Dynamically reconfigurable holographic metasurface aperture for a Mills-Cross monochromatic microwave camera

We present a reconfigurable, dynamic beam steering holographic metasurface aperture to synthesize a microwave camera at K-band frequencies. The aperture consists of a 1D printed microstrip transmission line with the front surface patterned into an array of slotshaped subwavelength metamaterial elements (or meta-elements) dynamically tuned between “ON” and “OFF” states using PIN diodes. The proposed aperture synthesizes a desired radiation pattern by converting the waveguide-mode to a free space radiation by means of a binary modulation scheme. This is achieved in a holographic manner; by interacting the waveguide-mode (reference-wave) with the metasurface layer (hologram layer). It is shown by means of full-wave simulations that using the developed metasurface aperture, the radiated wavefronts can be engineered in an all-electronic manner without the need for complex phase-shifting circuits or mechanical scanning apparatus. Using the dynamic beam steering capability of the developed antenna, we synthesize a Mills-Cross composite aperture, forming a single-frequency all-electronic microwave camera. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement OCIS codes: (110.0110) Imaging systems; (110.1220) Apertures; (350.4010) Microwaves; (090.2910) Holography, microwave; (110.1758) Computational imaging; (110.2970) Image detection systems. References and links 1. C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An Overview of the Theory and Applications of Metasurfaces: The Two-Dimensional Equivalents of Metamaterials,” IEEE Antennas Propag. Mag. 54(2), 10–35 (2012). 2. C. A. Balanis, Modern antenna handbook, 2nd ed. (John Wiley & Sons, 2011). 3. G. Minatti, F. Caminita, E. Martini, M. Sabbadini, and S. Maci, “Synthesis of Modulated-Metasurface Antennas with Amplitude, Phase, and Polarization Control,” IEEE Trans. Antenn. Propag. 64(9), 3907–3919 (2016). 4. O. Yurduseven and D. R. Smith, “Dual-Polarization Printed Holographic Multibeam Metasurface Antenna,” IEEE Antennas Wirel. Propag. Lett. 16, 2738–2741 (2017). 5. M. C. Johnson, S. L. Brunton, N. B. Kundtz, and J. N. Kutz, “Sidelobe Canceling for Reconfigurable Holographic Metamaterial Antenna,” IEEE Trans. Antenn. Propag. 63(4), 1881–1886 (2015). 6. O. Yurduseven, D. L. Marks, J. N. Gollub, and D. R. Smith, “Design and Analysis of a Reconfigurable Holographic Metasurface Aperture for Dynamic Focusing in the Fresnel Zone,” IEEE Access 5, 15055–15065 (2017). 7. S. Pandi, C. A. Balanis, and C. R. Birtcher, “Design of scalar impedance holographic metasurfaces for antenna beam formation with desired polarization,” IEEE Trans. Antenn. Propag. 63(7), 3016–3024 (2015). 8. D. R. Smith, O. Yurduseven, L. P. Mancera, P. Bowen, and N. B. Kundtz, “Analysis of a Waveguide-Fed Metasurface Antenna,” Phys. Rev. Appl. 8(5), 054048 (2017). 9. N. Kundtz, “Next generation communications for next generation satellites,” Microw. J. 57(8), 56–64 (2014). 10. E. Brookner, “Metamaterial advances for radar and communications,” Microw. J. 59(11), 22–42 (2016). 11. R. C. Hansen, Phased array antennas, 2nd ed. (John Wiley & Sons, 2009). 12. D. M. Sheen, D. L. McMakin, and T. E. Hall, “Three-dimensional millimeter-wave imaging for concealed weapon detection,” IEEE Trans. Microw. Theory Tech. 49(9), 1581–1592 (2001). 13. D. Smith, O. Yurduseven, B. Livingstone, and V. Schejbal, “Microwave imaging using indirect holographic techniques,” IEEE Antennas Propag. Mag. 56(1), 104–117 (2014). 14. J. A. Martinez-Lorenzo, F. Quivira, and C. M. Rappaport, “SAR imaging of suicide bombers wearing concealed explosive threats,” Prog. Electromagnetics Res. 125, 255–272 (2012). Vol. 26, No. 5 | 5 Mar 2018 | OPTICS EXPRESS 5281 #318154 https://doi.org/10.1364/OE.26.005298 Journal © 2018 Received 22 Dec 2017; revised 14 Feb 2018; accepted 14 Feb 2018; published 21 Feb 2018 15. F. Qi, I. Ocket, D. Schreurs, and B. Nauwelaers, “A system-level simulator for indoor mmW SAR imaging and its applications,” Opt. Express 20(21), 23811–23820 (2012). 16. J. Laviada, A. Arboleya-Arboleya, Y. Alvarez-Lopez, C. Garcia-Gonzalez, and F. Las-Heras, “Phaseless Synthetic Aperture Radar with Efficient Sampling for Broadband Near-Field Imaging: Theory and Validation,” IEEE Trans. Antenn. Propag. 63(2), 573–584 (2015). 17. A. J. Fenn, D. H. Temme, W. P. Delaney, and W. E. Courtney, “The development of phased array radar technology,” Linc. Lab. J. 12(2), 321–340 (2000). 18. S. Withington, G. Saklatvala, and M. P. Hobson, “Partially coherent analysis of imaging and interferometric phased arrays: noise, correlations, and fluctuations,” J. Opt. Soc. Am. A 23(6), 1340–1348 (2006). 19. B. H. Ku, P. Schmalenberg, O. Inac, O. D. Gurbuz, J. S. Lee, K. Shiozaki, and G. M. Rebeiz, “A 77–81-GHz 16element phased-array receiver with ±50° beam scanning for advanced automotive radars,” IEEE Trans. Microw. Theory Tech. 62(11), 2823–2832 (2014). 20. 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,” IEEE International Symposium on Phased Array Systems and Technology, 551–558 (2010). 21. O. Yurduseven, J. N. Gollub, D. L. Marks, and D. R. Smith, “Frequency-diverse microwave imaging using planar Mills-Cross cavity apertures,” Opt. Express 24(8), 8907–8925 (2016). 22. T. Fromenteze, O. Yurduseven, M. Boyarsky, J. Gollub, D. L. Marks, and D. R. Smith, “Computational polarimetric microwave imaging,” Opt. Express 25(22), 27488–27505 (2017). 23. J. Hunt, T. Driscoll, A. Mrozack, G. Lipworth, M. Reynolds, D. Brady, and D. R. Smith, “Metamaterial apertures for computational imaging,” Science 339(6117), 310–313 (2013). 24. O. Yurduseven, V. R. Gowda, J. N. Gollub, and D. R. Smith, “Printed aperiodic cavity for computational and microwave imaging,” IEEE Microw. Wirel. Compon. Lett. 26(5), 367–369 (2016). 25. JJ. N. Gollub, O. Yurduseven, K. P. Trofatter, D. Arnitz, M. F. Imani, T. Sleasman, M. Boyarsky, A. Rose, A. Pedross-Engel, H. Odabasi, T. Zvolensky, G. Lipworth, D. Brady, D. L. Marks, M. S. Reynolds, and D. R. Smith, “Large metasurface aperture for millimeter wave computational imaging at the human-scale,” Sci. Rep. 7, 42650 (2017). 26. D. L. Marks, O. Yurduseven, and D. R. Smith, “Cavity-backed metasurface antennas and their application to frequency diversity imaging,” J. Opt. Soc. Am. A 34(4), 472–480 (2017). 27. O. Yurduseven, T. Fromenteze, D. L. Marks, J. N. Gollub, and D. R. Smith, “Frequency-diverse computational microwave phaseless imaging,” IEEE Antennas Wirel. Propag. Lett. 16, 2808–2811 (2017). 28. T. Sleasman, M. F. Imani, J. N. Gollub, and D. R. Smith, “Dynamic metamaterial aperture for microwave imaging,” Appl. Phys. Lett. 107(20), 204104 (2015). 29. P. Hariharan, Optical Holography: Principles, Techniques and Applications (Cambridge University, 1996). 30. MACOM MA4AGFCP910, https://www.macom.com/products/product-detail/MA4AGFCP910, accessed on 20 November 2017. 31. Y. Fan, T. Qiao, F. Zhang, Q. Fu, J. Dong, B. Kong, and H. Li, “An electromagnetic modulator based on electrically controllable metamaterial analogue to electromagnetically induced transparency,” Sci. Rep. 7, 40441 (2017). 32. 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(31), 9343–9353 (2015). 33. 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,” Prog. Electromagnetics Res. 150, 97–107 (2015). 34. D. L. Marks, J. Gollub, and D. R. Smith, “Spatially resolving antenna arrays using frequency diversity,” J. Opt. Soc. Am. A 33(5), 899–912 (2016). 35. O. Yurduseven, J. N. Gollub, A. Rose, D. L. Marks, and D. R. Smith, “Design and simulation of a frequencydiverse aperture for imaging of human-scale targets,” IEEE Access 4, 5436–5451 (2016).


Introduction
Metasurfaces are artificial structures synthesized using an array of subwavelength elements distributed in a periodic or non-periodic fashion [1,2]. These artificial surfaces can be used to modulate the radiated wavefronts, enabling the synthetization of a radiation pattern of interest [3][4][5][6][7][8][9][10]. This simple yet powerful approach circumvents the need for phase shifting circuits or mechanical moving apparatus to achieve reconfigurable operation, significantly simplifying the hardware architecture. Traditional dynamic beam forming techniques heavily rely on using the concept of electronically scanned antennas (ESAs) leveraging the phase array technology [11]. Although high-fidelity beam control has been achieved, phased arrays can be limited in key system metrics, such as system cost, power consumption and hardware complexity. Conventionally, in a phased array aperture, each antenna requires a phase shifting circuit, resulting in a complex system architecture. Moreover, due to the insertion loss of these circuits, power amplifiers are also needed, increasing the power consumption and cost of such systems. Alternatively, leveraging metamaterials and holography, artificial surfaces can be designed to synthesize a desired radiation pattern. Using such surfaces, conversion of a surface-wave [3] or a guided-mode [4] into a free-space radiation has been successfully achieved. Although encouraging results have been demonstrated, a major limitation to these techniques is the static operation, suggesting that such apertures are not reconfigurable and require designing a new antenna when the desired radiation pattern is changed. With the recent developments within the printed-circuit-board (PCB) technology combined with the efforts to commercialize the concept of metasurfaces [9,10], dynamically reconfigurable metasurface antennas have become a reality. Such an antenna presented in [5] leverages liquid-crystal as the control mechanism to achieve dynamic beam forming.
Conventional imaging modalities within the microwave and millimeter-wave frequency regimes can be understood as versions of synthetic aperture radar (SAR) [12][13][14][15][16] and phasedarray ESA technology [17][18][19][20]. Both these techniques are realized by means of raster scanning the scene at the Nyquist limit either mechanically (SAR) or electronically (ESAs). The mechanical scanning of the scene limits the data acquisition time for SAR while ESA systems can exhibit complex system hardware and high power consumption due to the requirement for phase-shifting circuits and power amplifiers. Recently, the use of metasurfaces to produce randomized quasi-orthogonal field patterns interrogating the imaged scene has gained traction as a means of addressing such limits of conventional imaging modalities. These approaches mainly rely on two techniques; (a) frequency-diversity [21-27] and (b) dynamic apertures [28]. In the frequency-diverse approach, the scene is encoded onto a set of measurements by means of a frequency-sweep over a wide frequency band while in the dynamic aperture approach the control of the field patterns is achieved using semiconductor elements over a narrow bandwidth.
In this paper, building on the near-field reconfigurability concept presented in [6] and the analytical framework shown in [8], we demonstrate a dynamically reconfigurable holographic metasurface aperture for electronic beam scanning and microwave imaging applications. The metasurface aperture consists of an array of subwavelength slot-shaped metamaterial elements (or meta-elements) sampling the guided-mode. The coupling response of the metaelements is electronically controlled using PIN diodes. Using PIN diodes as the control mechanism instead of liquid-crystal is advantageous for applications where superior switching speeds can be required. Interacting the holographic metasurface layer with the guided-mode reference produces an electronically-scanned radiation pattern. We demonstrate the application of the electronic beam steering capability of the proposed metasurface antenna for microwave imaging applications, without the need for any phase shifting circuits or mechanical scanning apparatus. Using a Mills-Cross system layout, we synthesize a 2D single-frequency (monochromatic) all-electronic SAR microwave camera. The synthesized microwave camera exhibits the merits of both an ESA system and a SAR system. Its operation is referred to as all-electronic because the presented camera does not involve a mechanical scanning process. It is also referred to as SAR camera due to the fact that the field patterns radiated by the dynamically reconfigurable holographic metasurface antenna raster scan the scene to be imaged, similar to a SAR system but in an all-electronic manner.
In comparison to the work presented in [6], the presented reconfigurable holographic metasurface aperture is a complete design, including all the layers (with the biasing circuitry) to achieve dynamic beam-forming. Different from [6] showing near-field focusing, the radiated beam patterns from the developed metasurface antenna are engineered to achieve allelectronic raster scanning of the scene to synthesize a microwave camera for imaging. Whereas the analytical framework presented in [8] can be considered the building block of the work presented in this research, different from [8] presenting static (non-reconfigurable) apertures, the main advance of this work is the development of the reconfigurability concept and its demonstration for imaging applications. In comparison to [21-28], rather than producing quasi-random radiated field patterns, the proposed aperture produces well-defined beam patterns that electronically raster scan the scene at 20 GHz. Whereas the frequencydiverse imaging shown in [21-27] requires a wideband operation, the metasurface antenna developed in this work relies on dynamic beam-forming using active elements and operates at a single frequency. Eliminating the use of large bandwidths can significantly simplify the signal source needed to feed such an aperture.

Metasurface antenna structure
The proposed metasurface aperture consists of two PCB layers, bottom (PCB 1 ) and top (PCB 2 ). The bottom PCB is a microstrip transmission line (accommodating the metasurface) while the top PCB is the DC bias circuitry. The antenna design is depicted in Fig. 1.
We first focus our attention to the bottom PCB microstrip structure, PCB 1 , consisting of the metasurface layer as depicted in Fig. 1(a). The microstrip consists of a double-sided, 1.524 mm thick substrate, Rogers 4003 (ε r = 3.38 and tanδ = 0.0027) and is fed through an edge-fed coaxial adaptor attached to one end while the other end is terminated in 50 Ω. The front surface of the microstrip is populated with an array of subwavelength size slot-shaped meta-elements forming the metasurface layer.
The meta-elements are placed with their long axes oriented along the direction of the magnetic field polarization axis, y-axis. As a result, the slot meta-elements couple to the magnetic field of the guided-mode, radiating into the free-space. The meta-elements are λ g /2.5 long and λ g /17.5 wide, where λ g is the wavelength within the dielectric at 20 GHz. The metaelements are excited in an off-resonance fashion to prevent them from acting as strong scatters and preserve the guided-mode reference [8]. The meta-element periodicity is λ g /3.3 or λ 0 /6, where λ 0 is the free-space wavelength. The metasurface layer consists of 79 slot-shaped meta-elements. As shown in Fig. 1(a) in detail, each meta-element on the metasurface layer has a PIN diode attached to its center.
We now focus our attention to the top PCB structure, PCB 2 , consisting of the DC biasing circuitry as shown in Fig. 1(b). PCB 2 is used to achieve the DC biasing of the PIN diodes on the metasurface layer (PCB 1 ). PCB 2 consists of a single-sided, 0.2 mm thick dielectric substrate, Rogers 4003. As shown in Fig. 1(b) in detail, the top surface of the substrate accommodates the DC biasing lines; two lines for each PIN diode, representing the positive ( + ) and ground connections. The DC biasing lines on PCB 2 are connected to the ports of the PIN diodes on PCB 1 through vias as shown in Figs. 1(b) and 1(c). An important aspect of the biasing circuit is the DC -RF isolation. From an RF perspective, it is desired that the DC lines biasing the PIN diodes are isolated from the RF circuitry. This prevents the DC biasing circuit from becoming a part of the RF circuit and therefore ensures the stable operation of the antenna. To achieve this, we employ radial stubs as shown in Fig. 1(b). The radial stubs are placed at λ g /4 distance from the vias, ensuring high RF impedance (while maintaining low DC impedance) when seen from the via inputs. It is also important to note that whereas the slot elements depicted in Fig. 1(a) result in a single-polarized radiation, for applications where polarimetric operation is of interest, slanted (45° rotated in the transverse xy-plane) slot configuration can be adopted [2]. In this work, we limit our study to the slot configuration shown in Fig. 1(a) and note that similar radiation characteristics but with multi-polarization features were observed using the slanted-slot configuration.

Holographic dynamic beam forming
The dynamic beam forming is achieved by interacting the metasurface layer with the quasi-TEM microstrip guided-mode (or the reference-wave) launched by the edge-fed coaxial port as depicted in Fig. 1(c). This holographic principle consists of two steps; first, the determination of the field distribution on the antenna aperture, P, that would produce the radiation pattern of interest. Second, the design of the metasurface layer that would create the determined field distribution on the antenna aperture, P, when excited by the reference-wave, similar to how a hologram is produced. In this work, the metasurface can be considered the hologram layer.
In order to steer the beam in a certain direction, we define a virtual point source [6] positioned in the direction of the desired steering angle. Backpropagating this point source onto the aperture of the antenna gives us the desired field distribution on the antenna aperture, P, that is required to produce a radiation steered in the direction of the point source. This backpropagation is achieved by means of a simple Green's function implementation, ' e jk − − = r r P (amplitude dependency is dropped), where r denotes the coordinates of the virtual point source and ' r denotes the coordinates of the metasurface antenna. It should be noted that the fields are scalar and bold font is used only to denote the vector-matrix notation while r governs the pointing direction of the radiation pattern of the dynamically reconfigurable holographic metasurface antenna. As the radiation pattern of the antenna performs an electronic raster scan of the scene, r changes as a function of the direction of the beam and therefore does not have a constant value.
The aperture of the metasurface antenna is discretized into an array of pixels at the periodicity of the meta-elements, λ g /3.3. As shown in Fig. 1, the coaxial port launches a quasi-TEM guided-mode into the microstrip with the magnetic field of the launched wave being modelled as , where H 0 is a constant. Having the guided-mode, H, on one side and the desired field distribution, P, on the other side of the aperture, our aim is to convert the guided-mode reference, H, to the desired aperture field distribution, P. From this definition, one can calculate a holographic phase grating from ∠ −∠ H P. In this description, the metasurface is the holographic phase grating. In other words, for each pixel (λ g /3.3 periodicity) on the aperture, the phase value of the hologram layer can be calculated as the difference between the phases of H and P, ∠ −∠ H P. When excited by the reference-wave, H, such a metasurface would produce P on the aperture of the antenna that would radiate a beam steered in the desired direction. It is evident that ∠ −∠ H P produces a phase value at each sampling point across the metasurface layer. As a result, we choose a phase threshold, selected to be ± 60°, suggesting that only the meta-elements positioned at points where the phase difference between H and P remains below the selected phase threshold are "ON", contributing to the radiation, while the rest of the meta-elements are "OFF", exhibiting no contribution to the radiation (binary modulation). This description has been given to steer the beam in one direction as an example and can be repeated to dynamically to steer the beam towards any other direction, which is required for dynamic beam steering.
The phase threshold is optimized by means of full-wave numerical simulations. The threshold parameter determines the number of ON and OFF meta-elements across the aperture. Increasing the threshold has the advantage of increasing the number of ON metaelements contributing to the radiation and therefore improving the radiation efficiency. However, this increase comes at the cost of increased sidelobes due to the worsening constructive interference caused by the increased phase difference between H and P. In this work, the developed holographic metasurface antenna is designed to achieve a maximum sidelobe level limit of −10 dB for all the scanning angles within the investigated field-of-view (FOV). With this goal in mind, the optimum phase threshold value is found to be ± 60°. In addition to this optimization process, no further optimization is carried out. We emphasize that the choice of the reference-wave has a significant importance in the design process of the reconfigurable holographic metasurface antenna. To design a hologram, different types of reference-waves can be used [4,6,29], such as a plane-wave reference, a Gaussian-wave reference or the guided-mode reference presented in this work. In our previous work in [6], we have shown that using a plane-wave reference results in not only the fundamental mode (the desired radiation pattern of interest) but also higher order spurious modes whereas using a guided-mode reference enables the suppression of these spurious modes. This is an important reason as to why the guided-mode reference is chosen as the reference-wave for the designed reconfigurable holographic metasurface antennas presented in this work. Moreover, the guided-mode reference launched by the coaxial feed ensures a planar antenna form-factor.
As mentioned earlier, each slot meta-element has a PIN diode attached to its center. The PIN diodes can be biased in two ways; forward-bias and reverse-bias. When reverse-biased, the PIN diodes act as open-circuit elements, suggesting that the meta-elements that they are attached to operate at the intended frequency ("ON" state), coupling to the waveguide mode and contributing to the radiation. When the PIN diodes are forward-biased, the meta-elements are short-circuit in the center ("OFF" state) and their resonance frequency is shifted to a higher frequency band that is out of interest. The short-circuit meta-elements do not couple to the guided-mode and therefore do not contribute to the radiation. To illustrate this phenomenon, we designed a simple microstrip waveguide with a single slot meta-element. Figure 2, shows the surface current distribution (amplitude) across the microstrip with the meta-element in "OFF" and "ON" states, respectively. Analyzing Fig. 2(a), it is evident that the "OFF" meta-element does not radiate while the "ON" meta-element in Fig. 2(b) alters the surface current distribution due to the coupling to the guided-mode and contributes to the radiation. The contrast in the radiated power levels between ON and OFF meta-elements is reported to be 10 dB at 20 GHz.

Results and discussion
The antenna of Fig. 1 was modeled with MACOM AlGaAs PIN diodes (MA4AGFCP910) [30]. Using PIN diodes, remarkable switching characteristics can be achieved at relatively small power levels [31]. When forward-biased, the insertion loss of the diodes remains below 1 dB while when reverse-biased, the isolation level is around −10 dB at 20 GHz. Biasing the diodes would typically require V = 0.7 V and I = 5 mA, suggesting that the maximum power consumption of the antenna is around 0.28 W, although it is unlikely that all diodes will be forward-biased at once.
For dynamic reconfiguration, we study electronic beam steering within the ± 30° range. The numerical simulations were performed using a full-wave electromagnetic (EM) solver, CST Microwave Studio. The simulation domain is a bounding box with the edges of the box being λ 0 /4 away from the antenna. Open boundary conditions were used. The whole structure (including the coaxial adaptors, bias traces and PIN diodes) was simulated. The obtained radiation patterns at 20 GHz are shown in Fig. 3. The far-field patterns presented in Fig. 3 exhibit excellent pointing accuracy with the side lobe levels remaining below −10 dB. Further reduction in the sidelobe levels can be achieved by amplitude tapering of the aperture, a wellknown technique in antenna theory [2]. The gain of the antenna is reported to be 14.6 dBi with 35% efficiency while the half-power-beamwidth (HPBW) is 4.1° and the polarization purity is above 20 dB. The efficiency reported in this work is the total efficiency of the antenna, taking into account the input impedance mismatch loss. The DC power needed to bias the PIN diodes is related to the DC bias circuitry, which is isolated from the RF circuitry, and therefore is not considered for the definition of the RF antenna efficiency. The total amount of power fed to the antenna is 0.5 W while the accepted power is 0.49 W, the radiated power is 0.17 W, the dissipated power due to dielectric loss is 0.16 W and the dissipated power due to conduction loss is 0.09 W (the rest is absorbed by the 50 Ω termination). The efficiency of the antenna can be further improved by reducing the loss tangent of the dielectric substrate, increasing the selected phase threshold and exciting the meta-elements closer to the resonance (at the expense of increased sidelobes), and using more advanced modulation schemes, such as a grayscale modulation [8]. It should be noted that, in addition to distorting the phase of the guided-mode reference, increasing the coupling of the metaelements to the guided-mode would increase the amount of radiation leaking out from the meta-elements as the guided-mode travels through the microstrip waveguide. This would effectively reduce the effective aperture size and widen the HPBW of the antenna. Therefore, an important criterion for the design of the metasurface aperture was the filling factor of the aperture to minimize the HPBW. As a result of achieving weak coupling between the metaelements and the guided-mode (due to the off-resonance excitation of the meta-elements), the amplitude of the guided-mode exhibits weak attenuation with the guided-mode filling the entire aperture. This suggest that there is a tradeoff between the radiation efficiency of the aperture and the aperture filling factor, which was optimized for the aperture filling factor for this work. From 4.1° HPBW, the effective aperture length is calculated to be 210 mm, corresponding to 97.2% of the physical length of the aperture, L = 216 mm, as depicted in Fig. 1(c). The signal-to-noise (SNR) level of an imaging system is a function of a number of parameters, including the imaging distance, the target to be imaged and the radiation efficiency of the antennas imaging the target. Keeping the other parameters (imaging distance and target to be imaged) the same, we have reported imaging SNR levels on the order of 20 dB using frequency-diverse antennas with similar radiation efficiencies in [24,25]. As a result, the imaging SNR was chosen to be 20 dB for the imaging system presented in this work. In Fig. 4, we analyze the S 11 pattern of the metasurface antenna as a function of the dynamic beam steering angle. As shown in Fig. 1(a), the characteristic impedance of the microstrip transmission line is tapered towards 50 Ω at the feeding ports of the aperture while the end of the microstrip is terminated in 50 Ω to prevent reflections and the formation of standing waves within the waveguide. As can be seen in Fig. 4, the aperture exhibits a good impedance match response with |S 11 | remaining below −10 dB at 20 GHz for all the steering scenarios investigated. Following the demonstration of the antenna performance, we now turn our attention to synthesizing a composite aperture for imaging applications. To this end, we use two antennas; a transmit aperture placed in a vertical orientation and a receive aperture placed in a horizontal orientation as depicted in Fig. 5. The synthesized composite aperture shown in Fig.  5(a) exhibits a sparse Mills-Cross system layout. The Mills-Cross system layout has the advantage of minimizing the number of antennas required while offering a similar effective aperture support in comparison to a fully-filled aperture and exhibiting minimized sampling redundancy [21]. Microwave imaging is an inverse problem, involving the reconstruction of the reflectivity (or contrast) function of an object from a set of measurements. It is important to note that, in this work, the word measurement does not refer to experiments. Instead, it refers to obtaining the scene information by means of interrogating the scene using the radiation patterns of the designed holographic metasurface antennas and observing the backscattered signal in simulations. The scene information is correlated to the measurements of the object scattered fields through a forward model as follows: (1) In Eq. (1), g is the measured signal from the scene (including the object to be imaged), S is the sensing (or measurement) matrix, f is the reflectivity (or contrast) function of the scene to be reconstructed and n is the measurement noise. In Eq. (1), M denotes the number of measurement modes, that is the number of possible combinations of the radiation patterns produced by the transmit and receive antennas, respectively. As depicted in Fig. 5, within the ± 30° FOV, the receive antenna raster scans the scene along the x-axis at 2° intervals, producing 31 scanning points. Similarly, the transmit antenna raster scans the scene along the y-axis at 2° intervals, producing 31 scanning points. As a result, the total number of measurement modes can be calculated as M = 31x31 = 961. N is the number of voxels into which the scene is discretized. Using the first Born approximation, the sensing matrix, S, can be obtained by the scalar product of the transmit and receive antenna radiated fields propagated to the scene using Green's functions [32]. An important distinction of the presented system from the frequency-diverse imaging technique shown in [21-27] occurs in the calculation of the S-matrix. Whereas the frequency-diverse technique presented in [21-27] leverages a frequency-sweep to generate spatially varying quasi-random radiation patterns to form the measurement modes and the S-matrix, the dynamically reconfigurable antennas within the synthetized microwave camera do not require a frequency-sweep. Instead, the spatially varying measurement modes of the synthesized reconfigurable camera are achieved using the ON/OFF switching capability of the PIN diodes at a single frequency and the Smatrix is formed in a monochromatic manner.
From the definition of the sensing matrix, it is evident that the radiated fields from the transmit and receive antennas need to be known to calculate the sensing matrix, S. Using CST Microwave Studio, we export the antenna radiated fields which are then imported into a MATLAB based in-house developed simulation software, the Virtualizer, for imaging [32]. The Virtualizer simulation tool enables us to study a desired imaging scenario by means of solving the forward model of Eq. (1) and applying an adjoint operation to Eq. (1) to reconstruct an estimate of the scene, f est .
Using the synthesized composite system, in Fig. 6, we image a gun phantom placed at z = 20 cm distance from the composite Mills-Cross aperture. The FOV for imaging is limited to ± 30°. Within the investigated FOV, each antenna performs an electronic raster scan, illuminating the scene at 0 2 θ Δ = intervals, selected in accordance with the angular equivalence of the Nyquist limit, 7.5 mm, corresponding to 2.1° at 20 GHz frequency and z = 20 cm distance. As a result, the total number of measurement modes is M = 961. The scene is discretized at the cross-range (xy-plane) resolution limit of the aperture, δ = 1.5 cm obtained by means of a point spread function (PSF) analysis [33], producing N = 4096 elements to be reconstructed. The microwave image of the gun phantom reconstructed using a single-shot matched filter technique [33] shown in Fig. 6(a) reveals a clear outline of the phantom, using only M = 961 measurements. The matched-filter algorithm is run on a Graphic Processing Unit (GPU), Nvidia GTX 980, and the reconstruction time is reported to be 0.08 s, exhibiting significant potential for real-time applications. Figure 6(b) demonstrates the normalized overall k-space pattern (K x -K y projection) obtained from the synthesized Mills-Cross aperture, exhibiting a filled k-space coverage with no nulls in the overall pattern. This is an important outcome in that filling the k-sphere ensures that the Fourier components of the target are captured [34,35]. Missing the Fourier components of the target would result in lack of information in the reconstructed image. Fig. 6. Imaging of a gun phantom (a) reconstructed image of the gun phantom (b) normalized k-space pattern produced by the synthesized Mills-Cross microwave camera. Imaging is done in Virtualizer.

Conclusion
We have designed a dynamically reconfigurable holographic metasurface aperture for electronic beam steering applications. The metasurface antenna exhibits a simple PCB architecture and is capable of dynamic beam forming without the need for phase shifting circuits or mechanical moving techniques. The beam forming capabilities of the holographic metasurface aperture have been numerically verified for 20 GHz operation within the K-band frequency regime. Using the developed metasurface antenna, high-fidelity dynamic beam steering within the range of ± 30° has been shown. Leveraging an in-house developed simulation software, the Virtualizer, we have demonstrated the application of the designed dynamically reconfigurable holographic metasurface aperture to synthesize an all-electronic microwave camera for imaging. Using the synthesized monochromatic camera, high-fidelity image of a gun phantom has been achieved in a sub-second time frame. The proposed antenna holds significant potential for imaging, non-destructive testing and wireless power transfer applications, where a simple, low-power and cost-effective antenna architecture can be highly desirable. Although shown for microwave frequencies, the developed aperture can readily be scaled to millimeter-wave and submillimeter-wave frequency regimes where superior imaging resolution is required.