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Abstract
We propose and demonstrate a continuous-wave vector THz imaging system utilizing a photonic generation of two-tone THz signals and self-mixing detection. The proposed system measures amplitude and phase information simultaneously without the local oscillator reference or phase rotation scheme that is required for heterodyne or homodyne detection. In addition, 2π phase ambiguity that occurs when the sample is thicker than the wavelength of THz radiation can be avoided. In this work, THz signal having two frequency components was generated with a uni-traveling-carrier photodiode and electro-optic modulator on the emitter side and detected with a Schottky barrier diode detector used as a self-mixer on the receiver side. The proposed THz vector imaging system exhibited a 50-dB signal to noise ratio and 0.012-rad phase fluctuation with 100-μs integration time at 325-GHz. With the system, we demonstrate two-dimensional THz phase contrast imaging. Considering the recent use of two-dimensional arrays of Schottky barrier diodes as a THz image sensor, the proposed system is greatly advantageous for realizing a real-time THz vector imaging system due to its simple receiver configuration.
© 2017 Optical Society of America
1. Introduction
Terahertz (THz) waves, which lie in the frequency range from 100 GHz to 10 THz, have unique properties. Their radiation is non-ionizing, and they have spectral fingerprints for many molecules. THz waves have a high penetration depth through nonpolar dielectric materials and rectilinear propagation properties. Because of these features, they are attracting great attention for non-contact and non-destructive testing applications [1–3], particularly in the form of two-dimensional imaging systems. In particular, vector imaging is attractive for its higher image contrast, which corresponds to the thickness or dielectric constant of the sample under test [4,5]. This feature enables to more accurate recognition, especially for weak-absorption materials or transparent ones.
Vector THz imaging systems can be realized with both pulse-based and continuous-wave (CW) signals. In general, pulse-based systems provide much wider operating bandwidth and can capture vector information of a sample under test over a large bandwidth at once [6-7]. However, recovering the vector information from the measured data requires additional computation (i.e., fast Fourier transformation). While state of the art pulsed-based THz system with high dynamic range is reported, the signal-to-noise (SNR) ratio of the recovered vector information is still limited due to the large bandwidth. In contrast, a CW system can provide operating bandwidth comparable to that with photonic generation techniques [8] while maintaining a high SNR ratio and fast acquisition time. In addition, fine spectral resolution and accurate phase measurement capability obviously make the CW system advantageous for fast vector imaging.
The vector detection of CW THz waves can be categorized into homodyne and heterodyne detection. The former has been achieved with a photomixer and photonic local oscillator (LO) reference signals. In many homodyne detection systems with photonic generation techniques, the phase can be measured with fine accuracy because the received and LO signals at the detector are actually from identical laser sources [8–10]. However, for this to work well, homodyne detection requires a complicated system configuration, particularly the coupling of the photonic LO reference signal to the receiver photomixer and its phase rotation. The phase rotation has generally been implemented with a mechanical delay stage that requires long data acquisition times and signal chopping [9]. On the other hand, self-heterodyne detection utilizing an electro-optic phase modulator for phase rotation provides fast and direct measurement with no signal chopping, but completed LO signal connection for sharing a reference signal is still required [11–15]. Heterodyne detection is commonly implemented with an independent LO reference signal. Therefore, it can overcome the drawbacks of homodyne detection arising from the phase rotation of the LO reference signals at receivers, which results in simple receiver structures. However, it suffers from the phase noise of the independent LO reference source, which prevents precise acquisition of the phase information in the vector measurement.
In this work, an alternative approach with a two-tone signal generation and square-law detection is proposed for THz vector measurement. Two-tone signal is generated with an electro-optic modulator biased at the double-sideband suppressed-carrier (DSB-SC) operation point and a uni-traveling carrier photodiode as a photomixer. The two-tone THz signal is then detected and down-converted by self-mixing in a Schottky barrier diode (SBD) detector. The proposed system does not require sharing the reference signal between the emitter and detector for measuring the phase response. This approach can also avoid the phase noise problem related to free-running lasers, which is an issue in heterodyne detection. In addition, considering the recent use of two-dimensional arrays of SBDs as a THz image sensor [16,17], the simple square-law detection in this scheme is highly advantageous for realizing a real-time THz vector imaging system.
2. Principle of the proposed THz system approach
Figure 1 shows a schematic diagram of the proposed system for THz vector imaging. In this approach, two-tone THz signal with a small frequency difference is generated by a photomixing technique and detected by an SBD. The proposed CW THz vector imaging system does not utilize direct phase rotation by a mechanical delay line and is insensitive to 2π phase ambiguity.
Fig. 1 Schematic diagram of the CW THz vector imaging system utilizing two-tone signal generation and square-law detection. DSB-SC: double-sideband suppressed carrier. UTC-PD: uni-traveling-carrier photodiode. SBD: Schottky barrier diode.
To generate the two-tone THz signal, an optical signal from laser 2 is modulated at the DSB-SC operation point as shown in Fig. 1. In this work, the DSB-SC modulation was achieved with a dual-drive Mach-Zehnder modulator (DD-MZM). Assuming that the powers of both arms of the DD-MZM are identical, the output of the DD-MZM can be described as
where E0, ω2, and φn2 are the amplitude, optical frequency, and phase noise of free-running laser 2, respectively, and Vπ is the half-wave voltage of the DD-MZM. V(t) is the applied driving voltage given bywhere VDC is the DC bias voltage, and Vm and ωm are the amplitude and frequency of the electrical driving signal, respectively. If DC bias voltage (VDC) is equal to the half-wave voltage (Vπ) of the DD-MZM, the output of the DD-MZM with optical carrier suppression can be expressed aswhere Jk is the Bessel function of the first order k. As described in Eq. (3), high-order harmonics except for the first-order harmonics can be minimized by tuning the amplitude of the electrical driving signal (Vm).The output of the DSB-SC modulation is combined with laser 1’s output, and they are injected into the UTC-PD. Assuming that only first-order harmonics in the double-sideband are dominant in the THz signal, the output of the DSB-SC modulation has two dominant frequencies of ω2 ± ωm, and thus the THz frequency generated by the UTC-PD can be defined as
where ω1 is the optical frequency of laser 1.The THz radiation with the two-tone signal passes through the sample under test and is detected by the SBD as shown in Fig. 1. The received THz signal in front of the SBD can be expressed as
where ASk and ϕTHzk are an attenuation and phase shift of the THz radiation by the sample inserted in the THz wave path at a frequency of ωTHzk (k = 1 and 2), and φn1 is the phase noise of laser 1.The THz signal described in Eq. (6) is squared in the SBD (i.e., self-mixing, square-law detection). If there is no abrupt change of an absorption coefficient and a refractive index in the measurement frequency region from ωTHz1 to ωTHz2, we can assume AS1 and AS2 are identical as AS. Then, the output of the SBD will be at DC, 2ωm, 2ωTHz1, and 2ωTHz2. Considering the limited output bandwidth of the SBD detector, the final output can be expressed as
As shown in Eq. (7), the output of the SBD is unaffected by the phase noises (φn1 and φn2) induced by the laser sources because they are canceled out during the self-mixing.The output signal at 2ωm is determined by the attenuation and phase delay of the THz signal induced by the sample. The output of the SBD described in Eq. (7) contains an amplitude variation and phase delay of the THz signal, and they can be extracted using a lock-in amplifier (LIA). Assuming no abrupt change of a refractive index in the freqeuncy region from ωTHz1 to ωTHz2, we can approximate identical reflective indices at ωTHz1 and ωTHz2and the phase delay induced by the same can be simplified as
where d, and c are the thickness of the sample and the velocity of light in vacuum, respectively. The nTHz1 and nTHz2 are the refractive indices of the sample at frequencies of ωTHz1 and ωTHz2, respectively. As described in Eq. (8), the thickness of the sample can be calculated using the phase delay (Δϕ). In the ordinary CW THz imaging system, 2π phase ambiguity limits the maximum detectable THz path length change, which is inversely proportional to the frequency of the THz signal. However, that of this scheme is inversely proportional to the DSB-SC modulation frequency regardless of the frequency of the THz signal. This feature enables the proposed system can measure thicker samples regardless of the frequency of the THz signal. If one want to enlarge the maximum detectable THz path length change to measure thick or high dielectric materials, simply lowering DSB-SC modulation frequency will provide high signal contrast in phase without 2π phase ambiguity.3. Experiment and results
A proof-of-concept experiment was performed using the experiment setup shown in Fig. 2. A two-channel laser source (TLG-200, Alnair Labs) with a linewidth of 100 kHz was used. The wavelength of one channel was set to 1551.91 nm and that of the other was set to 1549.32 nm, which corresponds to a beat frequency of 323 GHz. The DSB-SC was achieved by a DD-MZM (EOSPACE), and a modulation frequency for the DSB-SC was set to 5 GHz. The output of the DD-MZM was combined with the output of another optical channel, and the combined optical signal was amplified by an erbium-doped fiber amplifier (EDFA, Furukawa Electric). A UTC-PD and SBD were used to generate and detect THz radiation. For lock-in detection, a 10-GHz reference signal and the received signal were down-converted to 0.5 MHz with RF mixers and an oscillator. Then, the amplitude and phase variations in the output of the SBD were extracted using an LIA (MFLI, Zurich Instruments). In all experiments, the integration time (or time constant) of the LIA was fixed at 100 μs.
Fig. 2 Experiment setup for the vector imaging system using the proposed approach. BPF: bandpass filter. LIA: lock-in amplifier.
In the DSB-SC modulation, the amplitude of the electrical driving signal (Vm) is adjusted to suppress other harmonics. Figure 3 shows the optical spectrum at the output of the DSB-SC modulator and the EDFA. As shown in Fig. 3(a), the optical signal of the laser 2 is modulated, and the first harmonic dominantly appears at 1549.28 and 1549.36 nm. The ratio of the first harmonic to the carrier suppressed is about 32 dB and the ratio of the first harmonic to the third harmonic ratio is more than 36 dB. Hence, the first harmonic is dominant in the THz radiation generated by the UTC-PD. The optical power of laser 1 is set 3 dB higher than that of the first harmonic, which provides maximum power efficiency in the proposed system. In this case, THz signal having frequency components of 323 ± 5 GHz is radiated by the UTC-PD, and the output of the SBD has a frequency component of 10 GHz. In this experiment, samples have no abrupt change of the absorption coefficient and the refractive index in 300 ~ 1000 GHz ranges and therefore 10-GHz DSB-SC frequency won’t cause serious error in the vector measurement.
The stability of the proposed system was investigated to ascertain its measurement reliability. In this experiment, the UTC-PD and the SBD were positioned face to face and the amplitude and phase response of the SBD output were measured. Figure 4 shows the amplitude and phase fluctuation of the LIA output. The amplitude response has a mean value of 72 mV and a standard deviation of 0.23 mV. The SNR of about 50 dB was estimated from the mean value and standard deviation of the amplitude response. In addition, the measured standard deviation of phase response calculated using the phase response of the LIA output shown in Fig. 4(b) was around 0.012 rad. Analyzing the possible rms phase error due to the SNR and phase noises of the signal sources, 50-dB SNR and 9.9995-GHz signal source are expected to cause measurement error of around 0.003 rad and 0.010 rad, respectively. Since the phase noises from the lasers cancel out during the self-mixing, the phase measurement sensitivity of the setup must be limited by the 9.9995-GHz signal source. If one drives the system at low DSB-SC frequency, for instance 1 MHz where phase noise is likely to be negligible, the proposed system would exhibit the SNR-limit behavior in the phase sensitivity [15]. The minimum detectable change in the THz path length, calculated using the modulation frequency and the measured standard deviation of the phase response, is estimated to be 57.5 μm.
Fig. 4 Stability of the (a) amplitude and (b) phase response of the LIA output. The time constant of the LIA is 100 μs.
Using the proposed system, THz transmission characteristics of polycarbonate plate with a thickness of 4.8 mm were measured. According to the literature [18], the refractive index of the polycarbonate plate is approximately constant in the frequency region of 300 GHz to 1 THz. The phase changes induced by the plate were measured at about 323 GHz. Figure 5 shows the amplitude and phase response without and with the plate. As shown in Fig. 5, THz radiation was attenuated to about 4.32 dB by the plate. From the difference in the phase response, the refractive index of the plate can be estimated. Using Eq. (8), we estimated it to be about n = 1.656 ± 0.01 at around 323 GHz, which is close to the reported value of 1.66 [18].
Fig. 5 (a) Amplitude and (b) phase response of the LIA with and without the 4.8-mm-thick polycarbonate plate. The time constant of the LIA is 100 μs.
To demonstrate the potential of the proposed system, we measured two-dimensional vector images of a sample made of polycarbonate, which is shown in Fig. 6(a). The polycarbonate plate was embossed with “THz” by laser etching. The thickness of the base plate is about 2.1 mm, and a height of each letter is about 2.7 mm. The plate was inside a paper envelope as shown in Fig. 6(b). In this experiment, a two-axis motorized stage was used to move the sample in the imaging plane. The velocity and translation range of the x-axis stage were set to 2 cm/s and 9 cm, respectively. The data acquisition time was about 4.5 seconds per line, and it was limited by the velocity of the x-axis stage. The velocity of the y-axis stage was set to 2 cm/s, and this stage translated the sample in 0.5-mm increments. Figure 7(a) and 7(b) show THz amplitude and phase contrast images, respectively. The contour of the plate and the embossed letters are clearly discernible in the amplitude and phase contrast images. Figure 7(c) and 7(d) show the amplitude and phase response, respectively, at the fixed y-axis in Fig. 7(a) and 7(b) by dotted lines. As shown in Fig. 7(d), the THz phase contrast image is more informative than the amplitude image. In the phase contrast image, the base plate and the embossed letters have a phase difference of about 0.28 and 0.39 rad, respectively. In the previous experiment, the refractive index of the plate was measured as 1.656. Therefore, the thickness of the plate and the height of the letters were estimated as 2.04 and 2.84 mm, respectively, which is close to the values measured with a Vernier caliper.
Fig. 6 Photographs of (a) the polycarbonate plate embossed with “THz” by laser etching and of (b) the paper envelope with the embossed plate inside.
Fig. 7 (a) Two-dimensional THz amplitude image and (b) phase contrast image of the embossed polycarbonate plate in the paper envelope. (c) Amplitude and (d) phase response at the fixed Y-axis in (a) and (b), shown by a dotted red line. The time constant of the LIA is 100 μs.
A similar measurement was performed on a slice of bacon as well. Figure 8 shows a photograph, THz amplitude image, and THz phase contrast image of the bacon slice. The vector response of the bacon slice is mapped in Fig. 8(b) and 8(c). The THz radiation passed through the bacon slice weakly because of its moisture content [19]. The phase contrast image of the bacon slice shows a distinct difference between the fatty and lean tissue of the bacon slice, which must arise from their different reflective indices. This result shows that the proposed approach can be extended to THz applications for food inspection and biomedical studies.
Fig. 8 (a) Photograph, (b) THz amplitude image, and (c) THz phase contrast image of the bacon slice.
4. Conclusion
A system utilizing two-tone signal generation and square-law detection was demonstrated for continuous-wave THz vector imaging. The proposed approach can extract the amplitude and phase response of the sample under test without phase rotation for homodyne detection or an additional LO source for heterodyne detection. We demonstrated a THz vector imaging system having a signal-to-noise ratio of 50 dB and a minimum detectable change in the THz path length of 57.5 μm at 323 GHz with 100-μs integration time per a point. Using the proposed system, two-dimensional vector imaging of the plate concealed in an envelope was performed. Moreover, the proposed vector imaging system mapped out the distribution of fat and lean in a bacon slice, which demonstrated that the proposed scheme can be extended to real-time THz inspection applications for food inspection and biomedical studies with an arrayed SBD image sensor.
Funding
Brain Research Program (NRF-2015R1A2A1A15055838, NRF of Korea).
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