Synthesizing a Frequency-Diverse Aperture for Security-Screening Applications Okan Yurduseven, Daniel L. Marks, Jonah N. Gollub, and David R. Smith Department of Electrical and Computer Engineering Duke University Durham, North Carolina, 27708, United States
[email protected] Abstract—We demonstrate the design of a frequency-diverse aperture for imaging of human size objects. Frequency-diversity is an all-electronic technique, allowing the imaging to be performed without any mechanical moving parts or active circuit components. Leveraging computational imaging algorithms, the concept of frequency-diverse imaging offers a simplified alternative to conventional techniques limited in key metrics, such as data acquisition speed, system complexity and cost. It is shown that the synthesized-frequency diverse aperture can reconstruct good quality images of a human-size target by means of a simple frequency sweep over the K-band frequency regime.
in an all-electronic manner with no mechanically moving parts. However, conventionally, phased array systems require precise phase controlling of the individual antennas within the system. For an aperture consists of an array of antennas and synthesized at the Nyquist limit, this requirement can be challenging. Traditionally, in order to have the ability to control the phase of each antenna within the system, these systems require phase shifting circuits. Moreover, to compensate for the insertion loss of such circuits, typically, power amplifiers and other active circuity also need to be used, further increasing the cost and complexity of the phased array systems.
Keywords—computational imaging; microwaves; frequencydiversity; inverse problem; reconstruction.
The concept of computational imaging has been demonstrated to hold significant potential to simplify the hardware system layer [3]. Leveraging the frequency-diversity, all-electronic operation can be achieved by means of a simple frequency sweep with no mechanically moving parts, phase shifting circuits and active circuitry are required [4]. In this paper, the development of a composite frequency-diverse aperture is demonstrated for imaging of human size targets.
I. INTRODUCTION Imaging using the microwave and millimeter-wave frequency regimes has been studied extensively in the literature [1-4]. A significant advantage associated to these schemes is that waves leveraging this part of the electromagnetic (EM) spectrum can penetrate through most materials that are opaque at optical frequencies. Moreover, radiation in these bands is nonionizing and thus ideally suited for a variety of emerging imaging applications, including security-screening, throughwall imaging, and biomedical imaging. Investigating the literature, the two most widely used imaging techniques can be given as versions of synthetic aperture radar (SAR) [1] and phased array systems [2]. In SAR technique, an antenna (or an array of antennas) is used to synthesize an effective aperture to interrogate the scene to be imaged. The synthetization of the aperture is achieved by means of a raster scanning with the antenna being mechanically scanned over the synthesized aperture at the Nyquist limit. Due to the mechanical sampling of the antenna in the spatial domain, the radiated fields of the antennas interrogating the scene are essentially orthogonal. As a result, using the SAR technique, good image fidelity has been achieved in the literature. However, conventional SAR techniques are limited in that data acquisition speed can be slow due to the mechanical scan requirement. One way to overcome this challenge is to achieve all-electronic operation and eliminate the mechanical scanning. To this end, the concept of electronically scanned antennas or phased array systems can be used to address this challenge. In fact, using this concept, a raster scanning aperture can be formed
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II. FREQUENCY-DIVERSE IMAGING Frequency-diverse imaging relies on the principle of using frequency-diverse antennas to interrogate the scene to be imaged. Frequency-diverse antennas have the ability to radiate pseudo-random radiation patterns that vary rapidly as function of the imaging frequency. As the frequency is swept, the transmit antennas illuminate the scene with spatially-random radiation patterns and the signal scattered from the scene is collected using an array of receive antennas. In view of this, the scene information is encoded onto a set of frequency points. Recovering the scene information from a set of measurements of the scattered field constitutes an inverse problem. In order to solve the inverse problem, the measured signal needs to be correlated to the scene, which is done by means of the first Born approximation given in (1) as follows Tx gi , j ( f ) ETx i , j (r, r '; f )Ei , j (r, r ''; f )fdv n
(1)
v
In (1), g denotes the measured signal from the scene and f is the reflectivity (or contrast) vector to be reconstructed while i and j are the indices for the transmit and receive antenna numbers, respectively. ETx and ERx are the fields radiated from the transmit and receive antennas, respectively, propagated to
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the scene volume. The noise term, n, represents the system noise modeled as a Gaussian. The dot product of the transmit and receive fields produces the measurement (or sensing) matrix, H. The integral equation in (1) is discretized as follows
g Mx1 HMxN f Nx1 nMx1
(2)
In (2), M is the total number of measurement modes supported by the system, which is given by number of transmit antennas x number of receive antennas x number of frequency points. For imaging we use the K-band frequency regime (17.526.5 GHz), sampled at 101 frequency points. The scene is discretized into N three-dimensional (3D) voxels at the resolution limit of the synthesized aperture. Analyzing (2), it is evident that the measurement matrix H does not have an exact inverse and reconstructing f requires computational algorithms, such as single-shot matched-filter and iterative least-squares techniques [3]. In this work, we make use of the least-squares algorithm with Tikhonov regularization.
conditioned measurement matrix, H, and second, less redundant information from the adjacent measurement modes. To image human-size objects, the small system shown in Fig. 1 needs to be scaled. To this end, as shown in Fig. 2(a), we synthesized a composite aperture, 2 m x 2 m, consisting of 24 transmit and 72 receive antennas. The Q-factor of the antennas was chosen to be Q=330 for this study. A gun phantom was attached to the imaged human-size object as shown in Fig. 2(b). It is known that the human skin is a good reflector at microwave frequencies. Therefore, to facilitate target detection, we apply depth color-coding in the reconstructed image. The color-coded least-squares reconstructed image is shown in Fig. 2(c), revealing a clear outline of the target.
III. COMPOSITE APERTURE FOR FREQUENCY-DIVERSE IMAGING Designing a frequency-diverse imaging system requires careful investigation of a number of system parameters, such as the quality factor (Q) of the antennas, system layout, and number of transmit and receive antennas filling the synthesized composite aperture. The Q-factor of the antennas determines the orthogonality of the measurement modes, and thus governs the redundancy of the information collected from the scene as the frequency is swept. In view of this, it is desirable that the Qfactor of a frequency-diverse antenna is maximized. However, in practice, the Q-factor of a frequency-diverse antenna is inversely proportional to the radiation efficiency, governing the signal-to-noise (SNR) ratio for imaging [4]. One way of analyzing the orthogonality of the measurement modes produced by a frequency-diverse antenna is to investigate the singular values decomposition (SVD) spectrum of the measurement modes. To this end, a small system consisting of two transmit and two receive antennas was designed. The Qfactor of the antennas was varied from Q=50 to Q=2000 and the measurement matrix, H, was calculated over a two-dimensional (2D) scene of 2 m x 2 m placed at d=1 m distance from the antennas as shown in Fig. 1(a). The SVD calculated from H as a function of the Q-factor are shown in Fig. 1(b).
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Fig. 2. Imaging of a human-size object with a gun phantom (a) synthesized aperture (transmit antennas are blue and receive antennas are red) (b) actual object (c) reconstructed image. IV. CONCLUSION We have demonstrated the development of a frequencydiverse aperture for imaging of human-size objects. It has been shown that using the developed system, imaging is performed by means of a simple frequency sweep over the K-band. The proposed technique holds significant potential to be employed in security-screening applications and can readily be extended to higher frequencies, such as millimeter-wave and terahertz. ACKNOWLEDGMENT This work was supported by the Department of Homeland Security, Science and Technology Directorate (Contract No. HSHQDC-12-C-00049). The published material represents the position of the author(s) and not necessarily that of the DHS. REFERENCES [1]
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Fig. 1. SVD analysis (a) synthesized system with the scene (b) SVD pattern of the system as a function of Q-factor. As can be seen in Fig. 1(b), increasing the Q-factor reduces the slope of the SVD curves, suggesting, first, a better
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D. Smith, O. Yurduseven, B. Livingstone and V. Schejbal, "Microwave imaging using indirect holographic techniques," IEEE Antennas and Propagation Magazine, vol. 56, no. 1, pp. 104-117, Feb. 2014. A. J. Fenn, D. H. Temme, W. P. Delaney, and W. E. Courtney, “The development of phased array radar technology,” Lincoln Laboratory Journal, vol. 12, no. 2, pp. 321–340, 2000. O. Yurduseven, M. F. Imani, H. Odabasi, J. Gollub, G. Lipworth, A. Rose, and D. R. Smith, "Resolution of the frequency diverse metamaterial aperture imager," Progress in Electromagnetics Research, vol. 150, 97107, 2015. O. Yurduseven, V. R. Gowda, J. N. Gollub and D. R. Smith, "Multistatic microwave imaging with arrays of planar cavities," IET Microwaves, Antennas & Propagation, vol. 10, no. 11, pp. 1174-1181, 8 20 2016.
