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Abstract
A walk-through millimeter wave imaging testbed using double multistatic cross arrays is presented. The imaging testbed consists of a vector network analyzer, a power amplifier, a low-noise amplifier, 36 SP6T electrical switchers, and double homemade multistatic cross arrays placed on both sides of the imaging area. The imaging algorithm based on the range migration algorithm is deduced, and the imaging performance is analyzed. The metallic ball experimental results show that the imaging resolution is close to the theoretical value, and demonstrate the imaging feasibility of the testbed working in mutual mode.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Millimeter wave (mmW) is an electromagnetic wave usually defined to be within nominal wavelength of 1∼10 mm and frequency of 30∼300 GHz. Based on a half power criterion, most clothing is transparent for mmW [1], and imaging systems using mmW are capable of penetrating common clothing barriers to form an image of a person as well as any concealed objects [2–4]. Since diffraction generally limits resolution to spot sizes of about half wavelength, millimeter scale spatial resolution is readily achievable [5]. Additionally, mmW is nonionizing, and needs 10,000 times less power than cell phones to illuminate a person under surveillance [6]. By virtue of these unique advantages, mmW imaging techniques could achieve detection of concealed threats of metallic and nonmetallic objects, e.g., plastic and liquid explosives, ceramic knives, contrabands, and narcotics [3,7].
The development of millimeter wave imaging technology for personnel screening has witnessed over half a century's pursuit and probe by several generations of scientists. In the development process, both higher security check throughput and better imaging performance have been spurring the continuous advance of millimeter wave imaging technology. In recent years, the walk-through system (WTS) has become a research hotspot in mmW imaging field. In 2014, Gonzalez-Valdes et al. proposed a new concept of WTS based on inhomogeneous multistatic sparse array [8]. Multiple frame images could be achieved during the movement of the passenger while passing through the WTS, and the detection performance could be enhanced since possible concealed threats are visible from different perspectives and could be tracked within different frames. Furthermore, three-dimensional (3D) numerical simulation results [9], and experimental measurements from a Ka-band (26.5 ∼ 40 GHz) measurement system [10] demonstrated the feasibility of the proposed WTS concept. However, the proposed WTS was just a conceptional model, the multistatic sparse array was realized by moving 2 transiter antennas and 2 receive antennas, and a specific multistatic antenna array was not presented. In 2016, Gumbmann and Ahmed investigated a WTS based on the multistatic perimeter array for security applications. The proposed WTS consisted of two synchronized imaging systems with 1.5 m distance. Each system worked in the 70∼80 GHz frequency range and consisted of 3008 transmit and receive antennas covering an area of 1 m by 2 m [11]. The proposed WTS was the superposition of two separate multistatic plane array imaging systems and did not demonstrate the special advantages of WTS sufficiently.
Since 2015, our group has been working on mmW WTS for personnel security screening. The range migration algorithm (RMA) for WTS [12] and related mmW propagation loss compensation technique [13] were proposed. A multistatic cross array was designed and used for mmW 3D imaging [14]. Recently, a walk-through mmW imaging testbed using double multistatic cross arrays was constructed, and the imaging resolution and contrast were tested by the metallic ball experiment. Especially, the imaging experiment of the testbed working in mutual mode could reveal the potential of multi-view imaging in WTS.
In this paper, an overview of the testbed hardware is made in Section II, followed by a detailed imaging performance discussion about multistatic cross array in Section III. Section IV presents the metallic ball experiments, demonstrating the imaging performances and advantages of the proposed testbed, and Section V concludes this paper.
2. Testbed design
The walk-through mmW imaging testbed consists of a vector network analyzer (VNA) (N5247A, Agilent, USA), a power amplifier (PA) (AV8023X, CETC, China), a low-noise amplifier (LNA) (QLA-26500-40000-20-30, Qualwave, China), 36 electrical switchers (SP6T, Radiall, France), and double home-made multistatic cross arrays, as shown in Fig. 1. Since our intended mmW imaging testbed is used for personnel security screening, the 26.5∼40 GHz frequency band, having suitable resolution and mature devices and components, is selected for the mmW detection. Port A of VNA generates mmW signals with 401 equally spaced discrete frequency points between 26.5 GHz and 40 GHz. A total of 36 SP6T electrical switchers make up a switch array for fully electronic scanning of transmit and receive channels. Double multistatic cross arrays are placed on both sides of the imaging area, and the distance between them is about 1.2 m. The measurement data, i.e. the S21 parameters from VNA, are collected sequentially with electronic channel scanning. The imaging testbed comprises a total number of 164 transmit channels and 164 receive channels, and collects the scattered echo coherently using stepped-frequency mode.
Following the multi-input-multi-output (MIMO) radar technique in multistatic array, only one single transmit antenna illuminates the imaging area at any time instance, the scattered echo is then sampled by all the receive antennas. The transmit channels must be switched sequentially for the data collection, while the receive channels could operate sequentially or simultaneously. Since the VNA only has two ports, the receiver in the proposed testbed must run in sequential mode. The echo data are collected for each transmitter-receiver pair and each selected frequency, resulting in a 3D data matrix of ${N_{Tx}} \cdot {N_{Rx}} \cdot {N_{freq}}$ complex values, where ${N_{Tx}}$, ${N_{Rx}}$, and ${N_{freq}}$ are the total number of transmit channels, receive channels and stepped frequencies, respectively. During the process of passengers’ walking through the double arrays, the reconstruction images of various angles and positions could be achieved.
2.1 Array design
In multistatic planar array, the transmit and receive antenna distributions could be chosen separately and designed to complement each other. In our home-made multistatic cross array, transmit antennas are placed vertically for forming a synthetic aperture in vertical direction, while receive antennas are placed horizontally for forming a synthetic aperture in horizontal direction. For a multistatic array with transmit aperture ${a_t}$ and receive aperture ${a_r}$, the array performance in the far distance operation is decided by the double convolution ${a_t}\ast{\ast} {a_r}$, which is the array effective aperture [15].
However, the array performance in the near distance deviates significantly and could be improved by increasing the redundancy in the array effective aperture [16]. Therefore, the tradeoff between the array performance and the array antenna number must be considered. The base spacing $\Delta a$ between the antennas in either transmit or receive aperture corresponds to the spacing in wave number domain and is responsible for alias-free imaging. For ideal isotropic antennas in multistatic array, the alias-free imaging could be achieved with $\frac{{{\lambda _c}}}{2}$ spacing, where ${\lambda _c} = 9$ mm represents the central wavelength in broadband mmW [17]. In our home-made multistatic cross array, $\Delta a$ is equal to 6 mm, i.e. $\frac{{2{\lambda _c}}}{3}$, due to the limited half power beamwidth of 90°. The array antennas number of transmit and receive aperture, M and N, are both 82, resulting in that the synthetic aperture length of transmit and receive antennas, ${L_v}$ and ${L_h}$, are both 486 mm, as shown in Fig. 2(a). In order to facilitate the installation and replacement of antennas, four antennas are integrated in one single dielectric slab, as shown in Figs. 2(b) and (c). The antennas utilize substrate integrated waveguide (SIW) and twin dipole structure to improve the radiation bandwidth and gain, and the key features of the antenna are listed in Table 1.
Fig. 2. Multistatic cross array geometry (a), photo of transmit antennas (b) and receive antennas (c).
Table 1. Antenna key features
In the testbed, double multistatic cross arrays are used to achieve an imaging area of around 50 cm × 50 cm. This results in a total of 164 transmit antennas and 164 receive antennas. Under the conditions of the same base antenna spacing and synthetic aperture size, its counterpart design using a monostatic dense array results in $82 \times 82 \times 2 \times 2 = 26896$ antennas. Therefore, the multistatic array contains only 2.44% of that number of antennas.
2.2 Imaging algorithm
In mmW imaging field, the popular imaging algorithms mainly include back projection algorithm (BPA) [18] and RMA [19]. BPA is to implement the image formation in space or time domain and is capable of applying to arbitrary arrays. Each echo is processed and back-projected over spherical shells to all reconstructed pixels, the values for each pixel are accumulated as more echoes are processed until all echoes have been processed and the final resolution achieved. However, BPA requires a large number of operations and has limitations in imaging efficiency [20]. RMA, which relies on Fourier transform (FT) and one-dimensional (1D) interpolation, is to implement the image formation in wave number domain and is capable of reconstructing image efficiently. Then RMA is invariably used for the reconstruction of 3D mmW images. Compared with other wave number imaging algorithms, such as range doppler (RD) algorithm and chirp scaling (CS) algorithm, RMA has better accuracy and efficiency [21].
Though the multistatic array is used in the proposed testbed, transmit and receive antennas only exist in 1D vertical and horizontal directions respectively. Therefore, the scattered echo is a 3D matrix rather than a five-dimensional (5D) matrix in a common multistatic planar array [17], and 3D RMA rather than MIMO-RMA is used in the proposed testbed. The image reconstruction process can be naturally split into four sequential steps, namely: a 2D cross-range FT, matched filtering, Stolt interpolation, and a 3D inverse Fourier transform (IFT).
The geometry of the proposed testbed is presented in Fig. 3. Double multistatic cross arrays are arranged in parallel in the $x - y$ plane, with a z coordinate of the arrays at $z = 0$ and $z = \textrm{H}$. Thus, the antenna elements represented by ${z_t}$ and ${z_r}$ will take the values of 0 or $\textrm{H}$. Under Born approximation and the assumption of isotropic scattering, the scattered field received by one of the receive antennas with the attenuation terms in free space omitted can be expressed as
The echo data are transformed into the 2D wave number domain
Based on geometry of Fig. 3, the following derivation can be decomposed into four situations according to the value of ${z_t}$ and ${z_r}$ [12].
Case 1: ${z_t} = 0$ and ${z_r} = 0$. The roundtrip distance is ${R_{t1}} + {R_{r1}}$ in Fig. 3.
The evaluation of the 2D Fourier integral in (2) by means of the method of stationary phase (MSP) results in [22]:
where ${k_{z1}} = \sqrt {{k^2} - k_x^2} + \sqrt {{k^2} - k_y^2} $ is the wave number in the range direction.Note that ${k_{z1}}$ must be real, and the region in the wave number domain where the asymptotic expansion of the MSP is valid deduces to
Generally, the phase of reference point, which is located in the center of imaging area, is used to achieve matched filtering:
The matched filter is necessary to introduce a motion compensation to the wave number domain echo data. The motion compensation corrects for the wavefront curvature of all scatterers at the same range as the imaging area center. After the matched filter, the transformed data continue being equally spaced in wave number ${k_r}$. To prepare the data for the last 3D IFT, Stolt interpolation is performed, and the echo data in wave number domain could be uniformly sampled in the ${k_{z1}}$ domain. Then, the 3D reconstructed image is obtained by simply applying a 3D IFT:
Case 2: ${z_t} = 0$ and ${z_r} = \textrm{H}$. The roundtrip distance is ${R_{t1}} + {R_{r2}}$ in Fig. 3.
The evaluation of the 2D Fourier integral in (2) is:
where ${k_{zx}} = \sqrt {{k^2} - k_x^2} $, ${k_{z2}} = \sqrt {{k^2} - k_y^2} - \sqrt {{k^2} - k_x^2} $.Then the 3D reconstructed image is:
The evaluation of the 2D Fourier integral in (2) is:
where ${k_{zy}} = \sqrt {{k^2} - k_y^2} $, ${k_{z3}} = \sqrt {{k^2} - k_x^2} - \sqrt {{k^2} - k_y^2} $.Then the 3D reconstructed image is:
Case 4: ${z_t} = \textrm{H}$ and ${z_r} = \textrm{H}$. The roundtrip distance is ${R_{t2}} + {R_{r2}}$ in Fig. 3.
The evaluation of the 2D Fourier integral in (2) is:
Then the 3D reconstructed image is:
3. Imaging performance analysis
The testbed imaging performance is well described by its point spread function (PSF) [23]. The PSF describes the response of an imaging system to a point object, followed by the BPA. As all the transmit antennas emit mmW to the point target, one single receive antenna at the middle of the receive array receives the scattered wave, the simulated PSF of the transmit array operating from 26.5 to 40 GHz and focusing centrally at 50 cm distance is shown in Fig. 4(a). Similarly, as one single transmit antenna at the middle of the transmit array emits mmW to the point target, all the receive antennas receive the scattered wave, the simulated PSF of the receive array is shown in Fig. 4(b). The aperture sizes of both arrays are equal, resulting in the same cross-range resolution. However, either transmit array or receive array only achieves focusing performance in one dimension, and both of them have strong sidelobes in their separate focusing directions.
Fig. 4. Transmit array PSF (a) and receive array PSF (b) for a central point target at 50 cm distance.
As the transmit and receive arrays are complement each other in the multistatic cross array, the simulated PSF has better focusing performance in both vertical and horizontal directions, and the sidelobes are depressed, as shown in Fig. 5. The simulated PSF of the transmit and receive array along both range and range direction is shown in Fig. 6, and the artifacts are also depressed.
Fig. 5. Cross-range 2D PSF for a central point target at 50 cm distance: (a) overview and (b) detailed view.
The imaging performances, including imaging resolution and contrast, could be achieved by measuring the PSF. Specifically, the imaging resolution could be got by measuring the half power main lobe beamwidth of PSF, while the imaging contrast could be got by measuring the peak to side lobe ratio of PSF. The theoretical imaging performances of the multistatic cross array for the point target located at 50 cm distance from the array are listed in Table 2.
Table 2. Reconstruction image performances
The foregoing analysis shows the imaging performance achieved by one single multistatic cross array in the proposed testbed. The unique advantage of the proposed testbed is that double multistatic cross arrays could work in mutual mode, resulting in that the multi-view reconstructed images could be got. Since double multistatic cross arrays are placed on both sides of imaging area, and the imaging process difference between separate mode and mutual mode exists only in matched filtering step, as shown in (6), (8), (10) and (12), the PSF simulated results and the theoretical imaging performance of the proposed testbed operated in separate or mutual mode is exactly the same. Additionally, the different working modes are used to reconstruct the target images from different angles, the superposition effect of multiple cases is not considered, and the simulated PSF results could be viewed as the reconstructed point target image achieved by the multistatic cross array working in a specific case.
4. Imaging results
To verify the imaging performance of the array in the proposed testbed, an experiment with a metallic ball (radius 40 mm) is performed in a microwave anechoic chamber, as shown in Fig. 7. In this scenario, the metallic ball is placed at a distance of $z \approx 0.6$ m from the antenna array. The top 36 transmit antennas in the vertical direction of array are sequentially selected to radiate mmW by electrical switchers, while all the 82 receive antennas in the horizontal direction of array are sequentially selected to receive scattered echo. Therefore, the synthetic aperture length in vertical and horizontal directions are 210 mm and 486 mm respectively. In all experiments, mmW waveforms are configured to vary from 26.5 GHz to 40 GHz and the bandwidth is 13.5 GHz, where the number of stepped frequencies is 401.
Fig. 7. Photos of the setup showing a metallic ball as target (a), and antennas with transmit and receive channel (b), in a microwave anechoic chamber.
The reconstructed images in $x - y$ plane and $x - z$ plane are shown in Fig. 8. In Fig. 8(a), the aperture length in vertical direction is about half of the aperture length in horizontal direction, resulting in that the resolution as well as sidelobe effect in horizontal direction is better than that in vertical direction. In order to analyze quantitatively the resolution and the contrast, cross-range and range profiles corresponding to the reconstructed images in Fig. 8 are given, as shown in Fig. 9.
Fig. 9. Profiles corresponding to the reconstructed images of Fig. 7 in (a) x direction, (b) y direction and (c) z direction.
To further verify the imaging performance of double arrays working in mutual mode, another experiment with a metallic ball (radius 40 mm) placed between arrays is performed, as shown in Fig. 10. The distance between arrays is 1.18 m, while the metallic ball is around 0.2 m off the centerline along the horizontal direction. The central uniformly distributed 36 transmit antennas in the vertical direction of array 1 are sequentially selected to radiate mmW by electrical switchers, while the uniformly distributed 40 transmit antennas in the horizontal direction of array 2 are sequentially selected to receive scattered echo. The interval distances of transmit and receive antennas are both 12 mm, resulting in that the synthetic aperture length in vertical and horizontal directions are 420 mm and 468 mm respectively.
Fig. 10. (a) Side view and (b) top view of the setup showing a metallic ball placed between two arrays.
The reconstructed images in $x - y$ plane and $x - z$ plane are shown in Fig. 11. Compared to the imaging results in the metallic ball using one single array, the sidelobe effect is more obvious in both horizontal and vertical directions. In order to analyze quantitatively the resolution and the contrast, cross-range and range profiles corresponding to the reconstructed images in Fig. 11 are given, as shown in Fig. 12.
Fig. 11. Imaging results of a metallic ball between arrays in $x - y$ plane (a) and $x - z$ plane (b).
Fig. 12. Profiles corresponding to the reconstructed images of Fig. 10 in (a) x direction, (b) y direction and (c) z direction.
The imaging performances of the proposed testbed in separate and mutual modes are summarized in Table 3. As the synthetic aperture length in experiments is equal to 486 mm, i.e. the synthetic aperture length used in Section imaging performance analysis, the imaging resolution in either separate mode or mutual mode is close to the theoretical resolution 11.7 mm. As the synthetic aperture length is only 210 mm, the imaging resolution in separate mode degrades to 36 mm. In the mutual mode experiment, the synthetic aperture length in x direction is 420 mm, and the metallic ball is around 0.2 m off the centerline in x direction, resulting in that the resolution is only 20 mm. The range resolution in separate mode is close to the theoretical resolution 12.0 mm, while the range resolution in mutual mode degrades to 34 mm. Additionally, the imaging contrast achieved by separate mode is also better than that in mutual mode.
Table 3. Reconstruction image performances in experimentsa
5. Conclusions
A walk-through mmW imaging testbed using double multistatic cross arrays has been presented here. The imaging testbed consists of a VNA, a PA, a LNA, 36 electrical switchers and double home-made multistatic cross arrays. Double multistatic cross arrays are placed on both sides of imaging area, and the distance between is 1.2 m. The 26.5∼40 GHz frequency band, having suitable resolution and mature devices and components, is selected for the mmW detection. Following the MIMO radar technique, only one single transmit antenna illuminates the imaging area at any time instance, the scattered echo is then sampled by all the receive antennas in two arrays. The imaging algorithm based on RMA is deduced, and the theoretical spatial resolution and contrast of the multistatic cross array are analyzed. The metallic ball experimental results show that the cross-range and range resolutions as well as the contrast using the proposed testbed have a satisfied consistency with the theoretical values. More importantly, the metallic ball experiment in mutual mode demonstrates the feasibility of muti-view imaging in WTS.
In summary, we have investigated a WTS concept for security applications. Our testbed is based on existing mmW technology and consists of double multistatic cross arrays. We have also conducted an experimental demonstration of our testbed to illustrate its imaging performance. In the future, the designed walk-through mmW imaging testbed will utilize solid state electrical switchers having much faster switch speed to achieve real-time imaging, and the on-the-moving human with contrabands imaging experiment will be conducted.
Funding
Major Scientific and Technological Innovation Projects of Shandong Province (2019JZZY010448); Natural Science Foundation of Shandong Province (ZR2020KF007, ZR2020QF015); National Natural Science Foundation of China (61875196).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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