Computational imaging systems leverage generalized measurements to produce high-fidelity images, enabling novel and often lower cost hardware platforms at the expense of increased processing. However, obtaining full resolution images across a large field-of-view (FOV) can lead to slow reconstruction times, limiting system performance where faster frame rates are desired. In many imaging scenarios, the highest resolution is needed only in smaller subdomains of interest within a scene, suggesting an aperture supporting multiple modalities of image capture with different resolutions can provide a path to system optimization. We explore this concept in the context of millimeter-wave imaging, presenting the design and simulation of a single frequency (75 GHz), multistatic, holographic spotlight aperture integrated into a K-band (17.5–26.5 GHz), frequency-diverse imager. The spotlight aperture – synthesized using an array of dynamically tuned, holographic, metasurface antennas – illuminates a constrained region-of-interest (ROI) identified from a low-resolution image, extracting a high-fidelity image of the constrained-ROI with a minimum number of measurement modes. The designs of both the static, frequency-diverse sub-aperture and the integrated dynamic spotlight aperture are evaluated using simulation techniques developed for large-scale synthetic apertures.
© 2017 Optical Society of America
Millimeter-waves are routinely used in imaging applications, including through-wall imaging [1,2], non-destructive testing [3–5], security-screening [6–10], and biomedical imaging [11–13]. Millimeter-waves are advantageous in that they are non-ionizing and considered safe for human exposure, and they can penetrate most optically opaque materials revealing concealed objects. While there are numerous approaches to constructing a millimeter-wave imaging system, traditionally, most implementations have been variants on either synthetic aperture radar (SAR) [14–17] or phased antenna arrays [18–21]. Both schemes have well known advantages, as well as challenges, in application.
Systems incorporating advanced computational imaging concepts [22–45] can leverage novel, more flexible and potentially inexpensive hardware, alleviating some of the difficulties with millimeter wave and, more generally, radio frequency (RF) apertures. In a recent computational imaging scheme, a frequency-diverse aperture has been introduced, which generates sequences of pseudo-random field patterns as a function of driving frequency. Scene information is then reconstructed from the set of complex field measurements obtained from a simple frequency sweep, rather than requiring mechanical scanning or electronic control of phase at every point in the aperture. Combined with computational imaging approaches, the frequency diverse aperture significantly simplifies hardware architecture and can exhibit relative fast data acquisition rates.
The radiation patterns generated by the frequency-diverse aperture generally extend over the entire field-of-view (FOV), scattering from all objects in the scene. As the radiation patterns are not typically orthogonal, oversampling is required to obtain diffraction-limited resolution, leading to large data sets that must be processed using computational imaging algorithms. If fewer measurements are used, the image can be reconstructed more quickly, but potentially with lower resolution and other artifacts related to incomplete sampling. In many situations, the larger scene does not need to be fully resolved, but rather only sub-domains of the scene or even constrained regions on larger targets. In this mode of use, potential constrained regions-of-interest (ROIs) can be identified by a lower resolution system and marked for potential further interrogation by a higher resolution system. Such a procedure might be relevant for security-screening, biomedical imaging and non-destructive testing applications, where potential threat objects, tumors and other types of abnormalities tend to occupy a small subsection on a target.
In the present study, we propose augmenting a millimeter-wave, frequency-diverse imaging system designed to produce wide FOV images at lower resolution, with a secondary “spotlight” imager – a multistatic array of dynamically tunable apertures capable of forming a variety of radiation patterns over a much smaller region. As an example, we also demonstrate the application of this hybrid system in the context of personnel-screening, in which an image of a human-size target is reconstructed, on which potential threat objects are identified. The spotlight aperture is focused on the location of the potential threat and the threat object imaged with a higher resolution, within a sub-second timeframe. Unlike a conventional phased array antenna, a multistatic array requires fewer dynamic elements, as the multistatic array is sparse and therefore covers a much smaller area, utilizing fewer sources and receivers over the aperture. This both reduces the cost of the number of active elements needed as well as enables the sparse array to be embedded within a larger frequency-diverse aperture, without interference issues between the two interspersed apertures. A further advantage of the multistatic, dynamic aperture is that it operates at a single frequency, so that only narrowband radio components are required, reducing the expense and complexity of the high-resolution system. The reduction in complexity of the spotlight system results from using the information from the low resolution system as a “prior,” constraining both the region of illumination as well as the reconstruction region.
The organization of this paper is as follows. In Section 2, we describe the imaging system, which consists of the frequency-diverse and spotlight apertures. We detail the holographic metasurface antenna design and its application to synthesize a dynamic aperture for spotlight imaging. In Section 3, we discuss reconstruction issues, present representative images using our numerical modeling approach. The resolution limits of the frequency-diverse and holographic spotlight apertures are examined by means of point spread function (PSF) analyses. The application of the imaging system for personnel-screening is also presented as an example. Finally, we provide some concluding remarks in Section 4.
2. Holographic metasurface antennas and creating spotlight mode for imaging
We consider a hybrid aperture comprising two composite sub-apertures, as depicted in Fig. 1. The first sub-aperture is a frequency-diverse aperture consisting of a collection of frequency-diverse antennas. The second sub-aperture consists of an array of dynamically tunable metasurface antennas. The frequency-diverse antennas radiate pseudo-random fields interrogating the entire scene and are used to reconstruct a low-resolution image of a target. The holographic antennas, comprising the spotlight aperture, create beams focused at a constrained-ROI enclosing the selected sub-section of the scene. Using the spotlight imager, the imaging is performed at a higher resolution over the constrained-ROI. In Fig. 1, we illustrate such a hybrid system for imaging an array of point-scatter objects.
As depicted in Fig. 1, the spotlight aperture is synthesized using an array of dynamically tuned holographic metasurface antennas. To explain this further, we can conceptualize a single holographic antenna, with the aperture of the antenna being discretized into pixels (or unit cells) of sub-wavelength dimensions, each of which has a separately controllable phase. Note that Fig. 2 illustrates a holographic phase pattern (or phase grating) on the aperture of the antenna that focuses a field to an arbitrarily selected point in space.
In Fig. 2, the point at which a focus is to be formed is within the radiative near-field (Fresnel zone) of the antenna. The complex amplitude of the hologram on the antenna required to create a focus at the desired point can be calculated using :
For this analysis, we apply a scalar approximation, assuming the field is linearly polarized along the z-direction; generalizing this analysis for co- and cross-polarized radiation is straightforward. In Eq. (2), r locates the fictitious point source while locates positions over the aperture plane. Since we are to consider a metasurface implementation, we imagine discretizing the aperture in a set of pixels, with referring to the pixel position. The size of the pixels is selected to be λ/5 – a reasonable value based on numerous metasurface prototype apertures that have been previously reported. Each pixel across the aperture is modeled as a polarizable magnetic dipole, with the polarizability defined based on the typical constraints of a Lorentzian resonator, for which the amplitude and phase are not independent. From Eqs. (1) and (2), the ideal hologram can be computed, which consists of the amplitude and phase added to the reference wave at every point over the aperture to produce the spotlight field. With the aperture discretized into a set of pixels, the complex amplitude at each point can be related to the required magnetic polarizability for a metasurface . Finally, using the reference wave as the source (and assuming the reference wave is not perturbed), the effective magnetic dipole moments can be calculated using m = αHref, and the fields radiated by the holographic metasurface antenna focused at the constrained-ROI can be obtained summing over the radiating magnetic dipole moments. These focused fields ensure a constant illumination on the imaged object when the spotlight mode is activated for imaging.
3. Imaging results and discussion
Reconstructing scene information from a set of measurements of fields scattered from targets in the scene constitutes an inverse problem. Solving the inverse problem requires that a model between the measured return signal and the scene is established, which is typically expressed asEq. (3), g is the measurement vector, H is the measurement (or sensing) matrix, f is the scene to be reconstructed and n is the measurement noise. We refer to Eq. (3) as the forward model, which applies both to the frequency-diverse and spotlight apertures, albeit with a different g, H, f, and n for each. Assuming the first Born approximation, which assumes the field scattered from a point in the scene is simply proportional to the incident field at that point, the measurement matrix elements, Hi,j, are simply proportional to the fields radiated by the transmit and receive antennas at a given point in the scene, rj, or Hi,j = ETx,i(rj)ERx,i(rj). Here, the subscript i indexes a given pair of transmit and receive antennas, in addition to frequency for a frequency-diverse aperture.
Each row of the sensing matrix corresponds to a measurement mode, such that the number of rows is equal to the number of measurements and the number of columns is equal to the number of voxels in the scene to be reconstructed. For the frequency-diverse aperture, the number of measurement modes is defined as M1 = number of transmit antennas x number of receive antennas x number of frequency points. The frequency-diverse aperture assumes 100 sampled points over the K-band frequency band (17.5-26.5 GHz) [44, 45], and is assumed to image entire large targets within the scene. Each of the targets is discretized into a collection of N1 three-dimensional (3D) voxels with dimensions consistent with the resolution limit of the aperture. The dimension of the measurement vector g is thus M1x1; the H-matrix has dimensions M1xN1; and the dimension of f is N1x1.
For the spotlight aperture, the holographic field patterns on the metasurface antennas are calculated at a single frequency, selected to be 75 GHz. As a result, the number of measurement modes is given as M2 = number of transmit antennas x number of receive antennas. The ROI to be imaged by the spotlight aperture is a sub-section (constrained-ROI) of the scene defined for the frequency-diverse aperture. The constrained-ROI is discretized into a number N2 of voxels, where the number is selected consistent with the resolution limit of the spotlight aperture. It should be emphasized that the proposed spotlight imager is a multistatic system, consisting of individually beam-focusing holographic metasurface antennas as opposed to a conventional phased array system, in which the antennas together form a beam and act as a single monostatic transceiver. As a result of restricting the imaging domain to a subset of the scene (constrained-ROI), the number of antennas required for the spotlight imager is minimized.
Imaging is fully simulated using a customized software package, which we refer to here as the Virtualizer . In the absence of noise, and assuming H to be square, the inverse problem defined in Eq. (3) would require calculation of the inverse of H. However, as H is not square (M≠N), there is no inverse that can be defined, and f can only be estimated from the measurement vector g using estimation techniques to find fest. A number of computational imaging algorithms can be used, ranging from simple matrix multiplication approaches, such as pseudo-inverse or matched filter, to more complex iterative techniques, such as least-squares or two-step iterative/shrinkage/thresholding (TwIST) [37, 47, 48]. Among these algorithms, the matched filter (or back propagation) technique is among the fastest as it does not require iteration, and therefore, is selected to be the reconstruction technique used for the frequency-diverse system imaging the entire scene. Using the matched filter algorithm, the scene is reconstructed by means of applying the conjugate-transpose of the measurement matrix, such that . For the spotlight imager, however, as a result of restricting the imaging domain to a subset of the scene and minimizing the number of antennas, more complex imaging algorithms can be utilized while still achieving fast image reconstruction. For the spotlight imager, we make use of the least-squares reconstruction technique. The least-squares technique minimizes the objective function by means of an L2-norm minimization, , to reconstruct an estimate of the constrained-ROI in an iterative manner.
As depicted in Fig. 1, the scene consists of an array of point-scatterers separated by a distance of 15 cm from each other and placed on a 5 x 5 regular grid at a distance of d = 1 m from the aperture. Imaging of a point-scatter target is important in that it enables the analysis of the point-spread-function (PSF) of the imaging aperture, revealing the resolution limits of the aperture through a full-width-half-maximum (FWHM) analysis. We first image the entire scene using the frequency-diverse aperture, as depicted in Fig. 3.
The overall dimension of the composite frequency-diverse aperture is chosen to be 2 m x 2 m, which provides reasonable resolution of human-scale targets . The frequency-diverse aperture consists of 24 transmit and 72 receive antennas while the K-band frequency-regime is sampled at 100 frequency points, producing M1 = 172,800 measurement modes. The scene enclosing the point-scatter array target is discretized in accordance with the diffraction limit of the frequency-diverse aperture, calculated to be δcr = 6 mm in cross-range and δr = 1.67 cm in range, respectively, using the SAR resolution equations . As a result, each voxel is selected to be Δy = Δz = 5 mm in cross-range and Δx = 1 cm in range, resulting in N1 = 17,956 voxels. Using the matched-filter technique, the reconstruction time is measured to be 1.6 s. The matched-filter image of the point-scatter array target reconstructed using the frequency-diverse aperture is shown in Fig. 4.
Figure 4(a) shows the front projection of the three-dimensional (3D) reconstructed image of the point-scatter array. The reconstructed image in Fig. 4(a) reveals a clear outline of the imaged point-scatter targets. By taking the projection of the 3D PSF pattern along the principle axes in the cross-range plane (y- and z-axes), and analyzing the −3 dB FWHM values in Fig. 4(b), the resolution limit of the frequency-diverse aperture is found to be 6.25 mm, exhibiting good agreement with the theoretical resolution limit calculated to be 6 mm. This agreement confirms that imaging is performed at the diffraction limit of the frequency-diverse aperture.
To obtain finer detail of sub-regions on the larger target, we design a spotlight imager operating at 75 GHz, which has a wavelength roughly a third that of the average wavelength of the K-band system. As depicted in Fig. 5, the spotlight imager consists of an array of transmit and receive dynamically-tuned holographic metasurface antennas, each having dimensions 10 cm x 10 cm, corresponding to an electrical size of 25λ x 25λ at 75 GHz. The size of the composite spotlight aperture synthesized using the individual holographic metasurface antennas is 90 cm x 90 cm, consisting of 40 transmit and 40 receive antennas. Using the spotlight imager, the field distribution on the holographic metasurface antennas is dynamically adjusted to focus the antenna radiated fields at a desired constrained-ROI. Note that the composite aperture must be coherent, which would require a phase calibration between all of the sub-array elements.
In Fig. 5, for example, we choose the center point-scatterer of the point-scatter array shown in Fig. 3 (labeled as “on-axis” in Fig. 1) as the constrained-ROI for spotlight imaging. The field (phase) distributions on the holographic metasurface antennas are calculated so that each antenna within the composite aperture produces a focused beam at the selected point-scatter at d = 1 m distance along the x-axis (x = 1 m, y = 0, z = 0). This suggests that for an object placed at the focal point, for any given transmit and receive antenna pair across the aperture, the focus is at the object, ensuring constant illumination on the object for all transmit and receive antenna pairs. In comparison to the frequency-diverse aperture supporting M1 = 172,800 measurement modes, the presented spotlight aperture uses only M2 = 1,600 measurement modes.
The selected distance, d = 1 m, remains within the Fresnel zone of the individual antennas d<5 m, calculated using 2D2/λ, where D is the size of the antenna, D = 10 cm. Although the least-squares reconstruction algorithm is adopted for the spotlight studies demonstrated in this work, for the imaging configuration shown in Fig. 5, as an example, the reconstruction is done using both the matched-filter and least-squares techniques.
Using the matched-filter technique, the image reconstruction is performed in 0.023 s while the least-squares reconstruction takes 0.2 s. It should be mentioned that the synthesized system can be thought of as a SAR aperture performing all-electronic spotlight imaging without the need for mechanical raster scanning. As a result, Fourier based SAR reconstruction algorithms, such as back-projection and range-migration [6, 9] can be applied to further reduce the image reconstruction time. The matched-filter and least-squares reconstructed PSF patterns are shown in Figs. 6(a) and 6(b). Comparing the two PSF patterns, it is evident that the least-squares reconstructed image exhibits superior resolution limits in comparison to the matched-filter reconstruction (narrower PSF lobe). Figure 6(c) shows the projection of the PSF patterns along the y- and z-axes in cross-range while Fig. 6(d) provides a close-up of the main lobes of the PSF patterns. Analyzing Figs. 6(c) and (d), we measure the −3 dB FWHM values of the PSF patterns to be 3.3 mm for matched-filter reconstruction and 2.3 mm for least-squares reconstruction. Discretizing the scene at the resolution limit of the spotlight aperture results in N2 = 1,936 voxels.
Comparing the matched-filter resolution limit of the holographic spotlight aperture, 3.3 mm, to the matched-filter resolution limit of the frequency-diverse aperture, 6.25 mm, it can be seen that the resolution of the spotlight aperture is improved by a factor of two. To understand the underlying reason behind this improvement, the operating characteristics of the two apertures need to be compared. While the holographic spotlight aperture operates at 75 GHz, the frequency-diverse aperture operates within the K-band frequency-regime (17.5-26.5 GHz), corresponding to a ratio in wavelengths of around three. If the frequency-diverse aperture were designed for 75 GHz, the expected resolution limit for the frequency-diverse aperture would be improved by this amount; 6.25 mm / 3≈2 mm. If both apertures were to operate at 75 GHz, the difference between the resolution limits (when the matched-filter algorithm is used) – 2 mm for the frequency diverse aperture and 3.3 mm for the spotlight aperture – is caused by the difference between the sizes of the composite apertures.
One can appreciate that as a result of tailoring the fields radiated by the dynamically-tuned holographic metasurface antennas for a constrained-ROI, the spotlight aperture can utilize a small number of measurement modes for reconstruction of an image near the diffraction limit. This is in comparison to reconstruction of the full scene at W-band or even the frequency-diverse K-band aperture at lower frequencies. The spotlight aperture makes use of the least-squares technique for image reconstruction, with the resolution of the spotlight aperture being equal to 2.3 mm, and reconstruct high fidelity images at sub-second reconstruction rates, suitable for real-time imaging applications.
Following the illustration of the on-axis spotlight imaging, we consider off-axis imaging using the synthesized spotlight aperture. Such a study is important in that the imaged sub-region may appear anywhere within a target, at any position in space (not necessarily along the optical axis), requiring the spotlight aperture to have the capability to dynamically select regions in the scene. We thus image an off-axis point-scatterer within the point-scatter array, highlighted as “off-axis” in Fig. 1. The selected point-scatterer is positioned at x = 1 m, y = 0.3 m and z = 0.3 m, respectively. The field-patterns on the dynamic holographic metasurface antennas calculated for the investigated offset imaging scenario are shown in Fig. 7.
The front-projection of the reconstructed 3D PSF pattern is shown in Fig. 8(a) while the FWHM analysis of the PSF pattern along the y- and z-axes in the cross-range plane is demonstrated in Fig. 8(b). The FWHM for the off-axis configuration is measured to be 2.7 mm, slightly larger than the FWHM for the on-axis configuration, 2.3 mm. This can be attributed to the fact that, as opposed to on-axis imaging, the point target sees the composite aperture at an offset angle, reducing the effective size of the aperture for imaging.
It should be noted that both the proposed dynamic spotlight aperture and conventional phased array systems require electronic reconfiguration. However, as mentioned earlier, in a conventional phased-array system, the antennas within the synthesized aperture together form a beam, acting as a single monostatic transceiver. The holographic metasurface antennas within dynamic spotlight aperture, on the other hand, achieve beam-focusing in an individual manner, enabling multistatic operation. Multistatic operation is useful in that it enables the target to be viewed from multiple angles for different transmit and receive antenna pairs (interrogating the target with a range of angular diversity); this optimizes the Fourier space support or “k-space” coverage . Moreover, for phased-array systems, each antenna within the synthesized aperture requires a phase-shifting circuit. These circuits exhibit considerable insertion losses, which are commonly compensated for using power amplifiers and other types of active circuitry. Thus, phased arrays can be expensive and consume significant amount of power. The holographic metasurface antennas, on the other hand, do not require any phase shifting circuits. Such antennas are currently available in the market, such as the mTenna manufactured by Kymeta and the metamaterial electronically scanning array (MESA) by Echodyne [50–54], and exhibit a cost-effective, low-power alternative to phased arrays.
To demonstrate the advantage of the spotlight imaging, we synthesize the same aperture as shown in Fig. 5, but make use of conventional antennas with no beam-focusing applied. For this example, the individual antennas within the aperture do not have pre-calculated hologram patterns and each antenna radiates in the broadside direction along the x-axis. That is, the excitation phase of the individual antenna elements is set to zero. For this study, the size of the antennas remains constant at 10 cm x 10 cm. The reconstructed PSF pattern is shown in Fig. 9(a) together with the FWHM analysis demonstrated in Fig. 9(b).
Comparing the PSF of the non-focusing aperture in Fig. 9(a) to that of the focusing spotlight aperture in Fig. 6(a), it can be seen that the PSF pattern is wider and exhibits stronger side lobes. Analyzing Fig. 9(b), the resolution of the non-focusing aperture, determined by the FWHM of the PSF pattern, is obtained to be 5.8 mm, almost 2.5 times larger in comparison to the resolution of the focusing spotlight aperture, 2.3 mm. This is because the antennas at the periphery of the aperture do not illuminate the on axis point target—only the antennas near the center of the array contribute to resolving the point target.
The spotlight imager of Fig. 5 consists of 40 transmit and 40 receive dynamic holographic metasurface antennas. In order to simplify the hardware architecture and reduce the system cost, it is desirable to reduce the number of holographic metasurface antennas within the synthesized spotlight aperture. In view of this, as an extreme example, instead of designing a spotlight aperture consisting of antennas focusing at the constrained-ROI, one can consider synthesizing an aperture using an array of simple wide-beamwidth antennas, such as point sources. Similar to spotlight imaging, having a wide-beamwidth ensures that the object is interrogated with a wide variety of spatial frequencies. This circumvents the requirement to achieve focusing for the individual antennas. In Figs. 10(a) and (b), we demonstrate such a system consisting of 40 transmit and 40 receive point sources, replacing the holographic metasurface antennas shown in Fig. 5. The PSF patterns reconstructed using this aperture are demonstrated in Figs. 10(c) and (d).
As can be seen in Fig. 10(c), the reconstructed PSF is aliased due to the sparse sampling of the aperture (violating the Nyquist sampling criteria). In Fig. 10(d), we analyze the FWHM of the PSF and observe the cross-range resolution to be 2.65 mm. The aliasing can be addressed by synthesizing the aperture at the Nyquist limit. However, constructing the composite aperture at the Nyquist limit would require 80,400 transmit and 80,400 receive point source antennas, respectively. Using finite size apertures (each discretized at the sub-wavelength limit) instead of point sources ensures that no aliasing is present and utilizes only a moderate number of antennas; for the presented spotlight imager in Fig. 5, a total of 80 antennas is used, for example.
In order to further reduce the number of metasurface antennas, we develop a sparse version of the spotlight imager of Fig. 5, which we refer to here as the sparse spotlight imager. To this end, we use a Mills-Cross system layout, in which the transmit antennas are placed along the top and bottom rows while the receive antennas are placed along the left and right columns of the composite aperture as shown in Fig. 11.
The sparse Mills-Cross spotlight imager shown in Fig. 11 consists of 18 transmit and 14 receive holographic metasurface antennas, producing only M2 = 252 measurement modes. In comparison to the spotlight imager of Fig. 5, using the sparse layout shown in Fig. 11, the number of transmit and receive antennas is reduced from 80 to 32. The PSF pattern of the sparse Mills-Cross spotlight imager is shown in Fig. 12(a) together with the FWHM analysis of the obtained PSF pattern shown in Fig. 12(b).
The sparse Mills-Cross spotlight imager achieves similar PSF characteristics to the spotlight imager shown in Fig. 5 but using significantly fewer holographic metasurface antennas. Analyzing the FWHM of the PSF patterns Fig. 12(b), we obtained the cross-range resolution of the sparse Mills-Cross spotlight imager to be 2.3 mm.
Finally, we integrate the designed W-band holographic spotlight imager into the K-band frequency-diverse system, using security screening as a motivating example. Due to size constraints, we choose the sparse Mills-Cross spotlight imager layout for integration. The integrated system is shown in Fig. 13, which shows how the two apertures may be incorporated together, fitting the spotlight imager antennas between the frequency-diverse antennas. It should be noted that the integration layout shown in Fig. 13 is just one example; other integration topologies are possible, such as scattering the holographic metasurface antennas in between the frequency-diverse antennas in a sparse manner as will be demonstrated later. As shown in Fig. 13, the frequency-diverse antennas are grouped in sub-arrays of 3 x 3 with some of the antennas within the sub-arrays displaced in an irregular fashion to ensure that the antennas within the spotlight aperture do not overlap with the frequency-diverse antennas.
For the presented application, the scene contains the imaged human-size target padded by a buffer region surrounding the target. The buffer region encompasses the volume that can be selected utilizing a structured light optical or infrared sensor. Such a sensor can find the surface of a human-size target within in some padding error around that surface [44, 45]. As a result, imaging is done over the padded-region depicted in Fig. 13 rather than over a rectangular volume enclosing the human-size target. This step reduces the number of voxels required for reconstruction (and therefore the computational complexity) for the frequency-diverse aperture by a factor of up to 86% .
As shown in Fig. 13, the human-size target has a gun phantom attached to the body as a threat object. First, the frequency-diverse system is used to image the entire scene at the resolution limit of the frequency-diverse aperture. As explained for the imaging scenario presented in Fig. 3, the frequency-diverse system consists of 24 transmit and 72 receive antennas, sampling the K-band at 100 frequency points. As a result, it supports M1 = 172,800 measurement modes. Discretizing the scene at the resolution limit of the frequency-diverse aperture, ∆y = 6.25 mm, ∆z = 6.25 mm, and ∆x = 1.5 cm, results in N1 = 184,393 voxels. For image reconstruction, the matched filter algorithm [37,47] is run on a Nvidia GeForce GTX 1080 graphics processing unit (GPU). The image reconstruction time is measured to be 7.15 s. It should be noted that faster image reconstruction can be achieved by using multiple GPUs running in parallel.
In Fig. 14(a), the presence of the threat-object—the gun phantom—is evident. Analyzing the reconstructed image in Fig. 14(a), the center position of the gun phantom is obtained to be x = 1.05 m, y = 0.08 m and z = 0.06 m. Once the location and morphology of the constrained-ROI are obtained for spotlight imaging, the field distribution to be radiated by the holographic metasurface antennas can be dynamically calculated so that each antenna focuses to the constrained-ROI, enclosing the gun phantom.
The spotlight imager supports M2 = 252 measurement modes while the constrained-ROI is sampled at the resolution limit of the spotlight aperture in the cross-range plane, ∆y = 2.3 mm and ∆z = 2.3 mm, resulting in N2 = 2,500 voxels. Image reconstruction is done using the least-squares reconstruction algorithm [37,47] with the reconstruction time measured to be 0.14 s. The spotlight reconstructed image of the gun phantom is shown in Fig. 14(b). As can be seen in Fig. 14(b), a good outline of the gun phantom is obtained using the spotlight imager, enabling the identification of the phantom. For comparison, the image of the same gun phantom reconstructed using the frequency-diverse aperture is shown in Fig. 14(c). Comparing the two images, it is evident that the image reconstructed using the spotlight aperture exhibits superior resolution and is more informative, enabling the identification of the phantom.
Figures 14(e) and 14(f) present examples of the radiated fields from a number of selected holographic metasurface antennas within the spotlight aperture. For this demonstration, as highlighted in Fig. 14(d), we randomly choose two pairs of holographic antennas; Tx1 (x = 0 m, y = −0.4 m, z = −0.4 m) and Rx1 (x = 0 m, y = −0.4 m, z = −0.35 m), forming the first column of the measurement matrix, H1,1:N, and Tx15 (x = 0 m, y = 0.1 m, z = 0.4 m) and Rx9 (x = 0 m, y = 0.4 m, z = −0.25 m) forming the 135th column of the measurement matrix, H135,1:N, where N denotes the number of voxels. Analyzing the magnitude of the measurement matrix, |H|, for these modes, it is evident in Figs. 14(e) and 14(f) that the fields radiated by the holographic antennas are tailored for the imaged constrained-ROI in that the antennas provide a constant illumination on the constrained-ROI and the beam-waist of the focused radiation is large enough to cover the gun phantom.
Leveraging the fact that the spotlight aperture images only the constrained-ROI – a sub-section of the scene – the layout of the integrated sparse Mills-Cross spotlight aperture can be further simplified by replacing the receive holographic metasurface antennas with wide-beamwidth point sources as shown in Fig. 15(a). The layout shown in Fig. 15(a) requires only 18 holographic metasurface antennas (transmit) in comparison to the spotlight layout shown in Fig. 13 synthesized using 32 holographic metasurface antennas.
It was demonstrated earlier in Fig. 10 that when the holographic antennas are replaced by point sources, the Nyquist sampling criterion is violated due to the spare sampling of the aperture, resulting in aliased images being formed. However, as the reconstruction is done over the constrained-ROI defined by the transmit antennas, these aliased images will remain outside the reconstruction domain and therefore be filtered off. Figure 15(b) demonstrates the image of the gun phantom reconstructed using the system layout shown in Fig. 15(a). Comparing the reconstructed images in Fig. 14(b) and Fig. 15(b), it can be concluded that both images reveal a clear outline of the phantom, albeit the image reconstructed using the system presented in Fig. 15(b) exhibiting more pronounced side lobes due to the sparse sampling of the aperture by the point source receive antennas.
Building on this study, one can consider replacing all the dynamic holographic metasurface antennas, including the transmit antennas shown in Fig. 15(a), with point sources as shown in Fig. 15(c). However, similar to Fig. 10 demonstrated earlier, this results in the aliased images of the phantom being shifted further into the constrained-ROI, making it difficult to discern the outline of the actual phantom as demonstrated in Fig. 15(d).
Finally, we analyze increasing the extent of the integrated Mills-Cross spotlight aperture of Fig. 13 to further improve the resolution of the spotlight imager. In view of this, we distribute the transmit and receive dynamic holographic metasurface antennas across the entire aperture of the frequency-diverse system as shown in Fig. 16(a). As depicted in Fig. 16(a), in this system layout, the holographic metasurface antennas are placed in between the K-band frequency-diverse antennas with no overlap between these two types of antennas being present. To demonstrate the improvement in the resolution of the spotlight imager due to the increased aperture size, a point-source target is imaged using the integrated spotlight imagers of Fig. 13 and Fig. 16(a), respectively, with the corresponding PSF patterns demonstrated in Fig. 16(b). Analyzing Fig. 16(b), while the FWHM of the spotlight aperture of Fig. 13 is measured to be 2.3 mm, the spotlight aperture of Fig. 16(a) exhibits a FWHM of 1.2 mm, suggesting an improved imaging resolution by a factor of almost two times, corresponding to the ratio between the extents of the spotlight apertures of Fig. 13 and Fig. 16(a), which are 90 cm x 90 cm and 2 m x 2 m, respectively.
The proposed W-band spotlight imager can be synthesized using dynamically reconfigurable holographic metasurface antennas applying amplitude or phase modulation to the reference wave. Such a reconfigurable aperture has recently been demonstrated in , where a binary hologram metasurface layer is used to convert a guided-mode reference wave to a focused beam radiation in the Fresnel zone. It should be noted that although the amplitude modulated holographic metasurface apertures are simple to design, in comparison to the phase modulated metasurface apertures, they can exhibit higher sidelobe levels which can cause artifacts in the reconstructed images. However, for the presented spotlight imager, such artifacts can easily be suppressed due to the multistatic operation.
We have designed a composite aperture that produces images using two sub-apertures operating at different frequency ranges. The lower resolution, K-band system makes use of frequency diverse metasurface aperture antennas for imaging of human-sized targets, while a high frequency (75 GHz) dynamic holographic metasurface antenna is used for obtaining higher resolution images of smaller regions. Since the lower frequency system provides information “priors” that inform the higher frequency system, the composite imager provides an interesting example of sensor fusion. For the high-resolution spotlight imager, sub-second reconstructions of smaller areas on larger targets have been demonstrated. A sparse version of the spotlight imager has also been designed and integrated with a K-band frequency-diverse aperture, and the application of this hybrid system has been demonstrated in the context of security screening. Imaging simulations show that the K-band frequency-diverse aperture facilities the detection of threat-objects, while the integrated W-band spotlight aperture enables the extraction of further information from these objects. From an implementation perspective, future work will investigate the accuracy of the position information provided by the frequency-diverse aperture and its effect on the images reconstructed using the spotlight aperture. The a-priori information obtained from the frequency-diverse system determines where to reconstruct for the high frequency spotlight aperture. In view of this, the lower resolution of the frequency-diverse aperture suggests that the voxels can leave an ambiguity in the range for the high-resolution spotlight imager. To address this challenge, multiple images of the constrained ROI can be taken at adjacent planes by using the a-prior information obtained from the frequency-diverse aperture as an initial guess. By adopting additional techniques, such as auto-focusing, the correct imaging distance can be determined. Although demonstrated for security-screening applications, the proposed imager has significant potential to be employed in a variety of applications, including biomedical imaging, non-destructive testing and remote-sensing, where high-resolution and fast image reconstruction are required over dynamically adjusted constrained ROIs. The synthesized spotlight aperture can readily be extended to even higher frequencies to achieve finer resolution limits.
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.
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