High-speed frequency-domain terahertz (THz) coherence tomography is demonstrated using frequency sweeping of continuous-wave THz radiation and beam steering. For axial scanning, THz frequency sweeping with a kHz sweep rate and a THz sweep range is executed using THz photomixing with an optical beat source consisting of a wavelength-swept laser and a distributed feedback laser diode. During the frequency sweep, frequency-domain THz interferograms are measured using coherent homodyne detection employing signal averaging for noise reduction and used as axial-scan data via fast Fourier transform. Axial-scan data are acquired while scanning a transverse range of 100 × 100 mm2 by use of a THz beam scanner with moving neither sample nor THz transmitter/receiver unit. It takes 100 s to acquire axial-scan data for 100 × 100 points with 5 averaged traces at a sweep rate of 1 kHz. THz tomographic images of a glass fiber reinforced polymer sample with artificial internal defects are presented, acquired using the tomography system.
© 2016 Optical Society of America
Terahertz (THz) tomography is usable for nondestructive inspection of nonconductive materials due to their transparency to THz radiation and is applicable to various fields including medicine, pharmacy, and material inspection [1–4]. There are two types of geometry for THz tomography: transmission and reflection. Transmission-mode tomography, called computed tomography, requires acquisition of projection images at various angles and image reconstruction [5–7]. Reflection-mode tomography utilizing time-of-flight information is more favorable for fast image acquisition than transmission-mode tomography, since the former requires neither rotation for projection angles nor image reconstruction [8,9].
Reflection-mode THz tomography can be divided into time-domain and frequency-domain THz tomography according to the A-scan method employed. In time-domain THz tomography, THz pulses generated using a femtosecond laser are used to directly acquire A-scan data in the time domain while scanning the time delay between a THz pulse and a femtosecond optical sampling pulse [8,9]. The cost and size of a time-domain THz tomography system can be reduced along with the use of a femtosecond fiber laser. The broadband spectrum or short duration of THz pulses offers a high axial resolution . In general, there is a trade-off between the A-scan rate and range, depending on time delay scanning methods. Recently, we demonstrated high-speed time-domain THz tomography using electronically controlled optical sampling for the A scan [11,12].
In frequency-domain THz tomography, A-scan data are obtained from the fast Fourier transform (FFT) of frequency-domain THz data acquired while varying the frequency of continuous-wave (CW) THz radiation. Frequency-domain THz tomography based on the frequency-modulated CW (FMCW) method using electronic devices has the advantages of fast image acquisition, small size, and a wide A-scan range, where a frequency modulation rate can amount to several kHz and electronic components are employed including an oscillator with a narrow linewidth . However, frequency-domain THz tomography using the FMCW method has the disadvantages of a low axial resolution and high cost, due to a frequency modulation range of less than 100 GHz and the use of high-frequency electronic devices.
Frequency-domain THz tomography using THz photomixing was reported recently, which involved a free-space Michelson interferometer [14,15]. It has the merits of low cost and compact size. In addition, it can have a high axial resolution and a wide A-scan range due to a broad frequency range and a narrow linewidth. However, slow laser frequency tuning in THz photomixing resulted in a long image acquisition time. Most recently, we implemented fast broadband THz frequency sweeping with a kHz sweep rate and a THz sweep range by using a wavelength-swept laser (WSL) as one of two lasers for THz photomixing . Frequency-domain THz interferograms could be rapidly measured in a coherent homodyne detection scheme during the frequency sweep.
In this paper, we demonstrate high-speed frequency-domain terahertz coherence tomography using the fast broadband frequency sweep of CW THz radiation and beam steering. For an A scan, frequency-domain THz interferograms are measured using coherent homodyne detection, employing signal averaging for noise reduction, with no free-space interferometer. A C scan is performed using a THz beam scanner. The axial resolution, the A-scan range, and the transverse resolution of this tomography system are demonstrated. THz tomographic images of a glass fiber reinforced polymer (GFRP) sample with artificial defects are also acquired to show the imaging performance of this tomography system.
2. Experimental setup
Our frequency-domain THz coherence tomography system is illustrated in Fig. 1. For an A scan, high-speed broadband THz frequency sweeping is performed using THz photomixing in which the optical beat source consists of a distributed feedback laser diode (DFB-LD) and a WSL . The WSL is based on a semiconductor optical amplifier and a fiber Fabry-Perot tunable filter . WSLs have been used previously for optical coherence tomography . The DFB-LD is operated at a fixed wavelength of 1545 nm, and the output wavelength of the WSL is swept from 1544 to 1558 nm at a 1 kHz sweep rate. Frequency-domain THz signals are measured in the frequency range up to 1.5 THz using coherent homodyne detection. The optical output of the WSL is amplified by an optical fiber amplifier and then combined with that of DFB-LD by a 3 dB fiber coupler. One of the two output arms of the coupler is connected to a THz CW transmitter module (TOPTICA Photonics) and the other is connected to a THz CW receiver module (TOPTICA Photonics) through a variable optical delay line. All the optical components are connected using polarization-maintaining (PM) fibers without the need to control the optical polarization.
CW THz radiation is emitted from the transmitter, which is biased using a waveform generator and irradiated by the optical beat source. The CW THz radiation is collimated by an off-axis parabolic mirror and passes through a silicon beam splitter. For a C scan, the transmitted beam is steered with an optical angle (θ) of −20 ~ + 20° along both the X and Y directions by a two-dimensional (2D) galvanometer scanner with a 25 mm aperture. The optical angle refers to the angle between the optical axis and the direction of the beam. Regardless of the optical angle, the THz beam is normally incident on a sample, placed on the focal plane, through a telecentric f-θ lens. Also, the position of the focal point on the focal plane is equal to the product of the focal length of the lens and the optical angle in both the X and Y directions. The telecentric f-θ lens with non-axial symmetry is made of polytetrafluoroethylene (PTFE) . The reflected THz beam from the sample propagates back to the beam splitter along its original path. The THz beam reflected by the beam splitter is focused on the receiver by an off-axis parabolic mirror. A photocurrent is generated from the receiver, which is biased by the electric field of the CW THz radiation and irradiated by the optical beat source. The photocurrent is amplified using a current preamplifier with a bandwidth of 220 kHz and a gain of 1 × 107 V/A.
A digital delay/pulse generator triggered by a wavelength trigger signal at 1545 nm produces a 1 kHz TTL signal . Data traces are consecutively acquired at 1 kHz from the preamplifier by a digitizer with a sampling rate of 3 MS/s triggered by the TTL signal. At the same time, the TTL signal triggers the waveform generator to provide the transmitter with a bias voltage modulated at half the sweep rate. The signal-to-noise ratio (SNR) of THz data can be enhanced by subtracting noise traces acquired with the bias off from THz data traces carrying noise acquired with the bias on and averaging the resultant THz data traces. Frequency-domain THz data are obtained by converting the time to the THz frequency using the time variation of the THz frequency. For the conversion, we measured the time variation of the optical frequency of the WSL and thus that of the THz frequency using a Fabry-Perot interferometer . FFT results of frequency-domain THz data are used as A-scan data. For a C scan, the galvanometer scanner is driven by another waveform generator triggered by the TTL signal . A-scan data are acquired while performing a raster scan with the THz beam scanner comprised of the galvanometer scanner and the telecentric f-θ lens. The total scan time depends on the number of points in a C-scan range of 100 × 100 mm2 and the number of averaged traces for each A-scan data. For example, it takes 100 s to acquire A-scan data for 100 × 100 points with 5 averaged traces and 4,000 s to acquire A-scan data for 200 × 200 points with 50 averaged traces.
3. Experimental results
The time delay can be varied by the variable optical delay line, which corresponds to the optical path length difference (OPLD) between the two paths: one path is the optical path from the coupler to the receiver and the other path is the optical path from the coupler to the transmitter plus the THz path from the transmitter to the receiver. Figure 2(a) shows a frequency-domain THz data measured at a time delay of 14 ps with a flat metal mirror placed on the focal plane. The frequency-domain THz data was obtained by averaging 5,000 traces acquired in 10 s. The photocurrent output from the receiver results from optoelectronic interference between the electric field of the incident CW THz radiation and the photocarriers excited by the optical beat source in the receiver. The photocurrent is expressed as19]. and depend on the THz frequency. The period of the interference pattern in the frequency-domain THz interferogram is equal to the reciprocal of the time delay. FFT of the frequency-domain THz interferogram results in a peak amplitude at the time delay in the time-delay domain. When FFT was performed over the entire measured frequency region, broadening of the peak was caused mainly by the dispersion of the antennas of the transmitter and receiver at low frequencies [16,20]. Other sources of the peak broadening include the dispersion of the silicon lenses of the transmitter and receiver modules, the silicon beam splitter, and the PTFE lens at low frequencies [21,22]. Thus, we tried conducting FFT over a frequency region from which a low-frequency region was excluded. Figure 2(b) shows normalized FFT amplitudes of the frequency-domain THz interferogram, obtained with different cut-off frequencies. The full width at half maximum (FWHM) of the FFT amplitude peaks is plotted versus the cut-off frequency in Fig. 2(c). The FWHM sharply decreases with the increase of the cut-off frequency at less than 0.2 THz and increases with the increase of the cut-off frequency at over 0.2 THz. The increase of the FWHM with the increasing cut-off frequency at over 0.2 THz is due to the decrease of the frequency range used for FFT. The minimum FWHM of about 2.99 ps is obtained with the cut-off frequency of 0.2 THz, corresponding to the axial resolution of 0.45 mm.
Frequency-domain THz interferograms were measured for Teflon sheets of varying thickness, and their normalized FFT amplitudes obtained with the cut-off frequency of 0.2 THz are displayed in Fig. 2(d). The peaks from the front and back surfaces are clearly resolved for the Teflon sheets with thickness of 0.3 and 1.0 mm but not for the sheets with thickness of 0.1 and 0.2 mm. The optical thicknesses of the Teflon sheets with thickness of 0.1, 0.2, 0.3, and 1.0 mm are evaluated as about 0.14, 0.29, 0.43, and 1.44 mm, respectively, with 1.44 of the refractive index of Teflon . Thus, the results are consistent with those obtained with the cut-off frequency of 0.2 THz in Figs. 2(b) and 2(c).
We measured THz interferograms for the flat metal mirror at different time delays and the maximum FFT amplitudes of the THz interferograms are plotted against the respective time delays in Fig. 3. The maximum FFT amplitude decreases with the increase of the time delay due to the coherence time of the WSL and the detection bandwidth determined by the preamplifier . The identical coherence time of the optical beat source and the THz wave is dominated by the coherence time of the WSL since the coherence time of the WSL is estimated as 49 ps at a 1 kHz sweep rate, even shorter than several tens of ns for the DFB-LD . In addition, the gain of the preamplifier decreases with the increase of the detection frequency, which is linearly proportional to the time delay by , where and are the detection frequency and the time delay, respectively, and represents the sweep speed of the THz frequency. Thus, both the coherence time of the WSL and the detection bandwidth cause the maximum FFT amplitude to decrease with the increasing time delay. The FFT amplitude of a frequency-domain noise data measured with 5 averaged traces is also shown in Fig. 3. The maximum FFT amplitude of the THz interferogram is well above the noise level in the time-delay range up to 100 ps. The available A-scan range can be estimated to be over 15 mm with 5 averaged traces. Therefore, the available A-scan range depends on the coherence time of the WSL, the detection bandwidth, and the SNR. The sweep rate and range of the WSL influence both the sweep speed of the THz frequency and the coherence time of the WSL and the SNR relies on the measurement time, i.e. the number of averaged traces . Thus, key factors determining the available A-scan range are the coherence time of the WSL, the bandwidth of the preamplifier, the sweep rate and range of the WSL, the SNR performance of the combination of the transmitter and receiver, and the measurement time.
C-scan images of the flat metal mirror covering the right and lower half of the C-scan area were obtained to estimate the transverse resolution of the tomography system, as shown in Fig. 4. The C-scan images comprised of 200 × 200 pixels were constructed from the maximum values of the A-scan data, each of which was obtained by averaging 50 frequency-domain THz interferogram traces and subsequently performing FFT with the cut-off frequency of 0.2 THz. The C-scan data were normalized using C-scan data for the flat metal mirror covering the whole C-scan area. In Fig. 4(a), the black line indicates the C-scan data along the X axis and the derivative of the black line is represented by the yellow line. The FWHM of the yellow line, i.e. the transverse resolution along the X axis is estimated as 4.1 mm. As indicated in Fig. 4(b), the transverse resolution along the Y axis is evaluated as 4.3 mm, almost similar to that along the X axis. If the THz beam is assumed to be a Gaussian beam, the FWHM of the beam spot on the focal plane is given by , where is the focal length of the lens, is the wavelength corresponding to the mean frequency, and is the input beam diameter . It was previously shown in the time-domain THz tomography that the aberration effect of the telecentric f-θ lens on the FWHM of the beam spot was negligible compared to the diffraction effect above . Since the FWHM of the beam spot represents the transverse resolution, the transverse resolution should depend on the cut-off frequency determining the mean frequency. Actually, we confirmed that the increase of the cut-off frequency resulted in a higher transverse resolution along with the increase of the mean frequency.
Using the tomography system, we acquired THz tomographic images of a GFRP sample with artificial internal defects, of which the schematic design is shown in Fig. 5(a). We previously presented three-dimensional (3D) tomographic images of the GFRP sample obtained from the time-domain THz tomography systems using sample moving and beam steering for the C scan [11,12]. The sample has a dimension of 100 × 100 × 3 mm3. Delaminations with 0.2 mm thickness are located at depths of 1 mm and 2 mm below the front surface and PTFE inserts with 0.025 mm thickness lie at a depth of 1.5 mm, as shown in Fig. 5(a). C-scan, B-scan, and 3D tomographic images of the sample are presented in Figs. 5(b), 5(c), and 5(d), respectively. It took 100 s to acquire A-scan data with 5 averaged traces for 100 × 100 points in the C-scan range. The C-scan image was constructed using the maximum values from the A-scan data, with data from the front and back surfaces excluded. The upper delaminations are more clearly visible than the lower ones due to attenuation of THz radiation by the GFRP. The PTFE inserts are invisible because the amplitudes of the reflected THz waves from the inserts are lower than the noise level owing to their thinness [11,12]. We have previously shown that the Fabry-Perot reflectivity of a defect depends on its thickness . Visualization 1 shows the B-scan images obtained along the X direction at different Y positions. In Visualization 1, the front surface and the upper delaminations are clearly visualized. The back surface and the lower delaminations are also visible. The front surface does not appear flat since the optical path length from the galvanometer scanner to the sample plane varies with the optical angle . For the 3D tomographic image, we compensated the raw 3D data for the OPLD using the OPLD data from the flat mirror. The 3D tomographic image was created by adjusting a threshold value to render values below the noise level as transparent and to render values above the noise level in colors. In the 3D image, the front surface and the upper delaminations are clearly visualized while the back surface and the lower delaminations are partially visible. To improve image quality, we acquired A-scan data with 50 averaged traces for 200 × 200 points, which took 4,000 s. The resulting images have better image quality, as shown in Figs. 5(e), 5(f), and 5(g).
We have demonstrated high-speed frequency-domain THz coherence tomography based on high-speed broadband frequency sweeping of CW THz radiation and beam steering. The use of a WSL along with a DFB-LD as a wavelength-fixed laser in THz photomixing enabled the THz frequency sweep with a kHz sweep rate and a THz sweep range. With no need for a free-space interferometer, coherent homodyne detection employing signal averaging was used to conveniently measure frequency-domain THz interferograms used as A-scan data via FFT. A-scan data were acquired while scanning a C-scan range of 100 × 100 mm2 by use of a THz beam scanner consisting of a 2D galvanometer scanner and a telecentric f-θ lens with moving neither sample nor transmitter/receiver unit. It took 100 s to acquire A-scan data for 100 × 100 points with 5 averaged traces at a 1 kHz sweep rate.
Due to the wide frequency sweep range and the coherence time of the WSL, this tomography technique provides a higher axial resolution but a narrower A-scan range than the FMCW THz tomography technique. Further improvements in the SNR and spectral bandwidth of the combined transmitter and receiver will allow for faster measurement and higher axial resolution. The use of a WSL with a longer coherence time will increase the available A-scan range .
Fast image acquisition, compact size, and low cost are important for practical applications of THz tomography. Frequency-domain THz tomography using THz photomixing can have advantages over time-domain THz tomography in cost and size because of the lack of a femtosecond laser. Since this high-speed frequency-domain THz coherence tomography technique can also provide fast image acquisition without moving an imaging target, it has the potential for practical applications to nondestructive inspection in industrial fields. In addition, the THz setup including the transmitter, receiver, and beam scanner could be advanced to a portable scanning head, prompting development of fast-scan portable THz tomography instruments.
This work was supported in part by the National Research Foundation of Korea – Grant funded by the Korean Government (NRF-2012M2A2A9035659) and in part by the Ministry of Science, ICT and Future Planning through the project KRISS-15011034.
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