**NDE Terahertz Wave Techniques for Measurement of Defect Detection on Composite Panels of Honeycomb Sandwiches**

#### **Kwang-Hee Im 1,\*, Sun-Kyu Kim 2, Jong-An Jung 3, Young-Tae Cho 4, Yong-Deuck Woo <sup>1</sup> and Chien-Ping Chiou <sup>5</sup>**


Received: 20 July 2020; Accepted: 19 August 2020; Published: 21 August 2020

**Abstract:** Terahertz wave (T-ray) technologies have become a popular topic in scientific research over the last two decades, and can be utilized in nondestructive evaluation (NDE) techniques. This study suggests an optimal scanning technique method for honeycomb sandwich composite panels, where skins were utilized with two different skins, namely, carbon fiber-reinforced plastic (CFRP) skin and glass fiber-reinforced plastic (GFRP) skin, as layers of the panel surfaces. Foreign objects were artificially inserted between the skins and honeycomb cells in the honeycomb sandwich composite panels. For this experiment, optimal T-ray scanning methods were performed to examine defects based on the angle between the one-ply thin fiber skin axis and the angle of the electric field (E-field) according to the amount of conductivity of the honeycomb sandwich composite panels. In order to confirm the fundamental characteristics of the terahertz waves, the refractive index values of the GFRP composites were experimentally obtained and analyzed, with the data agreeing with known solutions. Terahertz waves (T-rays) were shown to have limited penetration in honeycomb sandwich composite panels when utilized with a skin of carbon fibers. Therefore, T-rays were found to interact with the electrical conductivity and electric field direction of honeycomb sandwich composite panels with glass fiber skins. The T-ray images were obtained regardless of the electric field direction and the fiber direction. In the honeycomb sandwich composite panels with carbon fiber skins, the T-ray images with higher signal-to-noise (S/N) ratios depended on the scanning angle between the angle of the carbon fiber and the angle of the electric field. Thus, the angle of optimum detection measurement was confirmed to be 90◦ between the E-field and the fiber direction, particularly when using a carbon fiber skin.

**Keywords:** terahertz waves; honeycomb sandwiches; foreign materials; time-of-flight; electric field

#### **1. Introduction**

Recently, utilization of terahertz wave (T-ray) technologies have increased exponentially in technical applications such as mechanical aviation, aerospace, and advanced medical fields, with field practical applications also revealing broad application prospects. T-rays, which have relatively short wavelength and high resolution, are widely used in fields of inspection using electric and electronic spectra. In particular, T-rays are critically important in security devices used in airports, advanced imaging, liquids, various industrial areas, and spectroscopic evaluation of advanced composite materials [1–5]. Terahertz time–domain spectroscopy (THz-TDS) plays an important role in contactless detection of discontinuity or defects, which are present in various composite materials. The THz system is based on photoconductivity and depends on the generation of low-cycle terahertz waveforms utilizing photoconductive sensors mounted with femtosecond (10–15 s) lasers [6]. This system has the ability to generate picosecond terahertz waves and obtain a high signal-to-noise ratio (S/N). This energy affects a wide range of bandwidths and the resistance of photoconductive switches could cause a temporary change in THz wave emission to be produced over the THz timescale baseline [6–9].

The other method uses a laser of two continuous waves (CW) via optical conversion and optical mixing. Much attention surrounds T-ray signals because of their use in monitoring, such as management and inspection of nonconductive products, chemical components, and physical properties and substance toxicity analysis. Since T-rays are employed in small, portable pieces of equipment using previously discovered foundation technologies, its range of applicability is wide and the utilization of these technologies may be significant.

More recently, the importance of fiber-reinforced plastics (FRP), which are used in industrial regions as well as state-of-the-art aviation sectors, was identified. Characteristic evaluations of refraction coefficient (n), absorption coefficient (α), and electrical conductivity of epoxy resin in composite materials, which are present in fibers, were conducted by directly applying T-rays to FRP-laminated plates. Furthermore, T-ray scan imaging techniques were studied to detect defects in carbon fiber-reinforced plastics (CFRP) composites. Carbon fibers are conductive, whereas epoxy matrices are not conductive. Therefore, the interaction between the conductivity of carbon fibers in CFRP-laminated plates and T-ray applications were identified. Measurements regarding nanoparticle detection and sizing were also made by using microcavity cost and challenge based on spectra estimations [4,10–14].

Composite panels of honeycomb sandwiches, which are excellent in terms of their lightness, were used in this study. Foreign materials were inserted during composite manufacture, leading to decreased strength, shape change, and poor adhesion. After the carbon fibers were utilized as a skin, the foreign materials became not more visible than if a transparent glass fiber skin was used. Detecting these foreign materials is an important step toward checking the soundness of composite materials. This approach focused on a technique to monitor foreign materials on the honeycomb cell cores of these panels. Assuming that the foreign materials (e.g., foils) were present between the upper side of the honeycomb cells and a thin layer of carbon/glass fibers used as a skin while manufacturing the honeycomb sandwich panels, several artificial honeycomb sandwich panels with foreign materials were produced. Two kinds of skins were utilized and defined as "carbon skin" or "glass skin", with the skins being unidirectional for both carbon and glass fibers.

Experimental results of T-rays are herein presented for honeycomb sandwich composite panels. We also demonstrate a technique for measuring the refractive index (n), which is one of the properties of various materials that use THz waves, and consider a correlation between the angle of the electric field and the fiber angle of CFRP and GFRP composite panels to consider conductivity. The investigation regarding T-rays was found to successfully monitor the soundness of honeycomb sandwich composite panels. Two kinds of glass- and carbon-skin honeycomb sandwich composite panels were tested to examine honeycomb sandwich composite panel defects and optimal scanning methods were confirmed regarding the angle of the electric field versus the angle of fibers in glass and carbon skins for honeycomb sandwich composite panels.

#### **2. Basic Theory Approach**

#### *Refractive Index Measurements*

A reflection mode for T-rays is applied in the time domain to calculate a refractive index by analyzing the signals of T-rays reflected from the specimen, and a refractive index is induced by catching two surface and bottom signals reflected through the specimen. Figure 1 shows the direction of the T-ray. When a T-ray is reflected from the THz pulse emitter, a refractive index can be solved by utilizing time-of-flight (TOF) for a sample [1].

**Figure 1.** Schematic setup of the direction of a T-ray under reflection mode.

This reflection mode aims to acquire a refractive index by obtaining a length where the reflected fiber optics are passed through the upper and lower sides of the specimen out of the T-ray TOF.

Figure 1 shows the shape and direction of a T-ray. T in the figure refers to the transmitter, and R refers to the receiver; d means the thickness of the sample. Assuming that the T-ray is perpendicular to the sample, the time difference (Δt) can be calculated as follows [2–6]:

$$
\Delta \mathbf{t} = \frac{2d}{v} \tag{1}
$$

As shown in Figure 1, the time difference (Δt) between the surface reflection wave and back reflector of the sample can be calculated by considering the time delay due to the sample thickness and the T-ray propagation path in reflection mode.

$$
\Delta \mathbf{t} = \frac{2l}{v} = \frac{\delta}{\mathbb{C}\_a} \tag{2}
$$

where *l* = *d*/*cos*θ*r*, δ = 2*lsin*2θ*<sup>a</sup>* = 2(*d*/*cos*θ*r*)*sin*θ2, *d* refers to the specimen thickness, *Ca* refers to the T-ray speed in the air, *n* refers to the refractive index, and *v* refers to the T-ray speed inside the sample [2].

The resonance frequency (Δf) can be expressed as follows when the time delay due to the sample thickness and inclined T-ray path are tracked [2,14].

$$\Delta \mathbf{f} = \frac{1}{\left(\frac{2d}{\cos \theta\_r} - \frac{\delta}{\mathbb{C}\_d}\right)} = \frac{1}{\left(\frac{2d}{\cos \theta\_r} - \frac{2d \sin^2 \theta\_d}{\cos \theta\_r \mathbb{C}\_d}\right)} = \frac{1}{\frac{2d}{\cos \theta\_r} \left(\frac{1}{v} - \frac{\sin^2 \theta\_d}{\mathbb{C}\_d}\right)}\tag{3}$$

where *d* refers to the sample thickness, θ*<sup>r</sup>* refers to the inclination angle inside the sample, and θ*<sup>a</sup>* refers to the inclination angle in the air. As presented above, the refractive index, which is one of the electromagnetic properties, can be obtained [2].

$$
\ln^4 - A n^2 - A \sin^2 \theta\_{p1} = 0 \tag{4}
$$

where *A* is *T*2*V*<sup>2</sup> *air*/4*d*<sup>2</sup> <sup>2</sup>. In addition, *T* refers to the transmission time through the specimen and θ*p*<sup>1</sup> denotes the inclination angle inside the sample.

The refractive index can be solved using Equation (5) under the transmission method [2].

$$\mathbf{n} = 1 + \frac{\Delta\_t V\_{air}}{t} \tag{5}$$

where Δ*<sup>t</sup>* refers to the time delay between trials with and without sample and *Vair* refers to light speed in the air (3 <sup>×</sup> <sup>10</sup>10cm/s).

#### **3. Experimental Device and Measurements**

#### *3.1. Measurement Device*

Figure 2 shows the test method of nondestructive evaluation (NDE) THz-TDS to test sample characteristics. The NDE system collected and analyzed specimen characteristics and signals. The T-ray system in this experiment was made by Tera View (England). The NDE device consisted of a time–domain spectroscope (TDS) pulse tool and a frequency–domain continuous wave (CW) tool, which are TDS technologies to generate and control T-ray pulses and detect defects. The THz-TDS system acquired signals and valid data with a structural characteristic and optical device to adjust and control T-rays. The TDS device had a frequency bandwidth from 50 GHz to 4 THz, a window range of 300 ps, and was able to implement focal lengths for both 50 mm and 150 mm (full width at half maximum (FWHM)) of T-ray beams. In addition, the TDS system measured either under transmission or reflection mode (a pitch–catch technique with a small angle). The CW system had a frequency bandwidth of 50 GHz to 1.5 THz, with a focal length ranging from 50 mm to 150 mm. The TDS device was connected to the CW device via optical fibers. Figure 3 shows a simplified diagram of the T-ray system, where θ means a different angle surface fiber and E-field direction for the THz-TDS system.

**Figure 2.** A photo of a T-ray system for measuring and imaging material properties under reflection mode.

**Figure 3.** A simplified overview of the terahertz (THz) measurement method.

#### *3.2. Measurement Technique*

Figure 3 shows the T-ray measurement configuration under reflection mode. At the emitter, a T-ray was generated and sent to the receiver. A preferred sample was prepared with matching focal points for both the emitter and the receiver to conduct the experiment. The inclination angle of the T-ray lens was set to 16.6◦. Figure 4 shows samples of carbon-skin and glass-skin honeycomb sandwich composite panels with foreign materials. For the case shown in Figure 4a, the foreign materials were invisible; however, the foreign materials in Figure 4b were visible. Figure 4c shows the locations of inserted foreign materials (brass foils). The dimensions of the foreign matters were 12.5 mm × 12.5 mm × 0.025 mm and 6.3 mm × 6.3 mm × 0.025 mm. Here, unidirectional carbon fibers were utilized and the diameter of fibers is 7 μm. The content of epoxy is around 37.0%.

(**a**)

**Figure 4.** Samples of carbon-skin and glass-skin honeycomb sandwich composite panels with foreign materials. (**a**) Carbon-skin honeycomb composite panel with foreign materials. (**b**) Glass-skin honeycomb composite panel with foreign materials. (**c**) Stacking sequence of honeycomb composite panel at the A-A' line.

#### **4. Results and Discussion**

#### *4.1. Measurement of the Refractive Index*

In order to measure the properties of the materials as T-ray parameters, T-ray pulses were acquired under transmission mode of GFRP composite materials. A time difference in reflection mode between the surface and bottom of the sample can clearly be seen in Figure 5. The GFRP specimen had a thickness of approximately 5.79 mm.

**Figure 5.** Terahertz time–domain spectroscopy (THz-TDS) pulses from a transmitted glass fiber-reinforced plastic (GFRP) sample (n = 1.95, Δt = 80.8 ps, thickness = 5.79 mm).

The time difference (Δt) measured using the reflective wave of the specimen was 80.8 ps. Thus, an optical time difference was easily obtained under reflection mode, which was one of the measurement techniques used to calculate the refractive index using Equation (2). The GFRP composite material and Poly methyl methacrylate (PMMA) and GFRP specimens were measured under reflection mode, as presented in Table 1. When compared to data in previous literature, less than 2.0% difference was revealed [6,12–15] due to the reflection mode measurement technique of T-rays during the experiment having unidirectional access considering a number of factors; therefore, the experiment was conducted conveniently. It was difficult to compare specimens with existing data because the GFRP samples were different from the existing samples in terms of manufacturing method and characteristics.



Note: \* Data in Refs. [3,9,10].

#### *4.2. Evaluation on Electric Field(E-Fields) of Composite Materials*

T-rays have limited transmitted power in conductive materials in contrast with nonconductive materials. Even if T-rays are applied and utilized in inspection of carbon fiber composites, in-depth studies are limited. In particular, carbon fiber-reinforced plastics (CFRP) consist of conductive carbon fibers and a nonconductive matrix. When the cross-section of CFRP composites is observed through a microscope, it can be seen to consist of various components, such as fibers and matrices, which significantly affect the conductivity. Because of this, a quantitative evaluation should be performed on characteristics of carbon fiber composites. According to previous study results, the electrical conductivity in the axial direction of a carbon fiber is approximately three orders of amount larger than in the radial direction of carbon fibers.

The CFRP composite is oriented in unidirectionally and the conductivity in a CFRP-laminated plate with various laminations is therefore affected. In particular, the mechanism that generates conductivity in the lateral direction (perpendicular to the fiber axis) depends on contact with fibers occurring between adjacent fibers. Few studies exist regarding the amount of electrical conductivity when using carbon fiber composites. Many studies [6,12–15] reported that the amount of conductivity (σ*l*) in the axial direction was between 1 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>S</sup>/m and 6 <sup>×</sup> 104 <sup>S</sup>/m and the amount of conductivity (σ*t*) in the radial direction was much wider, in the range of 2 S/m up to 600 S/m [16–18], as evidenced by Equation (6).

$$
\sigma = \sigma\_l \cos^2 \theta + \sigma\_l \sin^2 \theta \tag{6}
$$

Since the T-rays are much larger than the conductivity in the radial fiber direction (σ*<sup>l</sup>* σ*t*), they can be significantly different according to the relative angle between the angle of carbon fibers and the angle of the electric field when transmitting through unidirectional CFRP composites [17,18]. When an electric T-ray field is parallel with the axial direction of the carbon fibers, conductivity becomes the largest value due to lower transmitted power to carbon fiber composites. However, when the direction of the electric field is perpendicular to the axis of carbon fibers, the conductivity decreases, whereas transmitted power becomes much greater. Using = 10<sup>4</sup> S/m, the skin depth of the unidirectional CFRP composite using T-rays could be 0.2 mm at 1 THz and 0.5 mm at 0.1 THz when the direction of the electric field is perpendicular to the axis of carbon fibers. The effect of transmitted power on angles of a 12-ply unidirectional CFRP composite-laminated plate was experimentally evaluated using a CW THz device. The T-ray transmitted power at the lower bandwidth (f—0.1 THz) of frequency was found to be greater than that of a noise level over 30 dB. Figure 6 shows the angular dependence of 0.1 THz reflection power. Figure 6a shows the angle between the carbon fiber orientation when the T-ray E-field was 0◦ and the peak-to-peak amplitude was approximately 2.25. Figure 6b shows the angle between the carbon fiber orientation when the T-ray E-field was 45.0◦ and the peak-to-peak amplitude was approximately 1.76. Figure 6c shows the angle between the carbon fiber orientation when the T-ray E-field was 90.0◦ and the peak-to-peak amplitude was approximately 1.70. The above results indicate that transmission power is easily achieved when the vector value in the T-ray E-field direction is 90.0◦, thereby demonstrating lower peak-to-peak amplitude. On the other hand, when the vector value is 0◦, the transmission power is difficult to generating, resulting in larger peak-to-peak amplitude of the reflection wave was larger and easier penetration.

**Figure 6.** *Cont.*

**Figure 6.** Angular dependence of reflection power of T-rays for carbon-skin honeycomb composite panels.

#### *4.3. THz Imaging of Foreign Marerials in Honeycomb Sandwich Composite Panels*

The brass foils attached to the bottom of the honeycomb sandwich composite panel using a carbon skin were detected to evaluate the characteristics of T-ray conductivity in the CFRP composite. The brass foils used here were 0.025 mm in thickness and two other dimensions of 12.5 mm × 12.5 mm and 6.3 mm × 6.3 mm. In particular, assuming that the direction of an electric field is perpendicular to the axial direction of carbon fibers and also parallel with the radial direction of carbon fibers, a different angle, θ, exists between the direction of the electric field and the direction of the carbon fibers. Defects were detected in this work under reflection mode using the TDS-THz system.

A correlation between the amount of conductivity and the S/N ratio of defective THz images can be expressed as σ*<sup>l</sup>* σ*t*, with Equation (6) expressed as σ σ*lcos*<sup>2</sup>θ. The direction of the E-field and the direction of the carbon fibers were used to analyze the T-ray scan images, showing 1-ply carbon fiber defects in the prepreg sheet. The transmitted power of the T-rays penetrating the 1-ply sheet depends on an angle made between the fiber direction and E-field, allowing the T-ray to be transmitted and reflected from the surface of the sample according to the orientation of the fibers. When considering the simple resistance R equation, a single resistance body was made [6,17,18], allowing us to calculate the conductivity alongside the correlation of conductivity with the S/N ratio in defects from T-ray detection images.

The conductivity is at a minimum when the angle of an electric field is located at a 90◦ angle to the direction of carbon fibers in single-ply according to Equation σ σ*lcos*<sup>2</sup>θ. A signal-to-noise (S/N) ratio of defect image is at its greatest when this sample is positioned in this 90◦ angle. The S/N ratio could be at its worst at 00(σ = 1.0σ*t*) angle, which exhibited the largest conductivity. This defect detection method was determined to be valid between the S/N ratio based on a simple model for conductivity according to qualitative matching with the experimental image results.

Therefore, the defect detection resolution of T-rays could be different, depending on the relationship between the direction of the electric field and the direction of the carbon fibers. Figure 7 shows the scanning methods under reflection mode according to various angles made between the T-ray E-field and the fiber direction. Figure 7a shows the top view containing foreign materials. This figure shows the position of the four brass foils attached to the cell in the honeycomb sandwich composite panel using the T-ray scan method. Figure 7b shows the side view of the honeycomb sandwich composite panel, in which the position of the foreign materials between the cell of the honeycomb sandwich panel and the fiber skin can be seen. The dimensions of the foreign materials were 12.5 mm × 12.5 mm × 0.025 mm and 6.3 mm × 6.3 mm × 0.025 mm.

(**a**) Top view of honeycomb sandwiches.

(**b**) Side view of honeycomb sandwiches.

Figure 8 shows the implemented scan image using T-ray reflection mode. The specimen was the honeycomb sandwich composite panel with a glass fiber skin containing foreign materials processed between the glass fiber skin and the cell panel. The glass fiber orientation was changed to 0.0◦, 45.0◦, and 90.0◦ depending on the direction of the E-field to check the defect detection performance during scanning conduction. Figure 8a shows the scan image with an angle of 0.0◦ between the E-field and the glass fiber orientation, where four foreign defects were detected. Figure 8b,c show the scan images at 45.0◦ and 90.0◦, where four foreign defects were detected. Thus, T-rays were transmitted through the glass fiber regardless of the T-ray direction due to the fiber glass used as a skin in the honeycomb sandwich panel being a nonconductive material and therefore not affecting the T-ray.

**Figure 8.** Terahertz scan images of glass-skin honeycomb sandwich composite panels with boned and brass foils (12.5 × 12.5 mm and 6.3 × 6.3 mm) at the bottom under time—domain spectroscopy (TDS) reflection mode.

Figure 9 shows the peak-to-peak amplitude-based scan image of a carbon-skin honeycomb sandwich composite panel by setting a time limit of the defection signals using T-ray reflection mode, as shown in Figure 7. The specimen was the honeycomb sandwich composite panel using a carbon fiber skin, in which the foreign matters were processed between the carbon fiber skin and the cell panel. The carbon fiber orientation was changed to 0.0◦, 45.0◦ and 90.0◦ depending on the E-field direction, and scanning was conducted to check the defect detection performance, similar to that seen in Figure 8. Figure 9a shows the scan image at 0.0◦ between the E-field and glass fiber orientation, where four foreign defects could not be detected. The surface image only showed the honeycomb cell shape at a regular distance. Figure 9b shows the scan image at 45.0◦ between the E-field and the glass fiber orientation, where four foreign defects were detected, despite the S/N ratio being somewhat low. Figure 9c shows the scan image at 90.0◦ between the E-field and the carbon fiber orientation where four foreign defects were detected due to the presence of the highest S/N ratio.

**Figure 9.** Terahertz scan images of carbon-skin honeycomb sandwiches composite panels with boned and brass foils (12.5 × 12.5 mm and 6.3 × 6.3 mm) at the bottom under TDS reflection mode.

The above results verify that foreign defect inspection of the honeycomb sandwich composite panel using a carbon fiber skin depends significantly on unidirectional carbon fiber locations according to the E-field direction. Figure 9 shows the TDS reflection mode scan image of defects which were observed in the carbon-skin honeycomb sandwich composite panel. Table 2 presents the conductivity levels of the carbon-skin honeycomb sandwich composite panel using the simplified model. Here, θ means the angle between the direction of an axial one-ply fiber and the direction of the electric field and ψ means the angle between the direction of an axial second-ply fiber and the direction of the electric field. These angles used were (a) θ = 0.0◦, (b) θ = 45.0◦, and (c) θ = 90.0◦. As shown in Equation (6), the resistance became minimal when the angle between the E-field and the carbon fiber orientation was 90.0◦. In particular, the resistance became maximal when the angle was 0◦. Thus, the T-ray could not penetrate the carbon-skin honeycomb sandwich composite panel at all, so the defects could not be detected, as shown in Figure 9a.


**Table 2.** Predicted simple resistor model of one-ply conductivity.

Figure 10 shows the resistance size of the E-field reception according to the carbon fiber orientation of the carbon-skin honeycomb sandwich composite panel. In particular, since the resistance was smallest when the angle between the carbon fiber orientation of the carbon-skin honeycomb sandwich composite panel and the E-field was 90.0◦, the defect signals could be optimized because the transmission rate of the T-ray was very high.

**Figure 10.** Relationship between the angle of the fiber and the E-field and normalized resistance in a unidirectional carbon composite laminate.

Therefore, when the CFRP skins were utilized as the top layers for the honeycomb sandwich composite panels, the foreign materials in the scanning images were most visible at 90.0◦; however, the foreign materials could not be clearly observed at other angles, particularly 0.0◦, because the T-rays were unable to penetrate the CFRP skin when the top surface fibers of the honeycomb sandwich composite panels were stacked.

#### **5. Conclusions**

This study aimed to investigate the application and utilization of a technique to measure the refractive index (n), which is one of the material properties in various materials using THz waves, and consider a correlation between the angle of an electric field and the fiber angles of CFRP and GFRP composite panels to analyze conductivity. T-ray investigations were successfully performed to monitor the soundness of honeycomb sandwiches composite panels, allowing us to obtain the following THz results of the honeycomb sandwich composite panels:


**Author Contributions:** K.-H.I. suggested and designed the experiments; S.-K.K., Y.-T.C. and Y.-D.W. performed the experiments; C.-P.C. and J.-A.J. helped in the accomplishment of ideas and the administration of the experiments. The data were discussed and analyzed and the manuscript was written and revised by all members. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) (No. 2018R1D1A1B07049775) and also experimentally helped by the CNDE at Iowa State University, USA.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **A 350-GHz Coupled Stack Oscillator with** −**0.8 dBm Output Power in 65-nm Bulk CMOS Process**

#### **Thanh Dat Nguyen and Jong-Phil Hong \***

School of Electrical Engineering, Chungbuk National University, Cheongju 28644, Korea; ntdat@cbnu.ac.kr **\*** Correspondence: jphong@cbnu.ac.kr

Received: 15 July 2020; Accepted: 27 July 2020; Published: 28 July 2020

**Abstract:** This paper presents a push-push coupled stack oscillator that achieves a high output power level at terahertz (THz) wave frequency. The proposed stack oscillator core adopts a frequency selective negative resistance topology to improve negative transconductance at the fundamental frequency and a transformer connected between gate and drain terminals of cross pair transistors to minimize the power loss at the second harmonic frequency. Next, the phases and the oscillation frequencies between the oscillator cores are locked by employing an inductor of frequency selective negative resistance topology. The proposed topology was implemented in a 65-nm bulk CMOS technology. The highest measured output power is −0.8 dBm at 353.2 GHz while dissipating 205 mW from a 2.8 V supply voltage.

**Keywords:** oscillator; THz; high output power; CMOS

#### **1. Introduction**

The terahertz (THz) frequency range, which is from 300 GHz to 3 THz, has recently gained much attention from researchers due to its wide range of applications such as high-speed communication, imaging security system, and spectroscopy [1,2]. In these applications, a high power and high frequency signal source is one of the most important components to create a system with superior quality. Among the technologies for designing a signal source, CMOS technology stands out as a reliable selection to build a high-quality signal source because of its low production cost and compact size. However, CMOS signal sources present some difficulties such as low maximum oscillation frequency (*fmax*) and low output power at the THz frequency range.

Though a fundamental frequency oscillator is widely adopted for generating an output signal having oscillation frequency smaller than *fmax* [3–7], but a fundamental frequency oscillator cannot generate a high frequency output signal that has oscillation frequency greater than *fmax*. Therefore, a harmonic frequency oscillator is a viable solution to overcome the low *fmax* of CMOS technology and to generate a high frequency output signal that has oscillation frequency greater than *fmax*. Nevertheless, only a limited output power extracted from a single oscillator core is a problem of harmonic frequency oscillator at this high frequency range [8,9].

This paper proposes a THz frequency CMOS coupled stack oscillator with a good output power level. The oscillator core uses a frequency selective negative resistance (FSNR) tank to increase the negative transconductance and the transformer-based topology to minimize the loss of the second harmonic power. The push-push topology is employed to generate a high oscillation frequency over *fmax* and multiple coupled oscillator cores to obtain a high output power. The proposed oscillator, implemented in a 65 nm bulk CMOS process, generates a maximum output power of −0.8 dBm at 350 GHz. In Section 2, the proposed signal source's structure is analyzed. Section 3 presents the measurement setups and measurement results of the proposed oscillator. Finally, Section 4 summarize the findings in this paper.

#### **2. The Proposed Signal Source**

Figure 1a shows a schematic of a conventional cross coupled oscillator (XCO). At the THz frequency, a conventional XCO suffers from low negative transconductance at the fundamental frequency and high loss at the second harmonic frequency because of the direct connection of a low gate impedance of transistors M1 and M2 to the second harmonic output path. In Figure 1b, a conventional stack oscillator with FSNR tank, implemented by transistors M3, M4, and inductor L2, is connected in parallel with the cross-coupled pair M1 and M2 to boost the total negative transconductance at the fundamental frequency, so a higher output power can be generated [2]. A novel stack oscillator, shown in Figure 1c, is proposed to minimize the loss at the second harmonic frequency of the conventional stack oscillator by connecting a transformer between gate and drain terminals of cross-coupled pair.

**Figure 1.** Schematics of (**a**) a conventional cross coupled oscillator (XCO), (**b**) a conventional stack oscillator, and (**c**) a proposed stack oscillator.

Figure 2 shows circuit simulation results for a negative transconductance at 180 GHz fundamental frequency of the conventional XCO, the conventional stack oscillator, and the proposed stack oscillator. All topologies have the same of transistor size W/L of 12 μm/60 nm, and the same voltage across the drain and source terminals of each transistor of 1V. The conventional XCO generates only 2 mS negative transconductance, and conventional stack oscillator generates 11.9 mS negative transconductance due to the extra negative transconductance added by FSNR tank. The negative transconductance of the proposed stack oscillator increases from 5.8 mS to 11.6 mS with a coupling factor k increases from 0.2 to 0.9.

**Figure 2.** Circuit simulation results of negative transconductance at the fundamental frequency of conventional XCO, conventional stack oscillator, and proposed stack oscillator.

The effectiveness of the transformer in the proposed stack oscillator in reducing the loss of the second harmonic output power is simulated and shown in Figure 3. In this simulation, we assume that both the conventional stack oscillator and the proposed stack oscillator generate 0 dBm power at the second harmonic frequency inside the oscillator tank. The gate impedance looking from the drain terminals of transistors in the proposed stack oscillator is increased with a decrease of the coupling factor k and increased from 3.5 Ω at k = 0.9 up to 39.7 Ω at k = 0.2 compared with that of the conventional stack oscillator. Therefore, the second harmonic output power of the proposed stack oscillator is improved from 0.4 dB at k = 0.9 up to 4.6 dB at k = 0.2 compared with that of the conventional stack oscillator.

**Figure 3.** Circuit simulation results of output power and gate impedance of conventional stack oscillator and proposed stack oscillator at the second harmonic frequency.

A combination of the FSNR tank and the transformer connected between gate and drain terminals of the cross-coupled pair in the proposed stack oscillator boosts the second harmonic output power. Figure 4 shows that the second harmonic output power of the proposed stack oscillator is higher than that of the conventional stack oscillator when k > 0.5. Since the minimum space between two metals at a top metal layer of the design process is 2 μm, a simulation result from the high frequency structure simulator (HFSS) that is one of ANSYS products [10] shows that a coplanar transformer has a maximum coupling factor k of 0.65. At k = 0.65, the output power of the proposed stack oscillator is higher than the output power of the conventional stack oscillator 1.7 dB, and the output power of the conventional XCO 14.6 dB.

**Figure 4.** Circuit simulation results of the second harmonic output power of XCO, conventional stack oscillator, and proposed stack oscillator.

To further improve the second harmonic output power, we propose a coupled stack oscillator, shown in Figure 5, with oscillator cores are the presented stack oscillators. To lock phase differences and oscillation frequencies between oscillator cores, the inductor L3 of the proposed stack oscillator is split into two inductors with the same inductance value of L3/2. These inductors are implemented as transmission lines TL1. One transmission line TL1 is connected to a gate of a FSNR transistor of the previous oscillator core, and another transmission line TL1 is connected to a gate of a FSNR transistor of the next oscillator core. A resistor RG is connected between two transmission lines TL1 to provide a gate bias voltage path for transistors M3 and M4, and to guarantee a differential operation between the adjacent oscillator cores. Transmission lines TL2 that are implemented at the drain terminals of transistors M3 and M4 allow a larger voltage swing at the fundamental frequency signal, so a higher output power can be obtained. Transmission lines TL3 combine the output power which is generated from each oscillator cores to an output port and perform output impedance matching at the second harmonic frequency.

**Figure 5.** Schematic of the proposed coupled stack oscillator.

#### **3. Measurement Results**

The proposed oscillator was fabricated in a 65 nm bulk CMOS process. Figure 6 shows a chip micrograph of the proposed stack coupled oscillator with a total implementation area of 549 <sup>×</sup> <sup>468</sup> <sup>μ</sup>m2. The output spectrum of the proposed oscillator was measured based on the spectrum measurement setup using an R&S FSW26 signal and spectrum analyzer, as shown in Figure 7a. A GGB DC Probe was connected to the power pads of the fabricated chip. The GGB DC probe with a GPPG pin configuration provided two paths to supply two different DC voltage levels that are a supply voltage VDD and a gate bias voltage VG to operate the fabricated circuit. The output pads were connected to a GGB model 500 B probe with GSG pin configuration to extract the output power. After that, the output power was conducted to a Farran WR-2 harmonic mixer. The Farran WR-2 down-conversion is a harmonic mixer with interface WR2 has a function of down-converting the frequency of the input signal by mixing input signal with a local oscillator (LO) signal. At the harmonic mixer, the output signal from the proposed stacked coupled oscillator was down-converted by mixing it with a LO signal generated from an R&S FSW26 signal and spectrum analyzer. The down-converted output signal from the harmonic mixer was received and the oscillation frequency was automatically calculated by the R&S FSW26 signal and spectrum analyzer. Figure 8a shows the measured oscillation frequency of

350 GHz. Figure 8b shows an oscillation frequency range of the proposed oscillator with a change of the supply voltage VDD from 2 V to 2.8 V and the gate bias voltage VG from 1 V to 1.4 V. As shown in Figure 8b, the oscillation frequency of the proposed oscillator increases with an increase of the supply voltage VDD and decrease with an increase of the gate bias voltage VG. The proposed oscillator has a minimum oscillation frequency of 345 GHz at VDD = 2 V and VG = 1.4 V and a maximum oscillation frequency of 353.2 GHz at VDD = 2.8 V and VG = 1 V.

Figure 7b shows a power measurement setup of the proposed stack coupled oscillator. The output power of the proposed coupled stack oscillator was measured by a PM5 power meter. The output pad was connected to a GGB model 500 B probe, a waveguide bend WR3, a waveguide tapper WR3.4-WR10, and a waveguide WR10 with insertion losses of 4 dB, 1 dB, 0.4 dB, and 0.3 dB, respectively. As shown in Figure 8c, the highest measured output power of the proposed coupled stack oscillator is 0.832 mW or −0.8 dBm at a supply voltage VDD of 2.8 V and a gate bias voltage VG of 1 V while the proposed stack coupled oscillator consumes 205 mW of DC power. Figure 8d shows an output power range of the proposed coupled oscillator. As shown in Figure 8d, the output power of the proposed coupled oscillator increases with an increase of the supply voltage VDD and decreases with an increase of the gate bias voltage VG. From overall oscillation frequency and output power measurement results, the proposed stacked coupled oscillator obtains a high frequency of 353.2 GHz with a high output power of −0.8 dBm at the same condition that is a high supply voltage VDD of 2.8 V and a low gate bias voltage VG of 1 V.

**Figure 6.** Chip micrograph of the proposed coupled stack oscillator.

**Figure 7.** (**a**) Output spectrum measurement setup; (**b**) output power measurement setup.

**Figure 8.** (**a**) Measured output spectrum, (**b**) oscillation frequency range, (**c**) measured the highest output power and (**d**) output power range of the proposed coupled stack oscillator.

Table 1 shows a comparison of the performance of the proposed oscillator with the state-of-the-art THz oscillators. Oscillators in [11–13] generate output signals at the fourth harmonic frequency, while the work in [14] generates an output signal at the second harmonic frequency with an unstack core oscillator structure. Similar to [14], this work also generates an output signal at the second harmonic frequency but with a stack core oscillator structure. Both a spectrum analyzer and a power meter can measure output power of the proposed oscillator, but the power measurement accuracy of each measurement device is different. Spectrum analyzer can accurately measure frequency spectrum but cannot accurately measure output power generated from oscillators. The reason of low accuracy of power measurement of a spectrum analyzer is that there is a harmonic mixer with a high loss of approximately 50 dBm in the spectrum measurement setup. This decreases power sensitivity of spectrum analyzer. In contrast, a power meter cannot measure frequency but can accurately measure output power generated from oscillators. The reason of high accuracy of power measurement of a power meter is that loss from measurement devices in the power measurement setup is low around several dBm. Therefore, power meter can show an accurate power measurement when calibration function is correctly applied. Because of these reasons, the output power of the proposed oscillator is −0.8 dBm. Among the state-of-the-art THz oscillators operating from 300 GHz to around 400 GHz, the proposed oscillator shows the highest output power of −0.8 dBm and the smallest implementation area of 0.25 mm2 while it has a high DC-to-RF efficiency of 0.41% at a high oscillation frequency of 350 GHz.


**Table 1.** Performance comparison with state-of-the-art terahertz (THz) oscillators.

#### **4. Conclusions**

This paper introduced a high-power THz CMOS signal source. The proposed signal source can generate a high output power level of −0.8 dBm at the THz frequency by employing an FSNR topology to increase the negative transconductance at the fundamental frequency and proposing a transformer which is connected between gate and drain terminals of cross-coupled pair to minimize the power loss at the second harmonic frequency. A coupled topology with the proposed coupled structure was also adopted to further increase the output power. Based on the verified measurement results, the proposed signal source is recommended operating with a supply voltage range from 2 V to 2.8 V.

**Author Contributions:** Conceptualization, T.D.N. and J.-P.H.; methodology, T.D.N. and J.-P.H.; circuit analysis, T.D.N. and J.-P.H.; investigation, T.D.N. and J.-P.H.; writing—original draft preparation, T.D.N.; writing—review and editing, T.D.N. and J.-P.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Korea Institute for Advancement of Technology (KIAT) grant funded by the Korea Government (MOTIE) (N0001883, The Competency Development Program for Industry Specialist). This work was also supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2018R1D1A1B07042607).

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Terahertz Displacement Sensing Based on Interface States of Hetero-Structures**

**Lan-Lan Xu 1,2, Ya-Xian Fan 1,3,\*, Huan Liu 1, Tao Zhang <sup>1</sup> and Zhi-Yong Tao 1,3,\***


Received: 10 July 2020; Accepted: 27 July 2020; Published: 28 July 2020

**Abstract:** Herein, we propose a nano displacement sensor based on the interface state of a terahertz hetero-structure waveguide. The waveguide consists of two periodically corrugated metallic tubes with different duty ratios, which can result in similar forbidden bands in their frequency spectra. It was found that the topological properties of these forbidden bands are different, and the hetero-structure can be formed by connecting these two waveguides. In the hetero-structure waveguide, the interface state of an extraordinary transmission can always arise within the former forbidden bands, the peak frequency of which is highly dependent on the cavity length at the interface of the two periodic waveguides. So, by carefully designing the structure's topological property, the hetero-structure waveguide can be efficiently used to produce a displacement sensor in the THz frequency range. The simulations show that the resolution of the displacement can be as small as 90 nm and the sensitivity can reach over 1.2 GHz/μm. Such a sensitive interface state of the proposed hetero-structure waveguide will greatly benefit THz applications of functional devices, including not only displacement sensors but also switches with high extinction ratios, tunable narrow-band filters, and frequency division multiplexers.

**Keywords:** resonances; periodic waveguides; reflection phases; topological properties

#### **1. Introduction**

In recent years, with the development of ultra-fast technologies, the research on terahertz (THz) technology has seen unprecedented progress [1–4]. THz waves have many unique advantages over the electromagnetic waves in the other bands, which allow THz technology to have considerable applications in some important areas, such as military, astronomy, radar, and medicine [5–8]. Due to its strong penetrability and low photonic energy, THz imaging technology will replace X-rays in medical examinations and will not cause harm to the human body [9]. It can also be used for detection in complex environments and identification of plastic weapons [10]. The characteristic spectra of many biomolecules and chemicals are also located in the THz band, including many drugs. So, it is also useful to employ THz waves in substance identification and biomedical research [11]. The broadband characteristics of THz waves result in their predictable applications in communication fields, and their wireless transmission speed can reach tens of Gb/s [12,13]. In the upcoming 6G Internet of Things, THz waves are also considered to be good candidates in short-range, bandwidth-aggressive services such as in the smart home scenario [14]. In THz systems, functional devices are essential to applications, including, of cause, displacement sensors. For example, in THz imaging, displacement sensing can correct the errors of relative motion between objects and probes, and it is expected to be adopted in calibrating the amplitude of characteristic peaks for different substances. In this era of interconnection of all things, most communications depend on THz waves, and displacement sensors can be integrated into smart devices to monitor and control their position changes.

The micro–nano displacement sensor as a device for high-precision monitoring has been used in automotive industry [15], small-scale manipulation [16,17], construction [18,19], micro-grippers [20], physiological sensing [21,22], and so on. The micro–nano displacement sensing technology of the communication optical band has been developed over many years, including plasmonic slot metamaterials [23], Fabry–Pérot interferometers [24], photonic crystal fibers [25], and so on. In 2011, Liu et al. reported a sensing structure with double-fiber Bragg gratings [26]. In 2014, Qu et al. presented an interferometric fiber-optic bending/micro-displacement sensor based on a plastic dual-core fiber with one end coated by a silver mirror [27]. In 2016, Gao et al. realized an optical displacement sensor based on anti-resonant reflecting guidance in a capillary covered hollow-core fiber [28]. However, a THz micro–nano displacement sensor of waveguide types that can be applied in THz systems without additional optical devices has not been reported yet. It will be very intriguing to realize THz micro–nano displacement sensing with high precision, small size, and easy integration. Hypersensitive THz displacement sensors could expand the applications of THz technology and pave the way for THz micro–nano positioning in the future smart life of all things connected.

Here, we propose a THz displacement sensor based on the hetero-structure waveguide, which can provide a sensitive spectrum response to a tiny displacement. Hetero-structures consist of semiconductor materials with different forbidden bands [29–31], which have been developed for artificial structures for years [32–36]. Further, the waveguides in the THz frequency range have been investigated numerically for functional devices [37,38]. The proposed hetero-structure contains a cylindrical waveguide with two different periodic corrugations on the wall. Based on their different topological properties, these two periodicities are used to generate an interface state, which can be recognized by a very narrow transmitted peak in its spectrum. It was found that the transmitted peak highly depends on the cavity length at the interface of two periodicities. Increasing the cavity length can result in red shift of the peak, which is very promising for use in fabricating a sensitive THz sensor. In the following section, the hetero-structure waveguide and its arising interface state are demonstrated. There is a transmitted peak arising in the former forbidden band due to the interface of the two periodic structures. The hetero-structure waveguide composed of two opaque periodic tubes become transparent at a certain frequency. The different topological properties of the two periodic structures can be explained by their reflection phases at the interface. The displacement THz sensor is proposed in Section 3 and the sensing performance is discussed in detail. Finally, the major findings about the super-high resolution and sensitivity are summarized.

#### **2. Hetero-Structure Waveguides**

Hetero-structure waveguides are usually combinations of multiple different tubes with unequal topological band gaps. Between each waveguide of the hetero-structures, interface states can always arise to produce an extraordinary transmitted peak in the former forbidden bands of periodic waveguides, which is very promising for high-resolution sensing due to its very narrow line width. Here, we propose a very simple corrugated waveguide system to demonstrate a THz micro–nano displacement sensor with very high precision. In waveguides with periodic wall corrugations, frequency gaps will appear around the resonant frequencies, in which the electromagnetic waves cannot pass through the structures. Bragg resonance will happen when the longitudinal wavenumbers of the same transverse modes satisfy the matching condition [39]. Connecting two periodic waveguides with similar Bragg gaps can result in an interface state with a very sharp transmitted peak in the overlapping frequency band gap when their topologies are different. These two waveguides have the same average radius *r*<sup>0</sup> and period Λ, the transmission spectra and geometry structures of which are

shown in Figure 1a–c. The duty ratio refers to the proportion of wide radius part in a period length, and it has been proved that different duty ratios can introduce different topological band gaps [40]. We selected different duty ratios 0.8 and 0.4 for Waveguides A and B, respectively, to achieve the different topologies.

In a hollow metallic cylindrical periodic waveguide, the lowest-order Bragg resonance happens at

$$f\_r = \frac{c}{2\pi} \sqrt{\frac{k\_r^2}{r\_0^2} + \left(\frac{\pi}{\Lambda}\right)^2} \tag{1}$$

for transverse magnetic (TM) waves with *kr* = 2.4048. To set the Bragg resonance around 1 THz, we selected the geometry parameters of the periodic waveguides as *R*<sup>I</sup> = 220 μm, *R*II = 180 μm, and Λ = 183 μm with *r*<sup>0</sup> = (*R*<sup>I</sup> + *R*II)/2 = 200 μm, where *R*<sup>I</sup> and *R*II are the wide and narrow radii of the structures, respectively. The hetero-structure waveguide was obtained by directly connecting the wide tube of Waveguide A and the narrow tube of Waveguide B.

We employed finite element method simulations on the waveguide structures with an axisymmetric model in COMSOL Multiphysics software. In the simulations, the refractive index of inside air was set to be 1, and perfect electrical boundary conditions were assigned to the walls of these three waveguides. As the THz source, a first-order TM mode was excited at the inlet of each waveguide, and the radiation condition was assigned to the outlet boundary. The 0.8–1.1 THz frequency range was selected with a step of 0.001 THz, and the electromagnetic fields were calculated in the whole waveguide.

**Figure 1.** Transmission spectrum and electric field *Ez* components of Waveguides A, B, and the hetero-structure of their combination. (**a**) The blue dash–dot, green dash, and red solid lines are the transmission spectra of Waveguides A and B and the hetero-structure, respectively. The electric fields *Ez* of Waveguides A (**b**) and B (**c**) and the hetero-structure (**d**) at 1.027 THz illustrate the energy attenuation and localization at the interface of the structure. The electric fields were normalized by their own maximum in each waveguide.

Defining the transmission coefficient *T* as the ratio of optical powers of the outlet and inlet, we calculated the transmission spectra of Waveguides A and B and the hetero-structure waveguide, and depicted them by the dash–dot, dashed, and solid lines in Figure 1a. It shows that Waveguide A has a band gap around 0.838–1.038 THz, and Waveguide B's is around 0.848–1.051 THz. The smaller duty ratio of Waveguide B leads to a small frequency shift of the whole Bragg gap to a higher frequency. However, these two waveguides have a common forbidden band in the frequency range of 0.848–1.038 THz, in which the THz radiation cannot pass through either Waveguide A or B. The frequency of 1.027 THz falls in this common forbidden band—that is to say, a THz wave at this frequency cannot pass through either of these two waveguides—but what a surprise that we find an extraordinary transmitted peak with a center frequency of 1.027 THz in the spectrum of the hetero-structure waveguide. The forbidden band becomes much wider than that of either of the two waveguides.

To verify the interface state arising, we also simulated the electric field distributions for these three different waveguides, and the *Ez* components of the electric fields at 1.027 THz are depicted in Figure 1b–d for Waveguides A and B and the hetero-structure, respectively. The electric fields were normalized by their own maxima in the figure. The THz waves enter the waveguide from the bottoms of Waveguides A and B in Figure 1b,c respectively. It can be observed that the THz wave decays along the direction of propagation. Fortunately, the frequency is very close to the edge of the forbidden bands. So, we find that Waveguide B with a smaller duty ratio is much more effective for THz attenuation. In any case, the THz radiation at 1.027 THz cannot pass through either Waveguide A or B. When we connect these two waveguides and excite a THz wave with the first TM mode at the left side of the hetero-structure waveguide, as shown in Figure 1d, the situation turns out to be totally different. The THz waves accumulate around the interface of Waveguides A and B, which is known as the interface state. Due to the energy accumulation, the former opaque waveguides become transparent to a special frequency THz wave, as shown in Figure 1a. It is because of the normalization to the maximum electric field that the *Ez* component at the outlet is smaller than 1. Based on the transmission spectrum and the electric field distribution, we confirm the interface state arising in the proposed hetero-structure waveguide.

The remarkable transmission feature is due to the different topological properties of the two waveguides, which can be identified by the Zak phases of the two Bragg bands [40]. It is also more convenient to investigate the reflection phase of each waveguide at the interface. If the phases have the same sign, the related Bragg gaps are of a similar topology. Otherwise, they are topologically different, and the interface state arises.

To achieve the reflection phase of each waveguide, we connected a straight tube to the corrugated one and simulated the *Ez* component of electric fields with an incident TM mode from the straight tube at 1.027 THz. A straight tube with a length of 1000 μm and radius of 200 μm was connected to the wide radius port of Waveguide A. For Waveguide B, it was connected to the narrow radius port. Thus, the reflection properties at the interface of each waveguide could be observed. The same straight tube with a perfect electrical boundary at the other end was also simulated for reference. The reflected components of the electric fields are shown in Figure 2a–c for Waveguide A, the perfect electrical boundary, and Waveguide B, respectively. For convenience, we also depict the amplitude of *Ez* by solid lines. With the aid of the added dashed line, we can conclude that the reflection phase of Waveguide A is delayed while that of Waveguide B is advanced when considering the perfect electrical boundary reference as a zero-phase case. The reflection phases of Waveguides A and B have opposite signs, indicating the topological difference of the two Bragg gaps. So, the interface state arises at 1.027 THz, where we found a narrow transmitted peak in the spectrum. Such an extraordinary peak with very narrow line width would be a good candidate for THz sensing applications.

**Figure 2.** *Ez* components of reflected electric fields at 1.027 THz for (**a**) Waveguide A, (**b**) the perfect electrical boundary, and (**c**) Waveguide B. The reflected phase of Waveguide A is delayed while that of Waveguide B is advanced relative to the THz waves reflected by the perfect electrical boundary.

#### **3. Micro–Nano Displacement Sensing**

To realize micro–nano displacement sensing, we propose the hetero-structure waveguide (Figure 3a) composed of two tubes with average inner radius 200 μm and period 183 μm based on the above analysis. The tube wall is suggested to be 10 μm thick silver (Ag), which has low loss in the THz frequency range. So, the outer radii are 190 μm and 230 μm for the narrow and wide parts, respectively. According to the duty ratios, the lengths of the wide and narrow tubes are 146.4 μm and 36.6 μm, respectively, for Waveguide A, whereas they are 73.2 μm and 109.8 μm for Waveguide B. To fabricate an integrated device, we have to increase the length of the wide tube at the right end of Waveguide A and add a ring at the left end of Waveguide B. The increased length is 276 μm and the outer radius of the ring should be 220 μm to make sure that they can be connected. The length can be mechanically changed within the range of 20–120 μm. Although the measurement cannot start from 0 μm due to the length of the narrow tube in Waveguide B, the measurement range of displacement can still reach 100 μm. The number of periods in each waveguide is 5.

We also performed simulations on different combinations of duty ratios. The duty ratios of Waveguides A and B were selected from 0.1 to 0.9 in intervals of 0.1. The results show that all connections of different duty ratios can create a similar extraordinary transmitted peak, that is to say, the interface state between the two periodic waveguides always arises in the former Bragg gaps due to the different topologies. However, the bandwidth and frequency shift of the peaks highly rely on the duty ratios. Only the duty ratio combination of 0.8 and 0.4 can result in the narrowest bandwidth and maximum displacement, which could be of extreme benefit for practical applications. So, the proposed structure with duty ratios 0.8 and 0.4 was analyzed in detail for THz displacement sensing.

In the displacement sensing, we first fix Waveguide A, then adjust the Waveguide B to a relative position to be measured, and finally fix Waveguide B to that position. In this way, Waveguide B moves relative to Waveguide A, which increases the length of the cavity between the two waveguides. The THz wave is incident from the narrow radius of Waveguide A and emitted from the wide radius of Waveguide B. The frequency of the transmitted peak shifts with the displacement, so that the hetero-structure waveguide realizes displacement sensing. The simulated transmission for different displacements is depicted in Figure 3b by different lines. The center frequency of the transmitted peak is 1.002 THz when the displacement is 20 μm in the hetero-structure waveguide. When Waveguide B moves away from Waveguide A, the length of the middle cylindrical waveguide increases and the peak frequency shifts to the low frequency range. All the transmissions are above 0.85, and the highest transmission of 0.948 is obtained when the displacement is 120 μm.

**Figure 3.** The THz micro–nano displacement sensor and its sensing performance. (**a**) Structure diagram of the hetero-structure waveguide sensor. The dark and light gray parts are Waveguides A and B, respectively. The red dashed line denotes the zero-displacement point and the inset is a magnification of the shifting structure with scales. (**b**) Transmitted peaks for the different displacements according to the scales. (**c**) Peak frequency shifting with increasing displacement.

To measure the displacement by THz waves, we define the frequency shift Δ*f* from the frequency of 1.026 THz at 0 μm. The former peak moves from 1.027 THz to 1.026 THz for the 0 μm waveguide because the real dielectric constant of Ag is considered in the simulations. The frequency shift Δ*f* according to the displacement is marked in Figure 3c by the circles, and we performed a linear fit (the dashed line) as follows:

$$
\Delta f = -1.260 \times L \tag{2}
$$

where *L* is the displacement in micrometers, and the frequency shift is in gigahertz. The fitting results show that when the hetero-structure waveguide is stretched 1 μm, the transmitted peak moves 1.260 GHz to a lower frequency. When *L* = 80 μm, the narrowest bandwidth is 2.580 GHz, and when *L* = 20 μm, the maximum bandwidth is 4.610 GHz. The maximum displacement that can be measured by the hetero-structure waveguide is 100 μm, the adjustable range of frequency is 0.877–1.002 THz, and the whole bandwidth is 124.5 GHz. So, the sensitivity of such a waveguide-type sensor can reach over 1.2 GHz/μm, and the minimum resolvable length is 2.073 μm when the displacement *L* is around 80 μm.

To realize the proposed structure, there are two ideas for fabrication. The first idea is to make a hollow metallic waveguide with substrates outside, as shown in Figure 4a. The deep lithography process can be employed to machine two half-cylinder polymers, and the metallic materials, such as Ag, can be sputtered on the two parts. To form the tube, we can hold the two parts together and eliminate a thin layer at the end of Waveguide B. The second idea is to produce a corrugated polymer core by 3D printing, as shown in Figure 4b. The two structures both end at the narrow radius parts. A silver film can be coated on the surface of the corrugated core, and a capillary coated with a silver film inside can be used to connect the two waveguides. Thus, the shifting parts are still hollow. When the proposed structure is ready, Waveguides A and B can be fixed to the two holders using epoxy glue [28]. With the aid of a 3D nano-positioning stage or optical micromanipulation, we can assemble the sensor to the test structures or THz systems.

**Figure 4.** Sketch maps of the device fabrication process with the substrates outside (**a**) or inside (**b**).

The number of periods is also an important parameter for the hetero-structure waveguide sensor and can directly affect its resolution. Here we studied the effects of the number of periods on the sensing performance. The number of periods of the two waveguides takes the same value and is denoted by *N*. The value of *N* ranges from 4 to 9, while the length *L* is fixed at 80 μm. The transmission spectra and the measurement resolutions of the micro–nano displacement sensor are shown in Figure 5a,b, respectively, in the cases of different *N*. The bandwidth becomes extremely narrow as the number of periods increases, but when the number of periods is greater than 8, the transmission gets a little bit smaller. When *N* = 9, the transmission is just over 0.2. When the number of periods is smaller than 7, the transmissions are all greater than 0.5. The variation of the measurement resolution according to

the number of periods *N* for the hetero-structure sensor is also depicted in Figure 5b by the crosses, with its fitting curve (the solid line) as

$$Rs = 7063 \times N^{-5.083} \tag{3}$$

**Figure 5.** Transmitted peaks (**a**) and measurement resolutions (**b**) for different numbers of periods.

The resolution of the sensor is defined as its smallest measurable displacement, which is inversely proportional to the fifth power of *N*. When increasing the number of periods, we can greatly improve the performance of the sensor. The resolution reaches 282 nm for *N* = 7, while it gets as small as 90 nm for *N* = 9. The related sensitivity is over 1.2 GHz/μm. This is a highly sensitive THz nano displacement sensor that can be used in various applications involving accurate displacement measurements. It can also be extended to a wider range of applications when cascade hetero-structure waveguides are considered.

Through simulation of the hetero-structure waveguide, it was proved that the structure can produce a very narrow THz pulse. By changing the connection length between Waveguides A and B, the frequency of the transmitted peak moves towards the low frequency range, thus determining the micro–nano displacement sensing function of the proposed structure in the THz region. For measuring car body paints, a THz transceiver was mounted on a robot [41]. The proposed sensor can be integrated to monitor tiny movements of the mechanical arms without any additional sources. Based on the recorded THz data, the extracted layer thickness can be corrected. In the Internet of Things, THz functional devices play a key role in communication and intelligence applications [42]. The integrated displacement sensor can not only provide more accurate locations of communication

nodes, but also monitor subtle changes of smart terminals. The structure design and performance simulations confirmed THz displacement sensing based on the hetero-structure waveguide.

#### **4. Conclusions**

We proposed a micro–nano displacement sensor based on hetero-structure waveguides in the THz frequency range. It is composed of two periodically corrugated waveguides that have similar Bragg forbidden bands. The THz waves cannot pass through either of these two periodic waveguides in the common frequency range of 0.848–1.038 THz. The topological analysis indicates that the Bragg gaps can present different topological properties, which can create an interface state with a very sharp transmitted peak in the THz spectrum when these two periodic waveguides are connected. Due to the topological difference of the Bragg gaps, the hetero-structure waveguide turns transparent at a certain frequency, where both the waveguides are otherwise opaque. Based on the interface state's induced transmission, we proposed a THz micro–nano displacement sensor by carefully connecting two corrugated waveguides. When the two waveguides are held by different structures, their relative displacement can be achieved by measuring the shift of transmission peaks, and the resolution can be improved by increasing the number of periods. The proposed hetero-structure waveguide-type sensor has excellent performance, such as a wide measurable range of 100 μm, minimum resolution of 90 nm, and maximum sensitivity of over 1.2 GHz/μm, which allow it various applications in many fields, such as chemical and biomedical sensing, micro-manipulation, imaging, and intelligent control. Besides displacement sensing applications, the proposed interface state of the hetero-structure waveguide can also be applied to other functional devices, such as switches, filters, and frequency division multiplexers.

**Author Contributions:** Conceptualization, Y.-X.F. and Z.-Y.T.; methodology, H.L. and L.-L.X.; validation, L.-L.X., and H.L.; formal analysis, Y.-X.F., T.Z., and Z.-Y.T.; writing—original draft preparation, L.-L.X.; writing—review and editing, Y.-X.F. and Z.-Y.T.; visualization, L.-L.X.; supervision, Y.-X.F. and Z.-Y.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Dean Project of Guangxi Key Laboratory of Wireless Broadband Communication and Signal Processing, the National Natural Science Foundation of China (11374071), and the Natural Science Foundation of Heilongjiang Province, China (A2018004).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **On-Chip Terahertz Detector Designed with Inset-Feed Rectangular Patch Antenna and Catadioptric Lens**

#### **Fan Zhao 1, Luhong Mao 1, Weilian Guo 2, Sheng Xie 2,\* and Clarence Augustine T. H. Tee <sup>3</sup>**


Received: 6 May 2020; Accepted: 19 June 2020; Published: 24 June 2020

**Abstract:** This study proposes an on-chip terahertz (THz) detector designed with on-chip inset-feed rectangular patch antenna and catadioptric lens. The detector incorporates a dual antenna and dual NMOSFET structure. Radiation efficiency of the antenna reached 89.4% with 6.89 dB gain by optimizing the antenna inset-feed and micro-strip line sizes. Simulated impedance was 85.55 − j19.81 Ω, and the impedance of the antenna with the ZEONEX horn-like catadioptric lens was 117.03 − j20.28 Ω. Maximum analyzed gain of two on-chip antennas with catadioptric lens was 17.14 dB resonating at 267 GHz. Maximum experimental gain of two on-chip patch antennas was 4.5 dB at 260 GHz, increasing to 10.67 dB at 250 GHz with the catadioptric lens. The proposed on-chip rectangular inset-feed patch antenna has a simple structure, compatible with CMOS processing and easily implemented. The horn-like catadioptric lens was integrated into the front end of the detector chip and hence is easily molded and manufactured, and it effectively reduced terahertz power absorption by the chip substrate. This greatly improved the detector responsivity and provided very high gain. Corresponding detector voltage responsivity with and without the lens was 95.67 kV/W with *NEP* = 12.8 pW/Hz0.5 at 250 GHz, and 19.2 kV/W with *NEP* = 67.2 pW/Hz0.5 at 260 GHz, respectively.

**Keywords:** THz detector; rectangular inset-feed patch antenna; catadioptric horn-like lens; CMOS process

#### **1. Introduction**

Terahertz (THz) detectors have been recently employed to assist security aspects for high-speed data communication, spectroscopy, concealed weapon detection, short-range radar, aviation assistance, cancer detection, and many more applications [1–4]. The THz spectrum region is in the middle of the microwave and infrared spectra and is sometimes known as sub-millimeter waves. Terahertz radiation ranges from 3 mm to 30 μm with corresponding frequencies of 0.1–10 THz [5–9], which penetrate plastics, paper, and wood. The THz region is sometimes called the "THz Gap" [10–12] because optical and microwave theory do not fully apply for this frequency range.

Specific terahertz antennas are required to radiate and receive terahertz waves, acting as transducers to convert high-frequency current or waveguide energy into spatial electromagnetic wave energy, and directional radiation for transmission or the reverse conversion for receiving. However, designing an on-chip antenna in the terahertz band is somewhat difficult, partly because the system's dynamic range and transmission distance between the THz wave source and detector are influenced by antenna gain. Dielectric layers between the CMOS top and bottom metal layers are too thin to construct a

high gain antenna [13,14], and lossy silicon substrates significantly reduce on-chip patch antenna performance. However, problems can be solved with reasonable on-chip antenna design considering antenna gain and bandwidth.

Annular on-chip single-ended slot antennas can achieve approximately 4.5 dB gain with 50% radiation efficiency [15]. Although directional front-end antennas are unsuitable for THz detectors [16,17], Taeguk log periodic dipole antennas (LPDAs) can achieve a maximum 7.8 dBi gain at 73 GHz and circular LPDA antennas can achieve a maximum 9.25 dBi gain at 85 GHz [17,18]. The total size of these two antennas is 4.5 <sup>×</sup> 10 mm2 and they have complicated structures. Rectangular antennas are the most common on-chip design, leveraging simple structure and being compatible with standard CMOS processing [18,19]. The proposed rectangular antenna from [20] was 237.5 <sup>×</sup> <sup>317</sup> <sup>μ</sup>m2 and operated at 300 GHz, but only achieved −2.1 dB gain. In contrast, the proposed THz dielectric resonator antenna (DRA) [21] employed a 500 μm resonator to greatly enhance antenna gain. The DRA was 290–310 μm wide and 390–410 μm long, considerably larger than the traditional rectangular patch antenna, and provided measured 6.7 dB maximum gain at 327 GHz. Thus, there is considerable ongoing research to improve THz detector antenna gain.

This study proposes an on-chip terahertz detector with on-chip rectangular inset-feed patch antennas that was implemented using a United Microelectronics Corporation (UMC) 0.18 μm standard CMOS process and ZEONEX RS420 (ZEON Corporation, Tokyo, Japan) horn-like catadioptric lens. Section 2 discusses the antenna design and Section 3 introduces the detector structure, combining plasma wave-based terahertz detection in NMOSFETs (TeraFETs). Section 4 describes the horn-like catadioptric lens and Section 5 details testing for the prototype proposed THz detector antenna and lens. Conclusions are presented in Section 6.

#### **2. On-Chip THz Antenna**

The UMC 0.18 μm CMOS process provides six metal layers with intermediate dielectric layers (SiO2) between them. The CMOS process can be used to design not only digital and analog circuits, but also optoelectronic devices [22–24]. The major advantage is that signals detected by the detector can be amplified and processed on the chip. However, silicon is lossy in the THz frequency range due to the short wavelength. Therefore, we implemented the antenna inset-feed patch in the Metal 6 (top metal) layer, using the Metal 1 (bottom metal) layer as a ground plane to reflect radiated power back to the NMOSFETs, hence reducing THz signal penetration into the lossy silicon substrate [20,21]. Metal 6 is 2.06 μm thick and the SiO2 CMOS process layer is 6.32 μm thick. Radiation efficiency was low because these layers were too thin to emit an EM field, e.g., a similar antenna design achieved only approximately 20% radiation efficiency in simulation [14,21], with −1.6 and 0.1 dB gains, respectively. In contrast, the proposed antenna achieved 89.4% simulated radiation efficiency and 6.89 dB simulated gain. Figure 1 shows a cross-section of the proposed CMOS structure and Figure 2 shows a suitable patch antenna design using UMC 0.18 μm CMOS technology. Patch height, dielectric substrate properties, and patch conductor thickness are fixed depending on the specific UMC technology employed. We adopted substrate thinning and increased the ground plane size to increase antenna gain, with a micro-strip feed line.

Rectangular patch antennas can fully meet CMOS process design rules, in contrast with circle, ring, and other irregularly shaped antennas. Harrington [25,26] provided analytical expressions to explain the relationship between antenna performance and this separation. The empirical relationships for rectangular patches can be expressed as follows [13,14]:

$$\mathcal{W} = \frac{\mathbf{c}}{2f\_0} \sqrt{\frac{2}{\varepsilon\_{SiO\_2}}} \tag{1}$$

$$\varepsilon\_{\rm eff} = \frac{\varepsilon\_{\rm SiO\_2} + 1}{2} + \frac{\varepsilon\_{\rm SiO\_2} - 1}{2} \left( 1 + 12 \frac{h}{W} \right)^{-1/2} \tag{2}$$

$$
\Delta L = 0.412h \frac{(\varepsilon\_{\rm eff} + 0.3) \left(W/h + 0.264\right)}{(\varepsilon\_{\rm eff} - 0.258) \left(W/h + 0.8\right)}\tag{3}
$$

and

$$L = \frac{c}{2f0\sqrt{\varepsilon\_{\text{eff}}}} - 2\Delta L \tag{4}$$

where *W* is the radiation patch width, *c* is the speed of light in free space, *f* <sup>0</sup> is the operating frequency, εeff is the effective dielectric constant, *h* = 6.32 μm (for the UMC 0.18 μm CMOS process) is the dielectric thickness between the patch and ground, ε*SiO*<sup>2</sup> is the SiO2 dielectric coefficient, and *L* is the patch length.

**Figure 1.** Cross-sectional view for the proposed United Microelectronics Corporation (UMC) 0.18 μm CMOS design.

**Figure 2.** Structures for the proposed on-chip patch antenna.

Figure 2 shows the patch antenna structure, where *Wg* is the ground plane width, *Lg* is the ground plane length, *Win* is the insertion width, *Lin* is the insertion distance, *W1* is the micro-strip line width, and *L1* is the micro-strip line length.

Micro-strip and impedance matching networks were used to increase the input impedance. Table 1 shows the dimensions and performances of the patch antennas. Resonance is approximately 270 GHz and bandwidth is the region where *S11* < −10 dB. Bandwidth for the patch antenna = 1.5 GHz with 271 GHz center frequency, and gain = 6.89 dB. Patch antenna (without lens) gain was higher than for other antennas, but still insufficient to provide a practical detector.

To ensure maximum power transmission, half the NMOSFET (TeraFET) channel impedance should be conjugated with the antenna output impedance. NMOSFET channel impedance depends on the gate voltage, hence the NMOSFETs should operate below the sub-threshold to obtain high impedance, forming a two-dimensional electronic fluid. The NMOSFET gate was powered by the antenna and matching network comprising a microstrip line and open stub line to achieve maximum power transmission. Performance comparison of terahertz antenna and lens are shown in Table 2, and without a lens or DRA, the patch antenna proposed in this study gets the highest gain of all.


**Table 1.** Proposed on-chip rectangular inset-feed patch antenna dimensions and performances [14].



Antenna radiation efficiency η*rad* is defined as the ratio of desired output power to supplied input power:

$$\eta\_{\rm rad} = \frac{P\_{\rm rad}}{P\_{\rm in}} = \frac{P\_{\rm in} - P\_{\rm loss}}{P\_{\rm in}} = 1 - \frac{P\_{\rm loss}}{P\_{\rm in}} \tag{5}$$

where *P*rad is power radiated by the antenna, *P*in is power supplied to the antenna input, and *P*loss is power lost in the antenna. Other factors could also contribute to effective transmitted power loss, including impedance mismatch at antenna input, or receiving antenna polarization mismatch. However, these losses are external to the antenna and could be eliminated by proper matching networks, or proper receiving antenna choice and positioning. Therefore, these losses are not usually attributed to the antenna, compared with dissipative losses due to metal conductivity or dielectric loss within the antenna.

#### **3. Terahertz Detector Circuit**

Figure 3a shows the proposed detector structure. The antenna output port is connected to the matching network, and the network is connected to an NMOSFET (TeraFET) for improved power transfer efficiency. DC photoresponse Δ*U* of the on-chip amplifier output terminal was measured with an SR830 (Standard Research System, INC, Sunnyvale, CA, USA) lock-in amplifier which measured the Δ*U* amplitude submerged by noise at a determined frequency. Thus, the detector is thermal noise limited, and the detector also includes a dual antenna and dual NMOSFET (TeraFET) structure, which provides degree of noise suppression.

**Figure 3.** (**a**) MOSFET detector structure and (**b**) matching network between on-chip antenna and NMOSFET.

Antenna impedance is the ratio of input voltage to input current at the antenna feed. The best-case scenario is that antenna impedance is purely resistive and equal to half of the characteristic NMOSFET (TeraFET) impedance. There is no power reflection at the feeder terminal and no standing wave at the feed line, and antenna impedance changes slowly with frequency. Ideal matching will eliminate reactance. The NMOSFET's characteristic resistive impedance can be adjusted by increasing the applied voltage for better performance. Impedance matching between the antenna and NMOSFET (TeraFET) was achieved using an L-type matching network comprising a microstrip open-stub and microstrip line section to reduce the imaginary part magnitude as much as possible through the matching network, as shown in Figure 3b. Selected section dimensions were *L2* = 105 μm, *W2* = 13.6 μm, *L3* = 222 μm, and *W3* = 13.36 μm.

Figure 4 shows the circuit diagram for the proposed readout amplifier, comprising two stages. Stage 1 uses a common-source structure with large differential NMOS input pair (M1 and M2), since increased size can reduce input-referred flicker noise. M3 and M4 are also large to similarly reduce any contribution to flicker noise. M5 and M6 operate in their linear region, acting as resistors to provide common-mode feedback. C0 is a 10 pF capacitor with larger equivalent resistance at low frequency. M8 must operate in the sub-threshold region to provide direct current bias for M1 and M2 to ensure that the alternating current signal passes through the capacitor to M2 and M7 gate.

**Figure 4.** Proposed low-noise amplifier (LNA).

Stage 2 uses a PMOS input device with a common-source single-ended structure. The R and C provide Miller compensation for circuit stability when operated as a closed loop.

The proposed on-chip low-noise amplifier (LNA) shown in Figure 4 compensates for low-gain antennas. Two key issues must be solved during circuit design, namely low-noise performance and amplification ability under low frequency. The amplifier, fabricated in the standard 0.18 μm CMOS process, provides 42 dB voltage gain and 4 MHz 3 dB bandwidth with capacitor feedback. Simulated input-referred noise is 17 nV/Hz1/<sup>2</sup> at 10 kHz and 113 nV/Hz1/<sup>2</sup> at 310 Hz. Amplifier power consumption is 3.5 mW with 1.8 V supply voltage. Figure 5 shows the input-referred noise curve.

**Figure 5.** Low-noise amplifier (LNA)'s input-referred noise.

#### **4. Catadioptric Horn-Like Lens**

Traditional catadioptric optical systems are commonly used for optical telescopes, telephoto lenses, early lighthouse focusing systems, searchlights, etc., with refraction achieved by lenses and reflection by curved mirrors. This lens can be easily integrated with THz detectors in contrast with conventional quasi-optical components, as shown in Figure 6. Terahertz detector front-end antennas have been physically coupled to back-end silicon lens previously to yield a compact system [10]. Therefore, this study proposes a THz detector with front-end antenna and lens symmetric about the z-axis to reduce signal loss in the substrate.

**Figure 6.** Cross-sectional view for the proposed catadioptric lens with inset 3D view of the lens.

Figure 7 shows a simulated lens, where the lens' out-radius *R1* = 3 mm and in-radius *R2* = 0.6 mm (*R1* is about ελ*0*, where λ*<sup>0</sup>* is the free-space wavelength [29]). Catadioptric lens length *L4* = 6 mm, corresponding to 2ελ*<sup>0</sup>* at 270 GHz. Length between out-radius and in-radius *L5* = 2 mm, approximately λ*0*. When A1, A2, and A3 rays radiate from the source, they are totally reflected at the reflection plane (B1, B2, and B3, respectively), which are then refracted at the refraction plane (C1, C2, and C3, respectively).

**Figure 7.** Simulated gain at 280 GHz (**a**,**b**) individual patch antenna, (**c**,**d**) two patch antennas working together, and (**e**,**f**) two patch antennas with catadioptric lens. Red and brown lines represent 2D simulated radiation pattern along Phi = 0◦ and 90◦ planes, respectively.

The THz wave power received by the antenna is proportional to the antenna area, hence the two antennas receive approximately twice the power as a single antenna. The signal is converted to a direct voltage signal by the detector. Although the two NMOSFETs (TeraFETs) are connected in parallel, the output voltage does not increase but the output current doubles. Since the equivalent impedance

for the low-noise amplifier input is large, the output current is converted into a voltage, hence doubling the voltage signal after passing through the low-noise amplifier.

Figures 6 and 7 show that the refracted rays are distributed and converged to the z-axis, and the distribution provides up to 17.14 dB total gain, considerably higher than that achieved without the lens. The catadioptric dielectric lens is easily fabricated and illuminated compared with a silicon lens [10]. Figure 8 shows *S11*, gain, and efficiency with respect to frequency, where Port 1 is shown in Figure 2. Figure 9b shows that the catadioptric dielectric lens also increases antenna impedance.

**Figure 8.** Simulation results for (**a**) *S11*, (**b**) gain, and (**c**) efficiency.

**Figure 9.** Output impedance: (**a**) patch antenna and (**b**) two patch antennas with catadioptric lens.

#### **5. Terahertz Chip Measurements**

The THz detector performance was modelled using Dyakonov–Shur plasma wave theory. Plasma waves at the insulator–metal interface can not only achieve THz wave detection but also achieve power amplification [11,30], where Δ*U* is the measured voltage from the SR830 at the amplifier output terminal, as shown in Figure 3a [31], and there is a positive correlation between Δ*U* and received power. Plasma waves are usually overdamped in CMOS structures [32,33], hence we propose a non-resonant broadband detector [34].

The method in [31] was used to determine voltage responsivity *RV* for a detector as follows:

$$R\_V = \frac{\Delta lI}{P\_{\rm det}} = \frac{\int\_0^L E(\mathbf{x})d\mathbf{x}}{L\_{THz}A\_{\rm det}}\tag{6}$$

where *Pdet* is the THz power received by antennas, *L* is the length of the NMOSFET (TeraFET); *E* is the electric field intensity caused by terahertz waves, *LTHz* is the THz power density on the antennas measured with a large aperture THz power meter [31,33,35,36], as shown in Table 3, and *Adet* <sup>≈</sup> 0.075 mm<sup>2</sup> is the rectangular inset-feed patch antenna size:

$$G\_A = \frac{\Delta U}{G \tau \left(\frac{\lambda}{4\pi R}\right)^2 R\_V P\_{BWO}}\tag{7}$$

following [21], where *GT* is the total gain due to the first and second lenses, and on-chip and lock-in amplifiers, as shown in Figure 10b, *R* = 40 cm is the distance between the backward wave oscillator (BWO) and detector, *PBWO* is the power of the BWO wave source [21], as shown in Table 3, and λ is the wavelength. By adjusting the position of the lenses and the THz power meter, the THz power meter position of maximum *LTHz* is recorded, then the THz power meter is replaced with detector chip.

**Figure 10.** (**a**) Measurement setup for the detectors, (**b**) micro-photo of the chip, (**c**) detector test platform, (**d**) *RV* and *NEP*, and (**e**) gain.


**Table 3.** NMOSFET test results.

The gain of the horn-like lens is as follows:

$$\mathbf{G}\_L = \frac{\mathbf{R}\_{Vavith\ lens}}{\mathbf{R}\_{Vavithout\ lens}} \tag{8}$$

NMOSFET channel thermal noise is the dominant noise source for a non-current biased NMOSFET detector. Noise equivalent power (NEP) determines the detector noise component with respect to the particular wavelength and measurement bandwidth, and represents the minimum optical power required for output signal-to-noise ratio = 1 [37]. Since the on-chip amplifier and detector are integrated on the same chip, low-noise amplifier noise cannot be measured separately. However, simulation shows low-noise amplifier *NEP* to be very small, hence amplifier flicker noise was negligible and need not be considered. Therefore, we estimated the detector *NEP* as follows:

$$NEP = \sqrt{4kTR\_{ds}}/R\_V\tag{9}$$

where *k* is the Boltzmann constant, *T* is the measurement environment temperature (nominally 300 K), and *Rds* is half of the drain-source resistance.

The NMOSFET threshold voltage was approximately 0.45 V. The detectors were tested with gate voltages from 0.15 V to 0.36 V and bias voltage = 0.238 V for maximum *RV*. The NMOSFET is most suitable to operate in the sub-threshold region, forming a two-dimensional electronic fluid, increasing channel resistance sufficiently, and most likely to obtain maximum *RV*.

Figure 10e shows that the detector with catadioptric dielectric lens achieved *RV* = 95.67 kV/W with *NEP* = 12.8 pW/Hz0.5 at 250 GHz, whereas it achieved *RV* = 19.2 kV/W with *NEP* = 67.2 pW/Hz0.5 at 260 GHz without the lens. Comparing Figure 10d with Figure 8, simulated frequencies for maximum *RV* differed from the measured case. The most likely cause was fabrication error. Figure 10e shows patch antenna gain with and without catadioptric lens calculated from Equations (6)–(8). *GA* is relatively meaningless due to the on-chip and lock-in amplifiers, but *GL* is accurate. Patch antenna gain with a catadioptric lens was slightly lower than the simulation result.

#### **6. Conclusions**

This study proposed a THz rectangular inset-feed patch antenna that can be easily achieved in CMOS technology and can be integrated perfectly with a low-noise amplifier. However, the antenna has narrow bandwidth and is sensitive to dielectric constant and shape. The dielectric constant cannot be changed by the circuit and antenna designer for standard CMOS processing, but antenna impedances and operating frequency can be controlled by reasonable on-chip antenna design considering antenna gain and bandwidth. A front-end ZEONEX RS420 catadioptric horn-like lens greatly improved voltage responsivity of the THz detector.

Two patch antennas with lens achieved 17.14 dB maximum simulated gain at 267 GHz, while the gain of two patch antennas is 4.5 dB at 260 GHz and the gain of two antennas with catadioptric lens is 10.67 dB at 250 GHz.

**Author Contributions:** Methodology, Investigation, Writing—original draft, and Data curation, F.Z.; Conceptualization, Supervision, and Project administration, L.M.; Resources, W.G.; Funding acquisition, S.X.; Writing—review and editing, C.A.T.H.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Natural Science Foundation of China (Grant No. 51425502) and the Tianjin Natural Science Foundation (Grant Nos. 18JCQNJC04800 and 18JCZDJC31800).

**Acknowledgments:** The authors wish to thank Cunlin Zhang, Physics Department, Capital Normal University, Beijing, China, for providing a THz BWO source to measure the detector.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Terahertz Synthetic Aperture Imaging with a Light Field Imaging System**

#### **Nanfang Lyu, Jian Zuo, Yuanmeng Zhao and Cunlin Zhang \***

Key Laboratory of Terahertz Optoelectronics, Ministry of Education, Beijing Key Laboratory for Terahertz Spectroscopy and Imaging, and Beijing Advanced Innovation Center for Imaging Technology, Department of Physics, Capital Normal University, 105th West 3rd Ring Road North, Beijing 100048, China; 2150602040@cnu.edu.cn (N.L.); jian.zuo@cnu.edu.cn (J.Z.); zhao.yuanmeng@cnu.edu.cn (Y.Z.)

**\*** Correspondence: cunlin\_zhang@cnu.edu.cn; Tel.: +86-10-6898-0838

Received: 29 February 2020; Accepted: 11 May 2020; Published: 18 May 2020

**Abstract:** In terahertz imaging systems based on Gaussian beam active illumination and focal plane array detectors, severe image distortion has been observed, which significantly reduces the resolving power of the imaging system. To solve this problem, a novel computational method, Light Field Imaging (LFI), has been introduced for terahertz imaging. A conventional transmission-type terahertz imaging system based on a gas-pumped terahertz source and terahertz Focal Plane Array Detectors (FPA) arrays is established to analyze the problem of image distortion. An experimental virtual camera array terahertz LFI system is also established. With the acquisition and reconstruction of synthetic aperture terahertz light fields, the improvement on resolving power and SNR performance have been validated.

**Keywords:** terahertz imaging; light field imaging; synthetic aperture imaging; image distortion; resolving power

#### **1. Introduction**

Terahertz imaging is a novel imaging method with promising application fields. Terahertz waves are electromagnetic waves with a wavelength between 30 and 3000 μm or a frequency between 0.1 and 10 THz. Terahertz waves have a low electron energy and a high penetration against dielectric materials, which make them applicable for see-through imaging for multiple materials such as plastic, ceramic, woods, papers and polymer composites [1–3]. Compared with common see-through imaging methods such as X-ray, microwave and ultrasonic imaging, terahertz imaging has advantages in penetration, non-destructive and resolving power, which make it a promising and irreplaceable imaging method in multiple application fields, including industrial Non-Destructive Testing (NDT)—[4,5], heritage conservation [6–8], aerospace [9], security [10–12], biology and medicine [13].

Thanks to the fast development of terahertz source and detector component techniques, terahertz Focal Plane Array Detectors (FPA) based on a microbolometer [14,15] and complementary metal oxide semiconductor (CMOS) [16–19] make fast, large-scale, high-resolution, incoherent terahertz imaging methods available. However, passive mode imaging in the terahertz region is infeasible for the see-through applications mentioned above, as little background radiation in the terahertz region exists in the environment, and the method is still limited by the performance of commercially available devices [20]. To ensure an acceptable signal-to-noise ratio (SNR) and resolve the power for samples with a certain thickness, most terahertz imaging applications rely on a high-power, collimated source for illumination [3]. The beam of a high power continuous-wave (CW) terahertz source such as a gas-pumped laser and quantum cascade laser (QCL) is a Gaussian beam. When used in active illumination imaging, the wavefront characteristics of the Gaussian beam would lead to distortion, which significantly reduces the resolving power. A beam homogenizer would help in reducing such distortion; however, a beam homogenizer diffuses beam energy, which leads to negative impacts in transmission-type imaging applications that require a sufficiently effective imaging depth and concentrated beam energy. Moreover, the microbolometer and CMOS terahertz FPA have issues in terms of Fixed Pattern Noise (FPN) [21,22], which leads to adverse effects on the SNR and the resolving power of the imaging result.

An optical system with a larger aperture will help to solve the problems mentioned above. However, limited by the size of the system and the cost of processing, enlarging the aperture size is impracticable in most applications. Introducing the Light Field Imaging (LFI) method will help to solve this problem. LFI is an incoherent computational imaging method which extracts information from data of higher dimensions and achieves a better performance compared with conventional methods [23]. In LFI, both the positional and directional information of the imaging object are gathered simultaneously, implementing enhancements in SNR, dynamic range, depth of field (DoF) and additional depth information about the images [24] with reconstruction algorithms. In the visible region, light field acquisition methods based on microlens arrays [24], camera arrays [25], and coded aperture compressive sensing [26] are now being widely studied. Moreover, the LFI technique is also utilized in multiple applications including dynamic refocusing [24], DoF extension [27], all-in-focus reconstruction [28], depth estimation [29,30], 3D reconstruction [31], super-resolution reconstruction [32,33], synthetic aperture imaging and high-speed photography [27].

Jain et al. [34] proved the feasibility of LFI in the terahertz waveband with a simplified experimental setup. In their experiments, the LFI of a point source and simple opaque object was implemented with a camera module of a low angular (approximately 1.5◦) and spatial (approximately 28 mm) resolution. In their study, the effects caused by the coherence of light sources and the aperture of the imaging system are not further discussed, which are important factors for practical imaging systems and objects. In fact, these effects cause the main differences in the image characteristics between the terahertz and visible region.

In this paper, a novel, incoherent synthetic aperture terahertz imaging method based on the LFI technique is demonstrated, and the performance improvements of the new method are validated. The phenomenon of image distortion happening in the terahertz imaging system with Gaussian beam illumination has been investigated. With microbolometer-based terahertz FPA detectors and a high-power gas-pumped terahertz source, a terahertz virtual camera array LFI system has been established. With the experiments of transmission-type imaging configuration, the effectiveness of the LFI method in removing the image distortion and improving the resolving power compared with a conventional setup is validated.

#### **2. Theory and Methods**

#### *2.1. Light Field Theory and Mathematical Model*

The plenoptic model is a model used to describe the "light field", i.e., the spatial propagation of light flowing. In particular, in the plenoptic model, the light flow is simplified as sizeless "rays", described by their position and direction and by the plenoptic function. Assuming that the rays emitted by light sources do not spatially overlap, the positional and directional information of light rays can be described using four dimensions.

In the case of a two-plane scheme, a 4D light field can be described with a 4D plenoptic function *LF*(*x*, *y*, *u*, *v*), which describes rays with the intersectional coordinates of two parallel planes.

Specifically, two planes *uv* and *xy* are defined with a fixed distance, and the rays will intersect with two lanes. The combination of all the rays passing through every coordinate on planes *uv* and *xy* create the full light field, as shown in Figure 1. The two-plane scheme is introduced for practical light field acquisition methods. For any combination of two dimensions in the 4D plenoptic function, for example, rays intersect with a certain (*u*, *v*) or certain (*x*, *y*) coordinate—we call this a 2D slice of the

4D plenoptic function. In practice, the "slice" is used to describe the sub-aperture images, macro-pixels or epipolar images of 4D light fields.

**Figure 1.** The two-plane scheme of 4D light field.

The procedure of LFI can be divided into two steps: the acquisition and the reconstruction. The acquisition phase physically gathers and resolves the 4D light field of the object, and the reconstruction phase generates enhanced images with the acquired 4D light field information.

#### *2.2. The Acquisition of the 4D Light Field*

Compared with conventional imaging, the acquisition of the 4D light field initiates both positional and directional resolution simultaneously, namely the resolving of individual light rays. Imagine an FPA imaging system, or "camera": light rays are focused by optic systems (called the main aperture) at the *uv* plane, then gathered, resolved and imaged by detector pixels at the *xy* plane. The pixels are the partitions of *xy* planes. The light signal received by pixels corresponds to the sum of light rays emitted from a certain position in all directions (which can be gathered by the main aperture). The light signal received by pixels is converted into images. We perform the same partition on the *uv* plane, and the partition on the *uv* plane is called a "sub-aperture". The lightbeams illuminated on a single pixel through the single sub-aperture could be approximately regarded as rays in the plenoptic model. Rays correspond to the partition of light emitted by a certain point source along a certain direction. In this case, besides the image plane in the image space, the conjugated plane of the *xy* plane in the object space can be regarded as the *xy* plane as well, after a simple coordinate transformation, as shown in Figure 2a.

For an FPA imaging system, when the imaging distance is long enough, relative to the focal length, the size of the aperture can be ignored, and the whole beam focused on a single pixel through the aperture can be regarded as an individual ray. Thus, the image recorded by the detector array can be regarded as a combination of rays in certain positions and different directions, namely a 2D slice

of the 4D light field. Arranging such cameras on the *uv* plane, the full light field can be recorded by recording all of its sub-aperture slices. With this camera array, the 4D light field can be acquired with a synthetic aperture equivalent to the size of the camera array, and its resolution depends on the resolution and spacing of the camera modules. In this case, the *xy* plane does not really exist in the image space, since there is no common image space for every single camera. Besides this, the common plane conjugated to image planes of all cameras (supposing they are regularly arranged and have the same optical parameters) in the object space is regarded as the *xy* plane, as shown in Figure 2b. In practice, the light field slices are acquired with a camera array consisting of multiple FPA cameras, or a virtual camera array for static light fields, with a limited number of cameras.

**Figure 2.** Light field acquisition and partition in (**a**) real aperture and (**b**) synthetic aperture.

#### *2.3. Light Field Reconstruction*

The reconstruction of a 4D light field is a simulation of the focusing and imaging procedures of the optical imaging system in a geometric optic manner, based on the 4D light field information.

For a given 4D light field *LF*(*x,y,u,v*), the planes, *uv*, *xy*, and the distance *F* between planes *uv* and *xy* are given.

When replacing the plane *xy* with the plane *x y* in the description, where the distance from plane *uv* is *z* = α*F*, the transformed plenoptic function could be described as

$$L\_z(\mathbf{x'}, \mathbf{y'}, \boldsymbol{\mu}, \boldsymbol{\upsilon}) = L\_F \Big( \mathbf{u} \Big( 1 - \frac{F}{z} \Big) + \mathbf{x'} \frac{F}{z}, \mathbf{v} \Big( 1 - \frac{F}{z} \Big) + \mathbf{y'} \frac{F}{z}, \boldsymbol{\mu}, \boldsymbol{\upsilon} \Big) \tag{1}$$

which is equal to shearing the plenoptic function in *xy* dimensions. The ray passing through the point (*x*0, *y*0, *z*) in space and the point (*u*,*v*,0) on the plane *uv* could be described as

$$S\_{x\_0, y\_0, z}(\mu, \upsilon) = L\_F \left( \mu \left( 1 - \frac{F}{z} \right) + x\_0 \frac{F}{z}, \upsilon \left( 1 - \frac{F}{z} \right) + y\_0 \frac{F}{z}, \mu, \upsilon \right) \tag{2}$$

Substituting the deferent points (*u,v*) in Equation (2) gives us the combination of the rays passing through the point (*x*0*, y*0*, z*). Assuming we know the depth *z*(*x*0*, y*0) of all points (*x*0, *y*0). in the scene, the Equation (2) could be transformed into

$$\begin{split} S\_{\mathbf{x}\_{0},y\_{0},z\left(\mathbf{x}\_{0},y\_{0}\right)}\left(\boldsymbol{\mu},\boldsymbol{\upsilon}\right) \\ = L\_{F}\Big(\mathbf{u}\Big(1-\frac{F}{z\left(\mathbf{x}\_{0},y\_{0}\right)}\Big)+\mathbf{x}\_{0}\frac{F}{z\left(\mathbf{x}\_{0},y\_{0}\right)},\boldsymbol{\upsilon}\Big(1-\frac{F}{z\left(\mathbf{x}\_{0},y\_{0}\right)}\Big) \\ +y\_{0}\frac{F}{z\left(\mathbf{x}\_{0},y\_{0}\right)},\boldsymbol{\mu},\boldsymbol{\upsilon}\Big) \end{split} \tag{3}$$

and the reconstructed image could be described as

$$\begin{aligned} E(\mathbf{x}\_{0}, y\_{0}) &= \iint L\_{z(\mathbf{x}\_{0}, y\_{0})}(\mathbf{x}', y', u, v) \mathrm{d}u \mathrm{d}v \\ &= \iint L\_{F} \Big( \mu \Big( 1 - \frac{F}{z(\mathbf{x}\_{0}, y\_{0})} \Big) + \chi\_{0} \frac{F}{z(\mathbf{x}\_{0}, y\_{0})}, v \Big( 1 - \frac{F}{z(\mathbf{x}\_{0}, y\_{0})} \Big) + \chi\_{0} \frac{F}{z(\mathbf{x}\_{0}, y\_{0})}, u, v \Big) \mathrm{d}u \mathrm{d}v \end{aligned} \tag{4}$$

As mentioned in Section 2.2, in practical light field acquisition, the 4D light field is discretized into pixels in all *xyuv* dimensions, and the slices of the light field in *uv* and *xy* dimensions are discretized into the 2D combination of pixels as well. Therefore, in the practical implementation of the reconstruction algorithm, the continuous integration in Equation (3) is transformed into the numerical sum of discretized pixels. For every discretized pixel (*x*0*,y*0) in the reconstructed image, the algorithm traverses all the slices (*u,v*) of the light field, searches for the pixels corresponding to the ray through (*u,v*), (*x ,y* ) and (*x*0*,y*0), and calculates the pixel values from all the slices.

If the input light field is from a single physical aperture, the algorithm simply simulates the imaging procedure in geometric optics and generates reconstructed images as a result. If the input light field is from the camera array described in Section 2.2, the algorithm generates reconstructed images based on a synthetic aperture.

#### **3. Experiment and Result**

#### *3.1. Distortion Analysis of Gaussian Beam Active Illuminated Terahertz Imaging*

In this section, the phenomenon of the image distortion observed in the active illuminated terahertz imaging process will be discussed.

In our experiment, a transmission-type terahertz imaging system based on Gaussian beam active illumination and an FPA terahertz camera has been established. In particular, the terahertz beam from the source is collimated by a Teflon collimation lens, transmitted through the object, and then received by the camera at different positions. In the experiment, the object and the source are fixed. The camera moves around and acquires images at different positions. The camera remains static when acquiring images to avoid motion blur. The experimental setup is shown in Figure 3.

**Figure 3.** Experimental setup of transmission-type terahertz imaging system.

In the experiment, a Coherent SIFIR–50 gas-pumped continuous-wave terahertz source is used as an illumination source. The terahertz source works at 2.52 THz, and the output power is about 50 mW, which provides a stable and good SNR performance. An INO IRXCAM-THz–384 terahertz camera module is used to acquire terahertz images. The camera uses FPA detectors based on uncooled microbolometers, with a 35 μm pixel size and a resolution of 384 × 288 pixels, and is capable of capturing images at a 50 fps rate. The camera module has Silicon imaging optics, with a 44-mm focal length, a field of view of about 17.3 × 13.0 degrees, and a spatial resolution of about 0.5 mm. In the experiment, an extra Teflon filter is mounted in front of the camera module to filter the unwanted infrared signal in the environment.

The imaging object of the experiment is a polypropylene composite Pelican case with bumped markings. The thickness of the case is about 4 mm, and the diameter and thickness of the bumped markings are about 5 mm and 0.2 mm, respectively, as shown in Figure 4. In the experiment, the distance between the source and the object is 2000 mm, and the distance between the object and the camera is 600 mm.

**Figure 4.** Visual photograph of (**a**) the polypropylene composite Pelican case and (**b**) the bumped markings, A and B.

Figure 5 is the image acquired by the camera when in different positions. For active illuminated imaging, when using a point source or collimated beam for illumination, only a portion of the beam that passes through both the object and the aperture contributes to the imaging result. This portion of the "effective" beam corresponds to a "bright spot" or "bright circle" in the terahertz image. Refraction and total reflection occur at the edges of the bumped markings, which results in a significant contrast in the acquired terahertz images.

**Figure 5.** Terahertz images of the bumped markings, A and B, with the markings at the center and the edge of the "effective" light spot, captured at different positions, with different markings at the center of the spot.

Ideally, the round bumped markings should be the same shape in the terahertz image as their original shapes. In the experiment, when located in the center of the spot, the markings are imaged correctly as a circle. However, when located near the edge of the spot, the markings are significantly distorted and appear to be drop-shaped. The phenomenon of distortion does not occur when illuminated by a planar homogenized source or incoherent sources in the infrared waveband. In practical applications, this distortion will significantly affect the resolving power of the imaging.

#### *3.2. Resolving Power Analysis of Terahertz LFI Setup*

In this section, compared with conventional transmission-type imaging, the improvement of terahertz LFI on the resolving power and image distortion mentioned in Section 3.1 will be discussed.

Based on the transmission-type terahertz imaging system mentioned in Section 3.1, a terahertz LFI system has been established. A virtual camera array based on a terahertz camera module and motorized translation stages are utilized to replace the single terahertz camera, in order to acquire the full 4D light field.

The camera module is fixed on a 2D translation stage, which can move in both x and y directions vertical to the optical axis of the camera. The translation stages drive the camera and acquire the slices of the full light field in different positions.

In the experiment, the Coherent SIFIR–50 source works at the frequency of 1.40 THz, with an output power of about 84 mW, which provides a better penetration for the sample used in this part of the experiment. The experimental setup is shown in Figure 6.

**Figure 6.** Experimental setup of terahertz virtual camera array system.

The imaging object is a resolving power test target with concentric circle and line pair patterns. The base material of the card is epoxy of 0.5 mm thickness, which is transparent to the terahertz wave. The concentric circle and line pair patterns are printed on the base with copper, which is opaque to the terahertz wave. The spacing between line pairs ranges from 0.125 mm to 3 mm, and the spacing between concentric circles ranges from 0.5 mm to 3 mm. The line widths of both line pairs and concentric circles are 1 mm, as shown in Figure 7. In the light field acquisition, the number of sub images is 11 × 31 sub-images, and the spacing is 5 × 5 mm. The distance between the source and the object is 2000 mm, and the distance between the object and the camera is 600 mm.

Figure 8 is one of the enlarged sub-aperture images; i.e., the imaging result of a single shot with a single camera. Compared with the results in Section 3.1, the result of line pairs and concentric circles suffered a severe and irregular distortion, which significantly reduced the resolving power of the imaging system for the patterns and made the positions and spacing of lines and circles almost indistinguishable. Moreover, the interference fringes and fixed pattern noise of the detectors further reduced the performance of the imaging result.

**Figure 7.** Visual photograph of the resolving power test target.

**Figure 8.** Terahertz image of the test target, captured by single camera in single shot.

Figure 9a,b shows the results of the light field reconstruction. Figure 9a is the result directly reconstructed by the 4D light field reconstruction algorithm, and Figure 9b is the result further enhanced with the Unsharp Mask (USM) algorithm. In reconstructed light field images, the complete portions of the object are clearly imaged. The distortion is almost removed, and the line and circle patterns are clearly distinguishable. The interference fringes and FPN are significantly suppressed as well. In the directly reconstructed image, the fourth line and the first circle with a spacing of 0.5 mm are clearly distinguishable. In the USM-enhanced image, although the suppression of noise is weakened, the resolving power of patterns is increased, since the third line, with a spacing of 0.375 mm, becomes distinguishable. Compared with the result of the conventional method, the performance and resolving power are significantly improved by using the synthetic aperture method, and the unrecognizable patterns as a result of the conventional method become fully recognizable with the synthetic aperture method.

**Figure 9.** Reconstructed image form full light field data, (**a**) directly reconstructed and (**b**) enhanced with Unsharp Mask (USM) algorithm.

#### **4. Conclusions**

In this paper, an experimental transmission-type terahertz imaging system and a virtual camera array terahertz LFI system were established based on a high-power gas-pumped terahertz source and terahertz focal plane array detectors. On the one hand, the phenomenon of image distortion occurred in terahertz imaging, and its influences on resolving power have been observed and analyzed; on the other hand, a novel synthetic aperture method based on the LFI technique was introduced, and its improvement of image performance and suppression of image distortion were validated in the experiments carried out.

In the imaging experiment on a resolving power test target, the conventional method showed an unacceptable result, where the distortion made the line and circle patterns completely indistinguishable, while the synthetic aperture method with USM sharpening enhancement showed a much better result: the line pairs with less than 0.5 mm spacing were clearly resolved.

The application field of terahertz imaging requires imaging methods with high efficiency, high performance and compact integration. Computational imaging methods such as LFI are promising approaches to overcome the disadvantages of current imaging methods caused by the limitations in terahertz sources and detector technologies and to fulfil further requirements in other potential application fields.

**Author Contributions:** Conceptualization, C.Z., N.L., J.Z., and Y.Z.; methodology, N.L.; software, N.L.; validation, C.Z., N.L., J.Z. and Y.Z.; formal analysis, N.L.; investigation, N.L.; resources, C.Z., J.Z. and Y.Z.; writing—original draft preparation, N.L.; writing—review and editing, C.Z.; visualization, N.L.; supervision, C.Z.; project administration, C.Z.; funding acquisition, C.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Key Scientific Instrument and Equipment Development Projects of China, grant number DH–2012YQ14005; and National Basic Research Program of China (973 Program), grant number 2014CB339806.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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