⇦Chinese Physics Letters, 2017, Vol. 34, No. 8, Article code 084206⇨ Terahertz Three-Dimensional Imaging Based on Computed Tomography with Photonics-Based Noise Source * Tao Zhou(周涛), Rong Zhang(张戎), Chen Yao(姚辰), Zhang-Long Fu(符张龙), Di-Xiang Shao(邵棣祥), Jun-Cheng Cao(曹俊诚)** Affiliations Key Laboratory of Terahertz Solid-State Technology, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050 Received 31 May 2017 ^*Supported by the National Basic Research Program of China under Grant No 2014CB339803, the Major National Development Project of Scientific Instrument and Equipment under Grant No 2011YQ150021, the National Natural Science Foundation of China under Grant Nos 61575214, 61574155, 61404149 and 61404150, and the Shanghai Municipal Commission of Science and Technology under Grant Nos 14530711300, 15560722000 and 15ZR1447500.
^**Corresponding author. Email: jccao@mail.sim.ac.cn Citation Text: Zhou T, Zhang R, Yao C, Fu Z L and Shao D X et al 2017 Chin. Phys. Lett. 34 084206 Abstract Computed tomography has been proven to be useful for non-destructive inspection of structures and materials. We build a three-dimensional imaging system with the photonically generated incoherent noise source and the Schottky barrier diode detector in the terahertz frequency band (90–140 GHz). Based on the computed tomography technique, the three-dimensional image of a ceramic sample is reconstructed successfully by stacking the slices at different heights. The imaging results not only indicate the ability of terahertz wave in the non-invasive sensing and non-destructive inspection applications, but also prove the effectiveness and superiority of the uni-traveling-carrier photodiode as a terahertz source in the imaging applications. DOI:10.1088/0256-307X/34/8/084206 PACS:42.79.Pw, 42.30.Wb © 2017 Chinese Physics Society Article Text The terahertz region is loosely defined as frequency range from 0.1 THz (100 GHz) to 10 THz, which is located between the microwave and far-infrared in the electromagnetic spectrum. Most imaging techniques used in the THz region originate from other frequency bands. THz three-dimensional (3D) imaging is realized by utilizing the computed tomography technique which is first used in x-rays.[1] Unlike x-rays, THz wave has much lower photon energy (1 THz$\sim$4.1 meV) which will not cause a dangerous ionizing effect when used on humans, and has better contrast when imaging soft materials. Since the first THz CT demonstration was reported in 2002 by Ferguson et al.,[2] it has been proposed for 3D imaging of different objects from food, pharmaceutical to biomedical fields.[3-7] For the present THz imaging techniques/systems, the THz time-domain system[8-10] is the most famous and frequently used coherent-detection system, which provides both phase and amplitude information of the THz electric field, while the system is experimentally sophisticated and expensive for the use of the femtosecond pulse laser. Others like the THz quantum cascade laser-based imaging systems, which provide high-power THz radiation and simple system design, but the device needs to work at very low temperature in a cryostat for thermal dissipation.[11-14] To solve these problems, making THz radiation through the photonics technique is a potential solution. The uni-traveling-carrier photodiode (UTC-PD) shows superior performance[15-17] in high-frequency applications because of its two characteristics: one is the electron-dominated transport in the whole structure resulting in a much shorter transit time and faster photoresponse; the other is higher output power because of higher saturation current due to the weak space charge effect in the depletion layer. Based on the UTC-PD device, THz radiation is obtained by photo-mixing of two optical signals whose frequency difference is located in the THz region. Furthermore, the photonics-based THz source provides other advantages such as compact, reliable, inexpensive and room-temperature operation. In this Letter, we first build a THz 3D imaging system based on a UTC-PD as source and a Schottky barrier diode (SBD) as detector; then we analyze the spatial resolution and reconstruct the cross-sectional images with the filtered back-projection (FBP) CT algorithm; finally we stack the slices to realize the 3D image demonstration and point out the places that need to be improved in the future. In the experiment, we adopt a low-coherence THz signal instead of a monochromatic signal for CT imaging, the reason is that the monochromatic wave will cause interference effect due to the reflections of signals at the surface of the sample, which results in a deterioration of signal intensities and brings beam-hardening effect in CT image reconstruction. To generate a low-coherence THz signal, a broadband amplified spontaneous emission (ASE), generated by the erbium-doped fiber amplifier (EDFA), is input into the UTC-PD module which converts every two frequency lights in the ASE noise into THz wave,[18] therefore, a low-coherence signal ranging from 90 GHz to 140 GHz is obtained and used as the imaging source. The block diagram of the THz 3D imaging system is shown in Fig. 1. The THz source module is indicated by the blue dashed box. The initial ASE noise signal is generated by the first EDFA and then modulated at frequency 50 kHz. After modulation, the noise signal is amplified by a second EDFA and input into the UTC-PD device to generate a THz wave. The THz wave is radiated into the free space via a horn antenna, collected by a pair of 90$^{\circ}$ off-axis parabolic mirrors (PM1: 2$''f$/2, PM2: 2$''f$/1) and then focused onto the sample which is placed on a rotation–translation stage. The transmitted THz signal with sample information is collected by another pair of PMs (PM3: 2$''f$/1, PM4: 2$''f$/2) and focused onto the SBD device for detection. The responsive photocurrent is extracted by a lock-in amplifier with the time constant 1 ms. The sample is rotated along the $Y$ axis and translated along the $X$ axis with a speed of 50 mm/s. The computer is used for synchronizing control of the sample motion and the data recording.

Fig. 1. Schematic diagram of the experimental setup for THz 3D imaging. The blue dashed box indicates the source module, and the red dot-dashed line represents the optical axis. EDFA: erbium-doped fiber amplifier; PM: parabolic mirror; SBD: Schottky barrier diode; LIA: lock-in amplifier.

Fig. 2. THz beam width measurement at the con-focus of PM2 and PM3. The intensity variation of the signal as the metallic plate is moved across the focus (blue line is along the $X$ direction and red line is along the $Y$ direction). The signals of both lines are normalized.

In the diffraction-limited system, the spatial resolution is determined by the focus size, which is measured by the 'knife-edge' method along the $X$ (horizontal) and $Y$ (vertical) directions. In each direction, we move a metallic plate across the focus, the signal power changes from 100% to 0% as shown in Fig. 2. The beam width of the focused THz wave is defined as the translation distance from 100% to 0% transmission, and the resolution is given as the full width at half maximum of the beam width. According to the method, the resolutions in $X$ and $Y$ directions are measured at 3.5 mm and 3.6 mm, respectively, which are comparable with the minimum differentiated distance ($\sim$3 mm) of the optical system according to the Rayleigh Criterion,[19] and the Rayleigh length is estimated at 15 mm. To build the cross-sectional images, the FBP method is adopted in CT reconstruction for its effectiveness and simplicity. This method is originated from the Radon transform theory, and can be briefly expressed as[20] $$\begin{align} I(r,\theta)=\sum\limits_k {(p(x_r,\varphi _k)\times h(x_r))},~~ \tag {1} \end{align} $$ where $I(r,\theta)$ is the 'intensity' of pixel $(r,\theta)$, $p(x_r,\varphi _k)$ is the projection value at angle $\varphi _k$, $h(x_r)$ is the filter, $x_r =r\cos (\theta -\varphi _k)$, and $k$ is the total number of angle sampling in the range of 180$^{\circ}$. This expression indicates that the projection of each angle contributes to the pixel value $I(r,\theta)$. In this work, the step of rotation angle is set at 6$^{\circ}$ ($k=30$) and the size of the reconstructed region is 84$\times$84 mm$^{2}$ including 7056 pixels.

Fig. 3. Reconstructed images of cross sections of the ceramic pot sample at three different heights are shown in grayscale (a) $h=68$ mm, (b) $h=30$ mm and (c) $h=14$ mm. (d) The sinogram of cross-sectional image (b) with 30 projections and 84 samples at each projection (angle). The red dashed lines in (a) and (c) indicate the intersecting positions for quantitative analysis of images.

Figures 3(a)–3(c) show three cross-sectional images of a ceramic pot sample at three heights for demonstration $h=68$ mm, $h=30$ mm and $h=14$ mm, respectively. The three reconstructed cross sections reveal the geometrical shapes at different heights of the sample. The structures are relatively distinct in consideration of the diffraction effect caused by long wavelength ($\sim$3 mm). Particularly, Fig. 3(d) shows the sinogram of the cross section at $h=30$ mm (Fig. 3(b)). The sinogram reveals different parts of the sample clearly based on the raw data before algorithm processing. It can be found that there are three shapes in Fig. 3(d), two curves and a parallelogram area, which are corresponding to the spout, handle and pot body, respectively. Figure 3(b) even reveals the structure of the transition part of the spout and pot body. A quantitative analysis is made by the intersecting line method,[21] the width of the spout and handles in Fig. 3(a) are measured around 9 mm and 15.5 mm, respectively, while the actual size are 7.2 mm and 12.8 mm; the width of the pot body in Fig. 3(c) is measured around 62 mm, the actual size is 58.4 mm. The quantitative results show agreement between the reconstructed images and the real sample in dimension.

Fig. 4. The 3D imaging of the ceramic pot. (a) Frontal view of the 3D image; (b), (c) and (d) the orthogonal sectional images. The central inset figure is the photograph of the sample.

To demonstrate the THz 3D imaging, we choose cross sections from bottom to top at 40 different heights, 2.0 mm apart. Firstly, an edge-enhancement processing is performed on the cross-sectional images, and then the slices are stacked to present a 3D view of the sample by the software of imageJ in volume mode display, as shown in Fig. 4. Figure 4(a) is a recording at the frontal view, and the shape features of the sample are revealed clearly in the 3D image as compared with the photograph of the sample (inset of Fig. 4). It is easy to identify the parts of spout, handle and pot body. Figures 4(b)–4(d) present the orthogonal sectional images for the inspection of the shape from different view angles. Obviously, the volume shape is also consistent with the real sample, meanwhile we find that the contours of the images are blurry and shapes of the spout and handle become slightly distorted; the reason lies in the comparable sizes of the spout and handle and the beam spot as well as the diffraction effect of the system and the reflection of the smooth surface of the sample. In future work a noise source at higher frequency could be used to improve the resolving ability of the system and to obtain a higher image quality. In conclusion, we have built a THz 3D imaging system using photonics-based noise source and an SBD detector. Cross-sectional images of the sample are reconstructed successfully by FBP algorithm, and the shape sizes are in agreement with the real sample quantitatively. The 3D image of the ceramic pot is displayed by stacking the 40 slices. This work demonstrates THz CT imaging by a new source with the photonics-based technique. The inherent characteristics of small, stable, system-compact and room-temperature operation make it promising to be applied in various THz applications such as non-invasive sensing and non-destructive inspection in the real world. References Representation of a Function by Its Line Integrals, with Some Radiological Applications. IIT-ray computed tomographyImaging with terahertz radiationTerahertz Pulse Imaging of ex vivo Basal Cell CarcinomaNon-destructive terahertz imaging of illicit drugs using spectral fingerprintsThree-dimensional terahertz computed tomography of human bonesThe Diagnosis of Human Liver Cancer by using THz Fiber-Scanning Near-Field ImagingFree-space coherent broadband terahertz time-domain spectroscopyA Compressed Terahertz Imaging MethodMeasurement of Refractive Index for High Reflectance Materials with Terahertz Time Domain Reflection SpectroscopyThree-dimensional imaging with a terahertz quantum cascade laserReal-time imaging using a 4.3-THz quantum cascade laser and a 320 /spl times/ 240 microbolometer focal-plane arrayReal-time terahertz imaging over a standoff distance (>25meters)High power-efficiency terahertz quantum cascade laserHigh-Speed and High-Output InP?InGaAs Unitraveling-Carrier PhotodiodesPhotonic generation of continuous THz wave using uni-traveling-carrier photodiodeDesign and Characterization of Evanescently Coupled Uni-Traveling Carrier Photodiodes with a Multimode Diluted Waveguide StructureThree Dimensional Millimeter- and Terahertz-Wave Imaging Based on Optical Coherence TomographyConfocal optical microscopyTerahertz Imaging With Quantum-Well Photodetectors

[1]	Cormack A M 1964 J. Appl. Phys. 35 2908
[2]	Ferguson B S, Wang S, Gray D, Abbott D and Zhang X C 2002 Opt. Lett. 27 1312
[3]	Chan W L, Deibel J and Mittleman D M 2007 Rep. Prog. Phys. 70 1325
[4]	Woodward R M, Wallace V P, Pye R J, Cole B E, Arnone D D, Linfield E H and Pepper M 2003 J. Invest. Dermatol. 120 72
[5]	Kawase K, Ogawa Y, Watanabe Y and Inoue H 2003 Opt. Express 11 2549
[6]	Bessou M, Chassagne B, Caumes J P, Pradere C, Maire P, Tondusson M and Abraham E 2012 Appl. Opt. 51 6738
[7]	Chen H, Ma S H, Yan W X, Wu X M and Wang Z 2013 Chin. Phys. Lett. 30 030702
[8]	Han P Y and Zhang X C 2001 Meas. Sci. Technol. 12 1747
[9]	Zhang M, Pan R, Xiong W, Xiong W, He T and Shen J L 2012 Chin. Phys. Lett. 29 104208
[10]	Sun W F, Wang X K and Zhang Y 2009 Chin. Phys. Lett. 26 114210
[11]	Nguyen K L, Johns M L, Gladden L F, Worrall C H, Alexander P, Beere H E, Pepper M, Ritchie D A, Alton J, Barbieri S and Linfield E H 2006 Opt. Express 14 2123
[12]	Lee A W M, Williams B S, Kumar S, Hu Q and Reno J L 2006 IEEE Photon. Technol. Lett. 18 1415
[13]	Lee A W M, Kumar S, Williams B S and Hu Q 2006 Appl. Phys. Lett. 89 141125
[14]	Li Y Y, Liu J Q, Liu F Q, Zhang J C, Zhai S Q, Zhou N, Wang L J, Liu S M and Wang Z G 2016 Chin. Phys. B 25 084206
[15]	Ito H, Kodama S, Muramoto Y, Furuta T, Nagatsuma T and Ishibashi T 2004 IEEE J. Sel. Top. Quantum Electron. 10 709
[16]	Ito H, Furuta T, Nakajima F, Yoshino K and Ishibashi T 2005 J. Lightwave Technol. 23 4016
[17]	Zhang Y X, Pan J Q, Zhao L J, Zhu H L and Wang W 2010 Chin. Phys. Lett. 27 028501
[18]	Toshiyuki I, Takayuki I and Tadao N 2013 IEICE Trans. Electron. E96-C 1210
[19]	Webb R H 1996 Rep. Prog. Phys. 59 427
[20]	Kak A C and Slaney M 1988 Principles Of Computerized Tomographic Imaging (New York: IEEE Press) chap 3 p 50
[21]	Zhou T, Zhang R, Guo X G, Tan Z Y, Chen Z, Chao J C and Liu H C 2012 IEEE Photon. Technol. Lett. 24 1109