth direction. It is measured with a fixed reference mirror in THz-SS-OCT which is a frequency-domain measurement, resulting in a simpler system. In addition, it is reported to have a large sensitivity advantage [20]. Further, although the bandwidth may be narrower than a pulse source, because a tunable frequency continuous-wave (CW) light source is employed for the THz-SS-OCT, it is more compact, has a lower cost, and uses easier to fabricate array devices. In a frequency modulated CW radar, costly RF components such as a directional coupler, a circulator for splitting the electromagnetic power, and a balanced mixer for heterodyne detection are used. However, in THz-SS-OCT, these parts can be replaced with an optical interferometer, resulting in a cheaper system. Hence, THz-SS-OCT can be advantageous due to its compactness and lower cost [21,22]. In addition, the possibility of nondestructive inspections using THz-SS-OCT has been demonstrated in recent years [23]. We have developed a THz-SS-OCT system using a compact CW diode THz wave source that is more robust against vibration and more advantageous for high power output than a photonics-based source. We also present the 3D imaging results obtained using our THz-SS-OCT system and its defect detection performance. The depth resolution in the SS-OCT using Fourier analysis is determined by the center wavelength and bandwidth of the light source.
In this study, in order to improve the depth resolution, we have applied an analytical method using an annihilating filter (AF) [24–27], and two types of noise reduction processes were applied to obtain sufficient performance of the AF method. The result is compared with the result of a conventional Fourier analysis, and we discuss this depth resolution enhancement effect.
2. Experiments
2.1 THz-SS-OCT system configuration
We constructed a THz-SS-OCT system using a CW-diode multiplier source (Virginia Diodes Inc. (VDI)) operating in the frequency range of 600–665 GHz. Its schematic is shown in Fig. 1. The THz source was a voltage-controlled 10–11 GHz yttrium ion garnet (YIG) oscillator frequency-multiplied by a factor of 60, and its output frequency was controlled by changing the output voltage of the DC power supply using a personal computer (PC). The maximum output power was 70 µW. For lock-in detection, the amplitude of the beam emitted from the source was modulated at 30 kHz using a rectangular waveform from a function generator. The THz beam was split into two parts by a silicon beam splitter (resistivity, 1.4 kΩ · cm): one to irradiate the reference mirror and the other to irradiate the sample. The interferogram produced by these reflected or backscattered beams was detected using a Schottky-barrier diode detector (WR1.5ZBD, 500–750 GHz, VDI). The detected signals were amplified by a lock-in amplifier and subsequently fed to a PC through a data acquisition system.
Fig. 1. Schematic of the THz-SS-OCT system (ITO: Indium tin oxide coated glass plate; M1–2: plane mirrors; L1–3: convex lenses; Si-BS: silicon beam splitter; DAQ: data acquisition system; SBD: Schottky-barrier diode detector).
2.2 Lateral resolution and measurable depth range
To evaluate the lateral spatial resolution and the depth of focus (DOF), we measured the change in the beam size along the optical axis near the beam waist position using the knife-edge method. Figure 2 depicts the schematic of the optical setup. The output frequency of the THz source was set to 633 GHz which is the central frequency of the source. The knife was moved by 40 mm, and the intensity data was acquired at 0.1-mm intervals. The horizontal and vertical beam profiles near the focal position are shown in Figs. 3(a) and 3(b), respectively. The blue dotted lines denote the differential data obtained from the raw measured data. The beam diameter (full width at half maximum (FWHM)) was determined by fitting these beam profiles with a Gaussian function, and it was 1.4 mm in both the horizontal and vertical directions. Figures 3(c) and 3(d) show the beam diameter in the depth direction at 0.4-mm steps in the horizontal and vertical directions, respectively. The DOF was determined by fitting the measured values depicted as dotted blue lines in Figs. 3(c) and 3(d) with a hyperbolic function; the DOF obtained in the horizontal and vertical directions were 27.7 mm and 27.5 mm, respectively.
Fig. 2. Schematic of the optical setup for knife-edge measurement (ITO: Indium tin oxide coated glass plate; M1–2: plane mirrors; L1–3: convex lenses; Si-BS: silicon beam splitter).
Fig. 3. Beam profiles near the focal position in (a) horizontal direction and (b) vertical direction. Relationship between the beam diameter (FWHM) and depth position in (c) horizontal direction and (d) vertical direction.
2.3 Depth resolution using Fourier analysis
In SS-OCT, the intensity profile in the depth direction is reconstructed through frequency analysis of the interferogram obtained by sweeping the source frequency (so-called ‘A-scan’). For frequency analysis, inverse fast Fourier transform (IFFT) is generally used. When the frequency spectrum of the light source follows a Gaussian function, the depth resolution is given by [28,29]
where Δλ is the FWHM bandwidth of the light source, λ0 is the center wavelength, and n is the refractive index of the object. In our interferogram measurements, the frequency is swept in the 600–665 GHz range, and the intensity is acquired at intervals of approximately 21 MHz. The interferograms are normalized to the measured reference spectrum and apodized by a Gaussian function with a center wavelength λ0 = 474 µm and bandwidth Δλ = 19 µm. In this case, the theoretical value of the depth resolution is derived to be Δz = 5.14 mm in air (n = 1) according to Eq. (1).To evaluate the depth resolution of our THz-SS-OCT system, the A-scan was repeated ten times using a plane mirror as the object. The number of data points were increased from 3051 to be 4096 by zero filling, and these data points were reconstructed into a depth profile using IFFT. Zero filling makes the depth interval narrower, and it does not affect the actual resolution. Figure 4 shows the result of one of the ten depth profiles near the object. The depth resolution (FWHM) was determined by fitting the profile with a Gaussian function shown in the figure. The mean and the standard deviation of the ten FWHM values was Δz = 5.54 ± 0.01 mm which was near the theoretical value of 5.14 mm.
Fig. 4. Depth profile obtained with Gaussian window apodization when using a plane mirror as the object.
3. Analytical method for depth-resolution enhancement
3.1 SS-OCT model parameter estimation
As shown in Fig. 5, consider the measurement of a multilayer-structured object with a piecewise-constant refractive index, n, using the SS-OCT system. Assuming that the object is lossless and multiple reflection can be neglected, the measured interferogram is modeled as
The second term of the above equation represents the interference between the lth and the mth boundaries of the object. If al and am are sufficiently small, the second term is considerably smaller than the first term. Therefore, Eq. (3) can be approximated to
Because k takes discrete values within a finite bandwidth in actual measurement, it is replaced with k = kmin + κΔk where kmin is the minimum wavenumber of the light source, Δk is the interval of the wavenumber, and κ is the index of the wavenumber. Then, Eq. (4) is rewritten as
Moreover, by introducing new parameters, ${A_l} = {a_l}{e^{i2\pi {b_l}{k_{\min }}}}$ and ${\gamma _l} = {e^{i2\pi {b_l}\Delta k}}$, the above equation is reduced to
Therefore, this equation gives a signal model of the SS-OCT which is determined by three kinds of parameters, L, ${A_l}$, and ${\gamma _l}$. Assuming that the number of boundaries L is known, ${\gamma _l}$ including the depth information is retrieved using an AF [24–27]. When the roots ${\gamma _l}$ and $\gamma _l^\ast $ of a polynomial
3.2 Noise reduction methods
The AF method as described in Section 3.1 was applied to enhance the depth resolution of our THz-SS-OCT system. The AF method is generally used to reconstruct a sparse signal such as an impulse train, and it is effective in retrieving original signal from a small number of measurement data. However, satisfactory analytical results may not be obtained using the AF method when the noise level of the measurement data becomes high. Therefore, we performed noise reduction on the interferogram data before reconstructing the interferogram into a depth profile. The whole procedure for the analysis is depicted in Fig. 6(a). The noise reduction process can be classified into two methods.
Fig. 6. (a) Procedure for the analysis, and the respective noise reduction process by (b) the BPF and (c) the SVD.
One is the reduction of the periodic noise using a bandpass filter (BPF), and the procedure depicted in Fig. 6(b). Periodic noise elements are generated in the interferogram due to multiple reflections in the measurement system and appear as peaks at positions other than the object position in the depth profile. The depth information around the object can be extracted by applying the bandpass filter to the depth profile, after which the interferogram can be reconstructed through FFT.
The other method involves iterative singular value decomposition (SVD) for reducing the additive white Gaussian noise (AWGN) [27,30,31], and the procedure is depicted in Fig. 6(c). An interferogram that includes AWGN Wκ is given by
where K is the number of data in an interferogram. The Toeplitz matrix (K – N + 1) × N described in the following equation is generated from ${\tilde{D}_\kappa }$:4. Results and discussion
4.1 Multilayer-sample 3D imaging
We performed 3D imaging to demonstrate the effectiveness of our THz-SS-OCT system. Figure 7 shows the multilayer plastic sample used as the object. The sample comprised three 0.3-mm-thick plastic plates separated by 13 mm. The plates on the 2nd and 3rd layers had a 6-mm slit in the center. This multilayer sample was mounted on a two-axis motorized stage, and raster scanned in a plane perpendicular to the beam direction with a scanning range of 24 × 24 mm and scanning step of 2 mm. At each position, an interferogram was obtained by sweeping the frequency of the THz source from 600–665 GHz and converted into an intensity profile in the depth direction using IFFT. The reconstructed 3D image at 1.7-mm steps in the depth direction is shown in Fig. 8(a); Fig. 8(b) shows the cross-sectional images of each plastic layer (also known as “C-scan images”). The slits in layers 2 and 3 were clearly reproduced, but that in layer 3 was affected by the shape of layer-2. This type of contamination needs to be corrected in the practical application of THz-OCT for multilayer objects.
4.2 Depth-resolution enhancement using the measured data
In Section 4.1, we had demonstrated 3D imaging of thin samples. On the hand, in practice, the inspection objects include construction materials such as tiles, mortars, adhesives, and concrete, which are thicker and more absorptive than the sample used in Section 4.1. In this case, a longer center-wavelength source is advantageous in terms of the penetration depth. However, as shown in Eq. (1), the OCT depth resolution is reduced for longer center wavelengths. To enhance the depth resolution, we applied an analytical method based on an AF, instead of the conventional IFFT. In order to examine the effectiveness of the depth-resolution enhancement by the AF method in the THz region, we analyzed the measured data of our THz-SS-OCT system, and compared the results obtained by IFFT with those by AF method. Interferograms were obtained by sweeping the frequency in the 600–665 GHz range at intervals of approximately 0.1 GHz. Plastic plates of different thicknesses (10 mm, 5 mm, and 1 mm) were used as the objects. The interferograms used for IFFT analysis were not apodized (Boxcar window) because the higher resolution can be obtained without apodization, though the side lobes of the depth profile increased. Moreover, 661 data points were used with zero filling, resulting in a total of 65,536 data points. As per IFFT analysis using the data measured in Section 2.3, the average depth resolution was Δz = 3.1 mm in air (n = 1).
Figures 9(a)–9(i) show the effect of the periodic noise reduction using the BPF described in Sect. 3.2. The depth profiles reconstructed by IFFT from the normalized interferogram before the BPF [Figs. 9(a)–9(c)] are denoted by solid blue lines in Figs. 9(d)–9(f). Although the sample was located approximately 80 mm from the zero-delay position, multiple peaks appeared at positions far from the sample position due to multiple reflections in the measurement system. The BPF was applied to reduce such noise. As depicted by the red lines in Figs. 9(d)–9(f), the depth profile was created by passing the 46–137 mm range around the sample position and cutting-off the other ranges with zero padding. The interferogram that reduced periodic noise was then obtained by performing FFT on the post-filtering depth profile [Figs. 9(g)–9(i)]. Between the prefiltering [Figs. 9(a)–9(c)] and postfiltering interferograms [Figs. 9(g)–9(i)], the beat signals produced by the two adjacent interfaces were very clear in the postfiltering one.
Fig. 9. Normalized interferograms at thicknesses of (a) 10 mm, (b) 5 mm, and (c) 1 mm; comparison of the depth profiles before and after filtering at thicknesses of (d) 10 mm, (e) 5 mm, and (f) 1 mm; filtered interferograms at thicknesses of (g) 10 mm, (h) 5 mm, and (i) 1 mm.
After the BPF processing, the AWGN included in the interferograms was reduced by the iterative SVD as mentioned in Sect. 3.2. As analysis conditions, the number of elements to be decomposed was 12, the number of remaining elements was four, which is twice the sample boundary, and the threshold was 0.04. Figures 10(a)–10(c) show the comparison results of the interferograms before and after SVD. Although significant improvement is not obvious, on zooming the frequency axis in these figures, it can be confirmed that the beat-signal envelope is smoothed, as indicated by the green arrows in Figs. 10(d)–10(f).
Fig. 10. Comparison of the interferograms before and after SVD at thicknesses of (a) 10 mm, (b) 5 mm, and (c) 1 mm, and their magnified frequency-axis view at thicknesses of (d) 10 mm, (e) 5 mm, and (f) 1 mm. The green arrow in the figures indicates the part where the envelope of the beat-signal is smooth.
These noise-reduced interferograms were converted into the depth profiles. The depth profiles shown in Figs. 11(a)–11(c) are the comparison between the analysis results of the AF method described in Section 3.1 and the IFFT analysis results. For thicknesses of 10 mm and 5 mm, the IFFT analysis results and the analysis results by the AF method could resolve the front- and back-surface reflections of the plastic plates. In contrast, for a thickness of 1 mm, the front and back surfaces could not be resolved by conventional IFFT analysis but could be resolved by the AF method. Based on this result, it was confirmed that a thickness of 1 mm could be resolved using the AF method. The depth resolution obtained by IFFT analysis without apodization was 2.0 mm in the sample (n = 1.59); the obtained resolution was 0.5 times higher than that of conventional IFFT analysis. Therefore, through the THz-SS-OCT measurements, it was confirmed that higher depth resolution beyond the limit of conventional IFFT analysis was obtained by analysis using the AF method. As shown in Figs. 11(a)–11(c), because the results using the AF method are obtained as impulses, the depth resolution appears infinitely high. However, in reality, the depth resolution may be limited by the fluctuations (repeatability) in repeated measurements. Therefore, the 1-mm-thick sample was repeatedly measured five times to evaluate the repeatability of the thickness. As a result, it was 0.22 mm at FWHM which is approximately one-tenth the IFFT resolution. This may be the potential resolution using the AF method. Furthermore, the interferograms were reconstructed as shown in Figs. 11(d)–11(f) by substituting the optimized parameters in Eq. (6). Based on these results, we confirmed that the optimized parameters well reproduced the input interferogram. Incidentally, the number of boundaries used for the analysis conditions of these results was six which does not match the number of sample surfaces. However, these extra signals are far from the sample position and have very small average amplitudes, less than one percent, compared with the signals from the boundaries of the sample. Therefore, the mismatch between the assumed number of boundaries and the number of sample boundaries may be due to minor residual noise. In future, it is necessary to examine methods for selecting a model with the optimal number of boundaries based on the analysis results of data including noise, for practical inspection.
Fig. 11. Comparison of the depth profiles obtained using the AF method and IFFT at thicknesses of (a) 10 mm, (b) 5 mm, and (c) 1 mm; comparison of the input and reconstructed interferograms based on the estimated parameters at thicknesses of (d) 10 mm, (e) 5 mm, and (f) 1 mm.
5. Conclusion
We constructed a THz-SS-OCT system using a CW-diode multiplier source operating in the 600–665 GHz range for inspection of defects in multilayer objects and evaluated its 3D spatial resolution. A lateral resolution of 1.4 mm was obtained using knife-edge, and depth resolutions with and without Gaussian window apodization were 5.5 mm and 3.1 mm in air (n = 1), respectively. Subsequently, we performed 3D imaging using a multilayer plastic sample as the object to demonstrate the effectiveness of our THz-SS-OCT system. Moreover, we examined the enhancement of the depth resolution through analysis by the AF method instead of the conventional IFFT analysis, and two types of noise reduction processes were applied to obtain sufficient performance of the AF method. It was experimentally confirmed that the front and back surfaces of a 1-mm-thick plastic plate (n = 1.59) could be resolved. This was approximately one-half the resolution of a conventional IFFT analysis. In addition, the repeatability of measured thicknesses was 0.22 mm, approximately one-tenth the resolution of an IFFT analysis, which may be the potential resolution when using the AF method in our system. Therefore, a higher depth resolution, compared with conventional IFFT analysis, is achieved by the AF method in THz-SS-OCT. For practical inspection applications, a longer center wavelength is advantageous because deeper penetration is required; however, in OCT, the depth resolution is reduced when the center wavelength is increased. Therefore, we believe that the enhancement of the depth resolution using the analysis by the AF method is effective. As the next step, we intend to construct a mobile THz-SS-OCT system in the longer wavelength band for 3D imaging of practical objects.
Funding
RIKEN -Topcon collaboration research project.
Acknowledgments
The authors thank Dr. K. Midorikawa, Dr. H. Minamide (RIKEN), Dr. Y. Tokizane (Tokushima University), Dr. Y. Fukuma, and Dr. Y. Moriguchi (Topcon Corporation) for the valuable discussions. The authors also thank all the members of the Terahertz Sensing and Imaging Research Team at RIKEN.
Disclosures
The authors declare no conflicts of interest.
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