Millimeter wave imaging systems are a promising candidate for several applications such as indoor security, industrial non-destructive evaluation, and automotive radar systems. In this paper, we compare the performance of various array configurations that can be enabled by recent automotive radar chips, for imaging applications. High resolution real-time imaging requires an extensive number of measurements which demands a large number of emitters and receivers. Hence, cost and size become major considerations in the design process. In an attempt to reduce the number of emitter and receiver elements, we compare various antenna array architectures to optimize the hardware implementation for high resolution imaging. We consider mono-static single-input-single-output (SISO), multi-static multiple-input-multiple-output (Full-MIMO), and hybrid localized MIMO-SISO (Local-MIMO) architectures. The computationally reconstructed image quality and point spread function from each architecture are compared and traded for the system engineering complexity and cost. We present measurement results from a Synthetic Aperture Radar (SAR) system based on an automotive radar sensor to ensure it is representative of the system’s physics. The comparative results of the SISO, Full-MIMO and Local-MIMO simulations provide for affordable alternatives to the high cost SISO approach.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Millimeter-Wave (mm-wave) radiation is the portion of the electromagnetic spectrum which lies between the microwave and far-infrared regions from 30 GHz to 300 GHz [1–5], which corresponds to the wavelength between 10 mm to 1 mm. This spectrum has shown its potential and capability for imaging applications with a compromise of spatial resolution and material penetration [6,7]. Compared to images formed using lower frequencies, mm-wave images have the advantage of superior spatial resolution due to shorter wavelength. Compared to far-infrared and higher frequencies, many common materials such as packaging material, plastics, and composites, are relatively transparent [4, 8] in the mm-wave. However due to the increased markets for communication and automotive radar, devices in 60 GHz to 82 GHz frequencies have become available in small packaging and low cost. New approaches involving design and manufacturing of more affordable components will continue to make mm-Wave imagers accessible for many applications. Millimeter wave imaging systems have shown great promises in diverse applications including: indoor security, non-destructive testing, and automotive radar [3,7,9–12].
Many groups have investigated antenna array configurations of millimeter wave imagers for security applications.Gonzalez-Valdes, et. al.  consider multistatic configurations with few transmitters and a large array of receivers. Gonzalez-Valdes also discussed imaging with sparse arrays enabled by compressed sensing . Gollub, et.al  demonstrated frequency diverse arrays and studied various approaches for the design of the transmitter and receiver meta surface tiles. Moulder, et. al.  developed a modular tile operating in the 24GHz–30GHz range with 48 transmitters and 48 receivers arranged in a rectangular boundary array. Moulder demonstrated how the tile is used to successfully build a larger array providing the resolution necessary for security imaging. All these approaches utilize custom hardware with a large commercialization step. In this paper, we present similar approaches for millimeter wave imaging but utilize hardware developed for automotive applications. Examples of this hardware are the chips developed by Texas instruments , imec , and other sensor companies.
In this research we investigate effective approaches for two-dimensional (2D) antenna array imaging [18–20] and explore ways to configure automotive radar technology for imaging applications. We investigate and compare the performance of array designs for various imager configurations. We use simulated data from a simple wave propagation model and synthetic data from an automotive radar chip operating at 79GHz center frequency with an equivalent bandwidth of 2GHz [18,19].
We use the inexpensive radar chip in three different architectures. The first architecture is a fully populated array of Single-Input-Single-Output (SISO) transceivers. The second architecture is sparse Full Multiple-Input-Multiple-Output (Full-MIMO) where all of the transmitters and receivers are synchronized across an aperture, which is difficult to achieve across large apertures. The third architecture is Local-MIMO, where a radar chip or chipset has multiple transmitters and receivers that are synchronized across the chip aperture and these “tiles” are placed across a larger array where the tiles are not synchronized. The comparison of image performance of these architectures allows cost and complexity to be traded. Image reconstruction is performed using a matched filter approach.
In section 2, we present the wave propagation model used to produce the simulated data for this study. In section 3, we explain the image reconstruction method  and discuss the sampling and corresponding resolution in Section 4. The various imager configurations and corresponding results are provided in Sections 5 and 6. The SAR measurement setup used to collect the experimental data is described in section 7. Finally, Sections 8 and 9 provide summary discussion and conclusions.
2. Wave propagation model
In this research, the Born approximation for wave propagation  and a point based sampling model are used to simulate the data. This approach has been used successfully by other groups to simulate imagery from large geometries using large arrays [23, 24]. The model assumes that transmitters, receivers and targets are isotropic elements without gain. The interactions between the transmitters and receivers occur through the target points and are decoupled from each other. The transmitters and receivers are single frequency devices that can be swept across frequency to generate frequency domain measurements. Although this model is limited, it provides sufficiently relevant simulation data for our system comparison. The transmitter is assumed to be an isotropic radiator and is characterized by position, amplitude, phase and frequency. Similar to the transmitter, the receiver is assumed to be an isotropic receiver which receives the fields radiated from all the target points. It is characterized by a position, but a phase and amplitude can be added to model distortion effects. The targets are also isotropic receivers and radiators uncoupled from each other. The target points are characterized by their position, amplitude and phase. The field at the input of the receiver is the coherent summation of fields from all target points. Target occlusion, specularity from complex target shapes, and multiple reflections are not observed with this model. Also, the effects of the transmitter and receiver directivity and the resulting illumination non-uniformity are not observed in the simulations. The resolution and aliasing, are captured in the simulations.
In the following, we explain the implementation method of the model. The field at the transmitter points is modulated by the transmitter phase and amplitude and is propagated to each target point. The field ETx(k, r̄Tx) at the transmitter is given by
3. Three dimensional image reconstruction
Numerous radar image formation algorithms have been developed, each with different levels of accuracy and complexity. The result of image reconstruction is the reflectivity function of the target, Atgt. The estimation can be achieved mathematically by the inversion of the forward propagation using matched filtering or Fourier transform methods [25–27]. Fourier transform methods are computationally efficient, and are straight forward to implement for mono-static configurations. For multi-static configurations, these are not trivial [6,28–32]. Matched filtering methods on the other hand, are straight forward to implement for both mono-static and multi-static array configurations but lack computational efficiency. Here we used the matched filter technique implemented in MATLAB . Matched filtering is a full space variant correlator and can reconstruct images with high accuracy irrespective of transmitter and receiver positions (i.e. multi-static vs. mono-static). Other algorithms such as the back projection algorithm  or Omega-K migration, holographic reconstruction technique  and other Fourier transform methods  have reduced computational burden but at the cost of reconstruction accuracy. The measurement configurations presented in this work require reconstruction from multi-static measurements. Implementation of the matched filter method for multi-static measurements, and the reconstruction accuracy, were important considerations in the analysis presented here.
3.1. Matched filter
The matched filter in the space domain is adapted from reference . The geometry of the measurement is shown in Fig. 1. The object is centered around the origin of the coordinate system and has a reflectivity function of Atgt(x, y, z) = Atgt(r̄). The bi-static response (receiver measurement) to a point scatterer at r̄ = (x, y, z) is given byEq. (9) can be expressed as a discrete sum of the stepped measurement positions (x′n, y′n, z′n). The frequency response is also typically discrete. The resulting summations is implemented in MATLAB and are given by: Eq. (10) varies with the position of the Tx-Rx pairs and with the position in space where the reflectivity function is reconstructed. The calculation of the kernel and the summation in Eq. (10) makes this method computationally inefficient, but the convenience of the bi-static formulation and reconstruction accuracy favor this method for analysis studies like the one presented in this work.
4. Sampling and resolution
To implement the image reconstruction algorithms, the collected data is discretized. In general, the discretization needs to fulfill the Nyquist sampling criterion. The sampling needed along the aperture is determined by different parameters including the wavelength, size of the target, and distance to the target. The Nyquist criterion is satisfied if the phase shift from a sample point to next is less than π radian. The worst case occurs when the target is very close to the aperture. For a spatial sample interval Δx, the lowest limit has a phase shift of not more than 2kΔx. Therefore, the sampling criterion is
The frequency sampling limit also can be determined in a similar way. The phase shift due to a change in wavenumber Δk is 2ΔkRmax, where Rmax is the maximum target range. So the phase shift is less than π radian which yields Δk < π/2Rmax or it can be expressed as
In terms of resolution, the performance of the mm-wave imaging systems is limited by the blur spot produced by diffraction. The spatial cross resolution of the reconstructed image can be expressed approximately by 
5. Imager configurations
To compare various imager configurations, we consider three primary architectures with six configurations: one configuration is mono-static, and five are multi-static. There are device and system benefits for each architecture (SISO, Full-MIMO, Local-MIMO). The trades consist of number of transmitter and receiver elements, full aperture measurement time, synchronization complexity, resolution, and aliasing limited field of view. The system performance of each architecture/configuration is compared. All architectures were designed to provide the same number of measurements to form an image. This is the common attribute of all architectures in this paper, while the number of the transmitters and receivers are reduced to make the imaging system affordable, compact, and reduce the required power. The measurement geometry is shown in Fig. 1(a). The source and receiver are assumed to be at position (x′, y′, z′), and the measured receiver response is E(x′Rx, y′Rx, z′Rx, k). A general point on the target is assumed to be at position (x, y, z). The target is characterized by a reflectivity function Atgt(x, y, z), which is the ratio of the reflected field to incident field. The target is a series of spheres arranged in a archimedian spiral, with locations described by:
The spiral target is arranged on xz coordinates with increased height on the y direction. It is a collection of 14 spheres separated by 1.5″ in the xz plane and 1.5″ on the y axis (Figs. 1(b), 1(c) and 1(d) show the target geometry in different cross sections). The reason for choosing this target geometry is to determine the resolution in three dimensions.
5.2. Mono-Static: Single-Input-Single-Output (SISO)
In the mono-static architecture/configuration, the transmitter and the receiver are collocated, or slightly separated(shown in Fig. 2). In the SISO simulation, we use an array of 150×150 transmitter and receiver elements spaced one wavelength apart in (3.8 mm) pitch. The aperture size is 570×570 mm2. We show a fewer number of transmitters and receivers in the figure for visualization clarity. This architecture requires the largest number of transmitters and receivers compared to the other architectures. The scan time for an array like this will be proportional to the number of transceiver pairs. The field of view that can be achieved will be dependent on the pitch of the antennas and the resolution can be calculated using Eq. (13). Since the transmitters and receivers are closely spaced, synchronization of the pair is trivial.
5.3. Multi-static: full multiple-input-multiple-output (Full-MIMO)
In the Full-MIMO architecture and configuration, transmitters are used to illuminate the object from different directions, and the receivers collect the scattered light from other directions. For clarity, again the schematic diagram shows fewer elements. In Full-MIMO, one line of transmitters and one line of receivers work together in a MIMO architecture that is fully coherent across the transmitters and receivers. A simple example design of a Full-MIMO array (Fig. 3) is a cross arrangement of antennas. The geometry includes two orthogonal, one-dimensional arrays of transmitters (Tx) and receivers (Rx). Each transmitter radiates to the target and reflects back and is received by the entire vertical receiver array. Other configurations are also possible, for example a rectangular boundary array  similar to the configurations in the next section. This configuration is more challenging to synchronize, for large arrays, compared to the cross configuration due to the larger separations between elements. In the cross configuration Full-MIMO simulation, the array includes 150 transmitter and 150 receiver elements with an antenna spacing of 3.8 mm. It acquires the same number of measurements as the SISO architecture described previously. Because the line arrays are focused in only one dimension, the equivalent SISO resolution aperture size is half of the full size as shown by the green dashed line in Fig. 3. Therefore, we also increased the pitch of the Full-MIMO with two wavelengths and calculated its effect on resolution results. This however, comes at the cost of aliasing and the corresponding reduction in imager field of view. The technical challenge of this architecture is that all transmitters and all receivers must be synchronized across the entire aperture which is sometimes not feasible. The benefit, is the reduced number of elements, and the reduced measurement time due to the simultaneous receiver measurements. Measurement time for this configuration is proportional to the number of transmitters.
5.4. Multi-static: local multiple-input-multiple-output (Local-MIMO)
The concept of the Local-MIMO approach is advantageous for planar multi-static array designs. The advantage lies in the fact that only local synchronization is required, and there are fewer elements than the SISO approach. Figure 4 shows an example of a Local-MIMO concept where the tiles are 2 rows of 5 transmitters crossed with 2 rows of 5 receivers. The aperture is divided into an array of MIMO tiles which are not synchronized with each other. We implemented two different types of Local-MIMO configurations. In the simulations, the first Local-MIMO architecture includes 2×5 transmitters and 5×2 receivers. This approach makes a square shape for each tile where there are 15×15 tiles in the total aperture. The second Local-MIMO approach has 2×15 transmitters and 15×2 receivers in each tile and there are 5×5 tiles in the total aperture. for both configurations the gap between the tiles is one wavelength and two wavelength (four configurations). The measurements in these configurations match the number of measurements of SISO and Full-MIMO configurations, but we use fewer transmitters and receivers. If we define the total number of elements in one side of SISO design as N which is 150 in our simulations, and L determines the number of elements in one side of the local tile which is equal to 5 for Local-MIMO type 1 and 15 for Local-MIMO type 2, the total number of elements used in the Local-MIMO architectures becomes (N/2L)2. Therefore, the number of required elements is reduced for Local-MIMO designs, while having the same number of measurements. The measurement time is also reduced by the same factor and will depend on the number of transmitters. As hinted earlier, the synchronization is possible at the tile level, in fact current advances in automotive radar have shown 16×12 MIMO configurations by daisy chaining several radar chips . The resolution and aliasing trades for the Local-Mimo cases will be similar to the Full MIMO case.
Finally, a random tile MIMO was implemented. The same configurations that were described above for Local-MIMO were implemented, however the positions of the tiles were randomized (Fig. 5). Two random Local-MIMO configurations were implemented. The same tile geometries as the Local-MIMO were modified with a random tile position. The random tile position offset was limited to one element pitch. Therefore, four configurations were simulated with the Local-MIMO architecture and their random variants.
6. Simulation comparison results
In this section, simulation results of the presented configurations are discussed. In this comparison, we use the 3D spiral shape target as described in section 5.1. The target was placed 2m away from the antenna array. We generated data by simulating mm-wave propagation against the spiral target and then reconstructed the image with the matched filter algorithm described in section 2. The spheres in the measurement were specular and this is not captured by the simulation point model. To account for this, we implemented a small diameter sphere in the simulation, 0.05 mm. This diameter matched well with the measurements. The output images were reconstructed for each configuration and were compared. The corresponding results in xz and xy cross sections are shown in Fig. 6 and Fig. 7 respectively. The x and y axes provide cross resolution and the z axis provides range resolution. The range resolution is larger than cross resolution as we expected. The SISO configuration image (Figs. 6(a), 7(a)) and the Full-MIMO configuration image (Figs. 6(b), 7(b)) are reconstructed with 1λ pitch between (transmitter/receiver) arrays in the xy plane. The Local-MIMO type 1 image (Figs. 6(c), 7(c)) and the Local-MIMO type 2 image (Figs. 6(d), 7(d)) are reconstructed with 2λ pitch between arrays within each tile and 1λ separation between tiles in the xy plane. The randomized Local-MIMO type 1 image (Figs. 6(e), 7(e)) and the Randomized Local-MIMO type 2 image (Figs. 6(f), 7(f)) are reconstructed with 2λ pitch between arrays within each tile and a random separation less than 1λ between tiles in the xy plane.
The SISO configuration provides high resolution but in comparison the resolution of the Full-MIMO configuration appears to be degraded. This is due to the fact that the virtual array of the Full-MIMO configuration is half of that of the SISO configuration, which leads to a lower resolution. Note that the virtual array is only a receiver array and is achieved by the convolution of the transmitter and receiver arrays [37, 38]. The equivalency with the SISO array is made only for resolution purposes through Eq. (13). Other configurations include Local-MIMO type 1 and 2 and the planar randomized Local-MIMO with two wavelength pitch. They provide image resolution similar to SISO because their equivalent aperture size is nearly the same as the SISO configuration. All configurations, except Full-MIMO, display comparable performance in image reconstruction with few minor artifacts. As illustrated in the reconstructed image of Local-MIMO type 1 (Figs. 6(c), 7(c)) and the randomized Local-MIMO type 1 (Figs. 6(e), 7(e)), there is an aliasing effect due to the pitch between the tiles in the design. The aliasing is from to the discontinuity of the composite array phase center pitch. As expected, this aliasing effect is mitigated when the element pitch in the tile is increased to two wavelengths while the inter-tile gap is maintained to one wavelength (Figs. 6(d), 6(f)). The phase center pitch in this case is one wavelength. This aliasing is also slightly disturbed when the tile placement is disturbed as is the case of randomized Local-MIMO type 1 and 2 (Figs. 6(e), 6(f)).
To run a more precise resolution comparison, the Point Spread Function (PSF) of each configuration was calculated and compared (Fig. 8). As discussed, since the equivalent aperture size of the Full-MIMO configuration with 1λ pitch between arrays is half of that of the SISO configuration with 1λ pitch, its reconstructed image resolution is lower than that reconstructed by the SISO configuration. Thus, the PSF of SISO proves to be about half the size of the PSF of the Full-MIMO configuration (Fig. 8(a)). We simulated a Full-MIMO, Local-MIMO type 1, and Local-MIMO type 2 configurations with 2λ pitch between arrays to compare with SISO configuration and confirm that this leads to a similar resolution. As expected, we achieved similar resolution and PSF size as the SISO configuration (Fig. 8(b)).
The improvement in resolution achieved through inner tile pitch increase (Full MIMO and Local MIMO with 2λ pitch) comes at the cost of field of view aliasing. From antenna array theory, the grating lobes of the array are a function of this pitch. In imaging, the grating lobes limit the usable filed of view of the imager. A pitch of 2λ would correspond to 0.5radian field of view. At a distance of 2 meters this corresponds to approximately one meter lateral field of view. The result of the simulation with a 2λ tile are shown in Fig. 9. The aliasing from a point target two meters away at the center of the cross range, is located at approximately one meter away from the actual target.
7. SISO measurements
For the mono-static case with SISO measurements, we performed a real Synthetic Aperture Radar (SAR) image. In the SAR measurement, the aperture was synthesized with many radar measurements. The synthesizing was done by raster-scanning the transmitter and receiver mechanically. This mono-static measurement corresponded to the SISO simulation, where the position of the transmitter and receiver were collocated in xy plane in a 2D array. The receiver collected the reflection field coherently over the scanned area and over all frequencies. By integrating the measured fields on position and frequency in the matched filter Eq. (10), the reflection function of the target was reconstructed.
The measurement setup is shown in Fig. 10(a). It includes the scanning stage on which the radar chip is mounted and scanned mechanically. The radar was designed and fabricated by imec [18,19]. The central frequency of the chip was 79 GHz, and the bandwidth was 2 GHz. The radar had a microstrip antenna and the beam profile covered 10° in elevation angle and 80° in azimuth direction. The output power was 10 dBm. We measured two targets, a resolution target similar to the simulated data and a mannequin with a weapon. The resolution target was composed from a collection of 14 Aluminum spheres where each sphere had 1.5 inches diameter and the spheres were arranged in a spiral shape as shown in Fig. 10(a). The measurement compromised a total number of 150×150 sequential scanning positions. The scanning step was equal to one wavelength of 3.8 mm and the target was placed in 2 m from the antenna array. As seen in Fig. 10, the simulation results matched the measured results, validating our simulations and corresponding comparisons.
The other target is used to demonstrate concealed weapon detection capability. We believed this demonstration could show the applicability of the three architectures using low cost automotive radar devices. In addition, using Local-MIMO similar resolution can be achieved. A fully dressed mannequin carrying a gun was imaged. The mannequin was placed two meters away from the antenna array and was scanned using 150×150 measurements with a pitch of one wavelength (3.8mm). First we imaged the mannequin with an uncovered gun. Figure 11(a) is the visible image of the mannequin, Fig. 11(b) is the mm-wave image of the gun, and Fig. 11(c) is the fusion of the mm-wave image and the visible image. Then we imaged the mannequin with a covered gun. The covered gun, which is obscured in the visible imaging system (Fig. 12(a)), is seen by mm-wave imaging system. The results are shown in mm-wave image of Fig. 12(b) and fusion image of Fig. 12(c).
In this study, we explored the design of sparse arrays for mm-wave imaging. We used a 79 GHz automotive radar chip, which is reasonably priced and accessible for automotive applications, as a pixel for our imaging system. Imaging applications require a large number of radar chips. Thus, they become expensive and need a substantial amount of power, integration and maintenance cost. We considered multi-static architectures to reduce the number of elements while retaining performance and image quality. In Table 1 we provide an overview of the architectures and configurations that were studied highlighting important system characteristics: number of elements, the measurement time, resolution, unaliased field of view, synchronization complexity, and physical size. We assigned a score to each characteristic based on the contribution to system cost and feasibility, and we tallied the scores for each configuration. The magnitude of the scores is arbitrary but is generally more negative as a function of increased cost, increased complexity, or reduced performance. For example, a large number of elements makes the system cost prohibitive, a large measurement time makes the system unattractive for many applications, reduced resolution has performance implications, and reduced field of view limits the application space. Field of view is more important than resolution for the numbers considered in this work. A large negative score means that the system is less feasible than one with a low negative score (closer to zero is better).
The SISO configuration provides good resolution but it requires many transmitters and receivers. So, prohibitive cost is the main issue for this configuration. Full-MIMO provides comparable resolution but it has technical challenges due to the phase synchronization between the arrays of transmitters and receivers over large apertures. These challenges will require substantial engineering effort to be resolved. Local-MIMO type 1 with two wavelength pitch provides similar resolution to the SISO configuration accompanied by aliasing of the field of view. The number of elements for this configuration is still large at over 2250 + 2250 transmit and receive elements. Local-MIMO type 2 provides results very similar to the Local-MIMO type 1 and SISO. The number of elements is manageable (750 + 750) and MIMO synchronization is also feasible although challenging.
Taking all the system characteristics onto account, the most feasible system is the Local MIMO type 2 with 1λ pitch. This system results in the fewer number of elements, has reasonable measurement time, and large field of view. Synchronization complexity is challenging but current reports from industry indicate that a 30×30 MIMO is possible . The resolution of this system is reasonable for many security applications, providing 1 cm resolution at 2 meter range.
We analyzed and compared the performance of different mm-wave imaging antenna array configurations. The SISO configuration provides good resolution but uses many transmitters and receivers. Full-MIMO provides comparable resolution but has technical challenges due to the synchronization among all transmitters and receivers. Local-MIMO type 1 provides very similar images to Full-MIMO, and Local-MIMO type 2 leads to comparable resolution while having fewer elements. Considering the key system characteristics, Local-MIMO type 2 is a feasible configuration for implementation of security imaging systems. The simulation model was validated using SISO measurements with an imec automotive radar device scanned in a two-dimensional grid. Examples of images from a concealed weapon scenario were shown. This work illustrates the feasibility of using automotive radar chips for mmw imaging applications such as security screening.
1. S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, and G. Williams et al., “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50, 043001 (2017). [CrossRef]
3. D. Dufour, L. Marchese, M. Terroux, H. Oulachgar, F. Généreux, M. Doucet, L. Mercier, B. Tremblay, C. Alain, and P. Beaupré et al., “Review of terahertz technology development at ino,” J. Infrared, Millimeter, Terahertz Waves 36, 922–946 (2015). [CrossRef]
4. F. Sanjuan, G. Gaborit, and J.-L. Coutaz, “Sub-wavelength terahertz imaging through optical rectification,” Sci. reports 8, 13492 (2018). [CrossRef]
5. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. photonics 1, 97 (2007). [CrossRef]
6. S. S. Ahmed, Electronic microwave imaging with planar multistatic arrays (Logos Verlag Berlin GmbH, 2014).
7. C. Jansen, S. Wietzke, O. Peters, M. Scheller, N. Vieweg, M. Salhi, N. Krumbholz, C. Jördens, T. Hochrein, and M. Koch, “Terahertz imaging: applications and perspectives,” Appl. Opt. 49, E48–E57 (2010). [CrossRef] [PubMed]
8. B. Nauwelaers, I. Ocket, Q. Feng, V. Tavakol, and D. Schreurs, “Is imaging with millimeter wave the same as optical imaging,” in European Conference on the Use of Modern Information and Communication Technologies (ECUMICT), (2008), pp. 1.
9. D. M. Sheen, D. L. McMakin, and T. E. Hall, “Three-dimensional millimeter-wave imaging for concealed weapon detection,” IEEE Transactions on microwave theory techniques 49, 1581–1592 (2001). [CrossRef]
11. C. Jansen, S. Wietzke, O. Peters, M. Scheller, N. Vieweg, M. Salhi, N. Krumbholz, C. Jördens, T. Hochrein, and M. Koch, “Terahertz imaging: applications and perspectives,” Appl. Opt. 49, E48–E57 (2010). [CrossRef] [PubMed]
12. R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue,” Phys. Medicine & Biol. 47, 3853 (2002). [CrossRef]
13. B. Gonzalez-Valdes, Y. Alvarez, S. Mantzavinos, C. M. Rappaport, F. Las-Heras, and J. A. Martinez-Lorenzo, “Improving security screening: A comparison of multistatic radar configurations for human body imaging,” IEEE Antennas Propag. Mag. 58, 35–47 (2016). [CrossRef]
14. B. Gonzalez-Valdes, G. Allan, Y. Rodriguez-Vaqueiro, Y. Alvarez, S. Mantzavinos, M. Nickerson, B. Berkowitz, J. Martı, F. Las-Heras, and C. M. Rappaport et al., “Sparse array optimization using simulated annealing and compressed sensing for near-field millimeter wave imaging,” IEEE Transactions on Antennas Propag. 62, 1716–1722 (2014). [CrossRef]
15. J. Gollub, O. Yurduseven, K. Trofatter, D. Arnitz, M. Imani, T. Sleasman, M. Boyarsky, A. Rose, A. Pedross-Engel, and H. Odabasi et al., “Large metasurface aperture for millimeter wave computational imaging at the human-scale,” Sci. reports 7, 42650 (2017). [CrossRef]
16. W. F. Moulder, J. D. Krieger, J. J. Majewski, C. M. Coldwell, H. T. Nguyen, D. T. Maurais-Galejs, T. L. Anderson, P. Dufilie, and J. S. Herd, “Development of a high-throughput microwave imaging system for concealed weapons detection,” in 2016 IEEE International Symposium on Phased Array Systems and Technology (PAST), (IEEE, 2016), pp. 1–6.
17. D. Wang, “Cascaded Radar and Body and Chassis Automotive Applications,” https://training.ti.com/sites/default/files/docs/cascaded-radar-and-body_chassis-automotive-applications.pdf/ (2019). [Online; accessed 28-April-2019].
18. A. Bourdoux, K. Parashar, and M. Bauduin, “Phenomenology of mutual interference of fmcw and pmcw automotive radars,” in Radar Conference (RadarConf), 2017 IEEE, (IEEE, 2017), pp. 1709–1714. [CrossRef]
19. D. Guermandi, Q. Shi, A. Dewilde, V. Derudder, U. Ahmad, A. Spagnolo, I. Ocket, A. Bourdoux, P. Wambacq, and J. Craninckx et al., “A 79-ghz 2×2 mimo pmcw radar soc in 28-nm cmos,” IEEE J. Solid-State Circuits 52, 2613–2626 (2017). [CrossRef]
20. N. Mohammadian, O. Furxhi, L. Zhang, P. Offermans, G. Ghazi, and R. Driggers, “Performance modeling of terahertz (thz) and millimeter waves (mmw) pupil plane imaging,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XXIX,, vol. 10625 (International Society for Optics and Photonics, 2018), p. 1062511.
21. L. A. Gorham and L. J. Moore, “Sar image formation toolbox for matlab,” in Algorithms for Synthetic Aperture Radar Imagery XVII,, vol. 7699 (International Society for Optics and Photonics, 2010), p. 769906. [CrossRef]
22. J. Goodman, Introduction to Fourier optics (McGraw-hill, 2008).
23. G. Lipworth, A. Rose, O. Yurduseven, V. R. Gowda, M. F. Imani, H. Odabasi, P. Trofatter, J. Gollub, and D. R. Smith, “Comprehensive simulation platform for a metamaterial imaging system,” Appl. opt. 54, 9343–9353 (2015). [CrossRef] [PubMed]
24. G. Lipworth, A. Mrozack, J. Hunt, D. L. Marks, T. Driscoll, D. Brady, and D. R. Smith, “Metamaterial apertures for coherent computational imaging on the physical layer,” JOSA A 30, 1603–1612 (2013). [CrossRef] [PubMed]
25. M. Born and E. Wolf, “Principles of optics, 7th (expanded) ed,” Camb. U. Press.Cambridge, UK890 (1999). [CrossRef]
26. M. Soumekh, Fourier array imaging (Prentice-Hall, Inc., 1994).
27. J. Fortuny, “Efficient algorithms for three-dimensional near-field synthetic aperture radar imaging,” Ph.D. thesis, Inst. for the Protection and Security of the Citizen Humanitarian Security Unit (2001).
28. J. M. Lopez-Sanchez and J. Fortuny-Guasch, “3-d radar imaging using range migration techniques,” IEEE Transactions on antennas propagation 48, 728–737 (2000). [CrossRef]
29. T. S. Ralston, G. L. Charvat, and J. E. Peabody, “Real-time through-wall imaging using an ultrawideband multiple-input multiple-output (mimo) phased array radar system,” in 2010 IEEE international symposium on phased array systems and technology, (IEEE, 2010), pp. 551–558. [CrossRef]
30. Y. Qi, W. Tan, Y. Wang, W. Hong, and Y. Wu, “3d bistatic omega-k imaging algorithm for near range microwave imaging systems with bistatic planar scanning geometry,” Prog. In Electromagn. Res. 121, 409–431 (2011). [CrossRef]
31. L. Pulido-Mancera, T. Fromenteze, T. Sleasman, M. Boyarsky, M. F. Imani, M. Reynolds, and D. Smith, “Application of range migration algorithms to imaging with a dynamic metasurface antenna,” JOSA B 33, 2082–2092 (2016). [CrossRef]
32. A. V. Diebold, L. Pulido-Mancera, T. Sleasman, M. Boyarsky, M. F. Imani, and D. R. Smith, “Generalized range migration algorithm for synthetic aperture radar image reconstruction of metasurface antenna measurements,” JOSA B 34, 2610–2623 (2017). [CrossRef]
33. A. W. Doerry, E. E. Bishop, and J. A. Miller, “Basics of backprojection algorithm for processing synthetic aperture radar images,” Sandia Natl. Lab. Report, No. SAND2016–1682 (2016).
35. M. Born and E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light (Elsevier, 2013).
36. R. J. Kozick and S. A. Kassam, “Synthetic aperture pulse-echo imaging with rectangular boundary arrays (acoustic imaging),” IEEE Transactions on Image Process. 2, 68–79 (1993). [CrossRef]
37. W.-Q. Wang, “Virtual antenna array analysis for mimo synthetic aperture radars,” Int. J. Antennas Propag. 2012587276 (2012). [CrossRef]
38. P. Liu, B. Lu, and X. Sun, “A method of two-dimensional mimo planar array design based on sub-array segmentation for through-wall imaging,” in PIERS Proceedings, (2014).