Amplitude and phase imaging using incoherent free-running self-oscillating device in millimeter- and terahertz-wave bands

To date, terahertz amplitude imaging has been employed to demonstrate the detection of prohibited drugs and explosives in envelopes and weapons, such as guns and knives, hidden in clothes and bags.^1–8 When phase and amplitude imaging are used in combination, objects with low-loss and minute changes in amplitude, such as dangerous objects made of thin dielectric glass or acrylic, can be detected as the phase changes with high sensitivity. These have been typically difficult to image at high contrast using amplitude imaging alone due to large transmissivity. Furthermore, in material identification applications based on the terahertz fingerprint spectrum, more accurate estimations are possible using both phase and amplitude information.

Recently, various techniques for terahertz amplitude and phase imaging have been proposed and demonstrated. The imaging system based on terahertz time-domain spectroscopy (terahertz TDS) provides the spectral information of objects.^9–13 The TDS system is a pulsed system covering a wide spectral range from several gigahertz to terahertz. Increasing the spectral power density, and hence the signal-to-noise ratio (SNR) of measurements in the linear regime, is difficult because the pulse energy spreads over a wide spectral range. However, this problem is mitigated by a system based on continuous wave (CW) technology, which provides a higher SNR and more linear measurements than a TDS-based system.^14–16 Previously, we imaged characters written in ink on a 90-μm paper surface using a photonics-based CW system and reported that terahertz amplitude imaging failed to identify the characters due to the lack of contrast while terahertz phase imaging succeeded in the task.¹⁷ 

Recently, it has been pointed out that nondestructive imaging inside a bag or envelope using a coherent CW terahertz source reduces the fidelity of the image due to interference phenomena.¹⁸ Amplitude imaging using an incoherent terahertz source generated by amplified spontaneous emission sources and the uni-traveling-carrier photodiode has been proposed to address this problem; however, this setup cannot measure the phase information.^19,20 When phase imaging is conducted using the incoherent CW terahertz source in combination with amplitude imaging, objects made of thin dielectric glass, acrylic, or polypropylene (low-loss materials in the terahertz band), which are difficult to identify at high contrast using amplitude imaging, can be detected as the phase changes at high sensitivity and without fidelity degradation due to interference.

In this study, we propose and demonstrate amplitude and phase imaging using an incoherent free-running self-oscillating device in the millimeter- and terahertz-wave bands to mitigate the interference phenomena in the CW-based imaging system. This technique is based on frequency and phase noise-cancellation electronics instead of interferometry; therefore, incoherent sources with relatively short coherence time can be deployed in a compact system. Moreover, the system is reliable and inexpensive as the diode-based free-running oscillator requires merely a DC power supply and the frequency noise-cancelling electronics consist of low-frequency circuitry. In the proof-of-concept experiments, we used a Gunn oscillator operating at 122.5 GHz as a millimeter-wave source and demonstrated that acrylic and polypropylene, which could not be identified using amplitude imaging, were identified using phase imaging. Furthermore, we obtained high-fidelity amplitude and phase imaging results with less influence of interference for objects that were wrapped in bubble wrap and hidden in an envelope. To extend this system to the higher frequency region and thereby improve its spatial resolution, the source can be easily replaced by resonant tunneling diodes^21,22 and terahertz quantum cascade lasers.^23,24

Figure 1 illustrates the measurement system, and Fig. 2 shows a photograph of the system. A Gunn oscillator was employed as the diode-based source. The measured output power of the Gunn oscillator was 18.1 mW, and the frequency of oscillation was ∼122.5 GHz. The optical frequency comb (OFC) was generated by phase modulating the 1550-nm laser beam with a Mach–Zehnder modulator (MZM). A signal with a frequency of f_OFC was input as a modulation signal to the MZM from the synthesizer. The ±5th comb components of the OFC were used as a local oscillator (LO) signal (f_LO) to detect the signal. The RF signal (f_RF) from the Gunn oscillator and the optical LO signal (f_LO) were photomixed in the InGaAs photoconductive antenna (PCA) from TOPTICA Photonics AG, leading to an IF photocurrent (f_IF) flow. In this experiment, we set the LO frequency as f_LO = 10 × f_OFC = 122.497 GHz, where f_OFC was set to 12.2497 GHz. Therefore, the IF frequency from the trans-impedance amplifier (TIA) was f_IF = 122.500 − 122.497 GHz = 3 MHz. The optical power for the photomixing was 12.5 dBm. The IF frequency was selected as 3 MHz to reduce the 1/f noise within the bandwidth of our used electronics. The photocurrent was converted to a voltage signal via a TIA with a gain of 10⁴ V/A.

First, to measure the oscillation-frequency fluctuations of the Gunn oscillator, as shown in Fig. 1, the switch after the TIA was connected to path 1 in the circuit, and the frequency of the IF signal was measured using a frequency counter. Because the frequency counter was synchronized with the synthesizer used to generate the LO signal, the relative frequency fluctuation between the Gunn oscillator and synthesizer can be evaluated. In imaging applications, the frequency fluctuations of the time constants in the lock-in amplifier (LIA), used to measure the amplitude and phase, are important parameters to assess the interference phenomena leading to the degradation of image fidelity. Because the time constant of the LIA was 20 ms, in this experiment, we measured the frequency fluctuation of the IF signal with a sampling rate of 0.1 for 20 ms. We assume that the frequency fluctuation follows a Gaussian normal distribution, which yields a 99.7% probability of the observed data being within ±3 times the standard deviation (σ). Hence, we define the frequency fluctuation within the time constant as ±3σ = ±95.937, i.e., ∼±100 kHz. In contrast, because it takes ∼15 min to obtain an entire image in this experiment, we measured the frequency fluctuation of the IF signal at a sampling interval of 40 ms for 15 min to evaluate the frequency drift on this time scale. Figure 3 shows the typical raw data of the measured frequency fluctuation and its moving average, taken for every 250 samples. A frequency drift of ∼400 kHz during 15 min was observed. From these results, it was observed that the Gunn oscillator has a frequency fluctuation of ∼200 kHz within the time constant of the LIA, and the frequency drift of ∼400 kHz occurs in 15 min, which is a typical imaging time.

Subsequently, we describe the circuit configuration for the imaging experiments. When imaging, in Fig. 1, the switch after the TIA is connected to path 2. PCA1 is fixed after the device under test (DUT) for the transmitted RF signal to be measured, whereas PCA2 is fixed at the reference point for the phase reference measurement. The reference signal measured using PCA2 is mixed with the frequency down-converted signal measured using PCA1 to cancel the frequency fluctuation of the RF signal.²⁵ The amplitude and phase information of the RF signal are measured using LIA1. In this scheme, IF Signal1 and IF Signal2 are expressed as follows:

where Δϕ is the relative phase between the RF signal and reference signal and ϕ_n is the relative phase fluctuation between the RF and LO signals. Here, for simplicity, we ignore the temporal difference between IF Signal1 and IF Signal2. IF Signal2 is first mixed with the signal (f_FG = 8.5 MHz) generated by the function generator using Mixer1. Mixer1 generates two types of frequency signals, f_IF2 − f_FG and f_IF2 + f_FG; however, only the f_IF2 + f_FG signal is extracted using a bandpass filter (BPF), and it is given as follows:

where ϕ_na(t) is the additive phase noise imposed by the BPF owing to the frequency fluctuations of IF Signal2. Because the frequency fluctuation of the Gunn oscillator was found to be ∼600 kHz, the center frequency and the bandwidth of the BPF were set to 11.5 and 5 MHz, respectively. If a source with a larger frequency fluctuation than the Gunn oscillator is used, the measurement is possible if the bandwidth of the BPF is wider; however, this gives rise to the concern of degrading the SNR. In contrast, if the frequency fluctuation is small, the bandwidth of the BPF can be made narrower, which is expected to improve the SNR. Nevertheless, the imaging results may be affected by the interference. If the sample to be measured is not wrapped by an envelope, a source with low-frequency fluctuation is preferred to perform imaging at a high SNR, as the interference caused by reflected waves on the sample surface is expected to have little effect.¹⁹ After that, the extracted signal (f_IF2 + f_FG) is mixed with IF Signal1 using Mixer2. The generated signal is as follows:

The common mode phase noise, ϕ_n(t), is canceled out, and only the phase difference between IF Signal1 and Signal2, Δϕ, and the additive phase noise, ϕ_na(t), added in the system are measured using LIA1 detection with a local reference signal, f_FG.²⁵ Here, the additive phase noise of ϕ_na(t) is mainly imposed by the BPF when the frequency fluctuates. This degrades the fidelity of the imaging results and causes a significant problem upon the use of a source with large frequency fluctuation. Furthermore, changes in amplitude measured by LIA1 occur because of variations in the output power of the source. Therefore, to calibrate the amplitude fluctuation and additive phase noise, we measured the reference amplitude (A′) and phase (P′) by self-mixing the reference signal measured using the PCA2. After passing the BPF, the signal (f_IF2 + f_FG) is mixed with IF Signal2 using Mixer3. The generated signal is as follows:

This signal is measured using LIA2 detection with a local reference signal, f_FG. The amplitude (A′) measured using LIA2 is influenced by the output power of the source, and phase (P′) measured using LIA2 is also subject to additive phase noise. Therefore, by using these measurements for the amplitude (A) and phase (P) values measured using LIA1, we correct for the change in amplitude due to the change in output power of the source and the change in phase due to the change in oscillation frequency by setting the amplitude to A/A′ and the phase to P − P′.

We evaluate the performance of the system by measuring the SNR and the standard deviation of the measured phase without placing the sample objects. In this measurement, the calibrated amplitude and phase were employed to calculate the SNR and the phase standard deviation. Figure 4 shows typical measured phase fluctuations. During this measurement time span (900 s), the measured SNR was 50.1 dB, and the standard deviation of the phase measurements was 1.08. When measured over a shorter period (30 s), the SNR was 56.9 dB, and the standard deviation of the phase measurements was 0.182. The minimum detectable thickness, δ_x, of the material placed in the free space was determined from the standard deviation of the phase measurement and refractive index of the material. The value of δ_x was calculated as

where c is the speed of light, σ_θ is the standard deviation of the phase measurement (in radians), n is the refractive index of the material, and f is the RF frequency.²⁶ Assuming f = 122.5 GHz and n = 1.6 (acrylic at 122.5 GHz),²⁷ δ_x = 2.1 μm was calculated with a σ_θ of 0.182 (0.003 rad).

Finally, to measure the resolution in this measurement system, we evaluated the spot diameter based on the knife-edge method. The spot size is determined from the distances at 90% and 10% of the maximum intensity of the signal.²⁸ We define this distance as Δd, and the relationship between Δd and spot size ω_s is given as follows:

We measured Δd = 9.0 mm, giving a spot size ω_s = 7.0 mm. Therefore, the spatial resolution in this experiment was 7.0 mm. The achieved spatial resolution was relatively large because the effective numerical aperture (NA) of the focusing setup was low. The beam was collimated through a plano-convex lens with a diameter of 47.5 mm. As the focal length of the focusing off-axis parabolic mirror was 101.6 mm, the NA was 0.234. The minimum spot size imposed by the diffraction limit in the coherent illumination system is given by 0.67λ/NA = 7.0 mm.²⁹ In practice, an approximate spatial resolution of 3 mm should be achievable in this frequency band after replacing the focusing optics with higher-NA optics. Moreover, sub-wavelength spatial resolution (0.55λ = 1.3 mm at 122.5 GHz) can be achieved by exploiting the terajet effect.¹⁴ 

Figure 5 presents the samples and imaging results. Three types of dielectrics were used as samples, namely, glass, acrylic, and polypropylene plates with thicknesses of 1.00, 1.00, and 0.77 mm, respectively. These dielectrics were then attached onto paper and placed in an envelope for imaging with transmitted waves. The measurement area was 80 × 80 mm², and the sample was swept and imaged in 1.00-mm steps using a precision XY-stage. The amplitude values were normalized by setting the maximum value to 1. In the amplitude imaging, we were able to capture the shape of an object owing to the effect of wave diffraction; however, it was difficult to identify the amplitude decay inside the object. Furthermore, the shape of the object using the wave diffraction effect can be captured only with thick glass and acrylic materials, whereas the visibility of thin polypropylene is considerably low in the amplitude imaging result. In contrast, for phase imaging, the difference in the optical path length of the object is significant, and the entire object made of polypropylene can be clearly visualized, not just its outline as in the amplitude imaging.

For a more detailed and quantitative comparison of the contrast differences in the amplitude and phase imaging, Fig. 6 shows the results obtained in extracting the measurement data for one line. The phase changes relative to “No Object” were negative for “Polypropylene” and “Acrylic” but positive for “Glass” because our system measured the wrapped phase. The actual phase change in the glass was −231.2, which is reasonable considering the thickness and refractive index of the glass (1.00 mm and 2.5 in this frequency band,³⁰ respectively).

From Fig. 6, the amplitude and phase change rates for each material were calculated. First, the average values of amplitude and phase in the red (Polypropylene), blue (Acrylic), green (No object), and orange (Glass) areas were calculated. Notably, the ten points that were not affected by the diffraction by the edge of the object were selected to calculate the average values for each material. Then, we calculated the difference between the amplitude and phase values between “No Object” and each material. Subsequently, considering that the range of possible amplitudes spans from 0 to 1 and that of the phase spans from −180 to 180 (assuming that the phase is not rotated by more than 360), we calculated the rate of change from the calculated differences in the amplitude and phase. Consequently, for glass, the amplitude change rate was 9.2%, whereas the phase change rate was 64.2%; for acrylic, the amplitude change rate was 5.2%, whereas the phase change rate was 27.5%; and for polypropylene, the amplitude change rate was 0.8%, whereas the phase change rate was 18.4%. These values indicate that the contrast of the imaging results is ∼7, 5, and 22 times higher for glass, acrylic, and polypropylene plates, respectively, in phase imaging compared to amplitude imaging. These results show that the phase imaging results exhibit higher contrast for low-loss materials. For the amplitude, all values for “No Object,” “Polypropylene,” “Acrylic,” and “Glass” are similar. However, for the phase, the samples can be distinguished from each other by the difference in their phase values.

Finally, we conducted an experiment to verify whether the use of an incoherent terahertz source can actually produce clear imaging results in a more realistic situation. Song et al.¹⁹ used a blade, paper clip, and wrench hidden in envelopes as the DUTs in their study. The authors reported that the interference effect was significant, resulting in poor image fidelity. The origin of the interference was attributed to the reflected waves at the sample surface.¹⁹ Following the study of Song et al.,¹⁹ we used not only dielectric materials but also metal hexagonal wrenches as the DUTs. Moreover, the DUTs were wrapped in bubble wrap and, subsequently, placed in an envelope, as shown in Fig. 7. The size of each bubble was ∼10 mm. The imaging result is shown in Fig. 8. For both the amplitude and phase results, the interference effect from reflected waves from the hexagonal wrench and bubble wrap was minimal, and high-fidelity images were obtained. Although the hexagonal wrench was visualized clearly in the amplitude imaging, it was not visible in the phase imaging results. The resolution calculated from the beam spot diameter in this experiment was 7.0 mm, whereas the width of the hexagonal wrench was ∼4 mm, which is smaller than the resolution. Therefore, some portion of the terahertz waves did not penetrate the hexagonal wrench, while other portions were detected. The detected terahertz-wave experiences no phase change; therefore, we cannot visualize the wrench in the phase imaging result. High-loss objects, even when they are not made of metal, have a lower SNR, making phase imaging less accurate. Hence, amplitude imaging is more suitable. However, in the case of low-loss dielectric materials, phase imaging is superior to amplitude imaging. Thus, when millimeter- and terahertz-wave imaging is applied for nondestructive testing, it is important to complementarily use both amplitude and phase imaging.

We propose and demonstrate a novel method to realize both amplitude and phase imaging using an incoherent free-running self-oscillating device. In the proof-of-concept experiments, we employed a Gunn oscillator as a millimeter-wave source and the PCA as a detector. The average SNR of the received signal during 15 min was 50.1 dB, whereas the average standard deviation of the phase was 1.08, even with the use of an incoherent source with the frequency fluctuation of ∼600 kHz during the measurement time. High-fidelity imaging results with a low interference effect were obtained in both amplitude and phase imaging, even in the case when the DUT was made of metal, which is highly susceptible to degrade the fidelity of the imaging results due to interference. The results show that phase imaging is capable of detecting thin dielectric materials at higher contrast than amplitude imaging, i.e., ∼7, 5, and 22 times higher in glass, acrylic, and polypropylene objects, respectively. The system is easily extendible to the higher frequency region by replacing the source by (for example) resonant tunneling diodes^21,22 and terahertz quantum cascade lasers.^23,24 The proposed method can be made more compact or integrated by replacing the PCA with diode-based mixers such as the Schottky-barrier diode and resonant tunnel diode.

The data that support the findings of this study are available within the article.