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Abstract
A holographic imaging system based on reconfigurable time-frequency division multiplexing metasurface (RTFDMM) has been designed, in an attempt to address the problems of insufficient flexibility, low signal-to-noise ratio (SNR), and low data of traditional metasurface imaging devices. The modified Gerchberg-Saxton (MGS) algorithm in the front end of this system has been proposed to calculate the phase distribution required by the diffraction metasurface at the back end. The 1-bit low loss reconfigurable metasurface has been desiged in X-band. To obtain the best imaging results, the appropriate ranges of imazging distance, pixel size and resolution ratio are given by adjusting the phase distribution of metasurface. Based on the MGS algorithm and the 1-bit metasurface, the high-quality imaging system has been successfully established through the time-frequency division multiplexing (TFDM) technology. The high SNR imaging can be generated with the expansion of the time domain, while the high data imaging can be yielded with the quantization of the frequency domain. The proof-of-concept has demonstrated that the high data, high SNR, and high flexibility of the RTFDMM are critical technologies for the advancement of detection imaging equipment. Therefore, there are great possibilities for RTFDMM holographic imaging system to be applied in the intelligent detection platform in the future.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, the research of metasurfaces involves various characteristics of electromagnetic (EM) waves, such as amplitude modulation [1–4], polarization modulation [5–8], phase modulation [9], beam modulation [10–12], etc. For application, metasurface holography (MH) is designed with the coding metasurfaces [13,14], which are composed of multiple phases and/or amplitudes state elements with specific coding sequences. In MH system, the traditional phase modulation device is replaced with metasurfaces, which significantly reduces the volume of the imaging device, so that the subwavelength size imaging device can generate a hologram with higher resolution and SNR. Metasurfaces possess special properties superior to those of natural electromagnetic materials, which ushers in a new age for the holographic imaging technology.
In terms of studies on MH, the type of imaging and the ability of metasurface are inextricably combined. The phase and amplitude of EM waves can be modulated directly by metasurfaces, simultaneously or independently, based on which their characteristics such as polarization and frequency can be modulated indirectly. Thus, the imaging types can be classified into non-multiplexing, polarization-multiplexing, frequency-multiplexing, multiple multiplexing-imaging, and so on.
As for non-multiplexing imaging, a high-efficiency holographic metasurface is generated by customizing the geometric phase of the plasmonic reflective array with 16-level phase-only modulation [15]. In this paper, a real low-profile holographic method has been proposed with a leaky-type 2-bit coding Fabry–Perot metasurface [16], through which the energy proportion of focal points can be modulated by adjusting the phase distribution based on the GS algorithm. Besides, in a study [17], a polarization-multiplexing metasurface hologram technology for reconstructing dual switchable dual images is realized by the incident linear-polarized wave. Some metasurfaces [18,19] are also designed for circular-polarization multiplexed metasurface holograms. In addition, a full-polarization-reconstructed metasurface that modulates the distribution of near-field energy with arbitrary output polarization EM waves is presented [20]. Frequency-division multiplexing (FDM) enhances the information-carrying capacity, especially in the optical field. A full-color hologram can be successfully constructed with multi-frequency elements and multi-level phase modulation [21–23]. Some metasurfaces based on both polarization- and frequency-multiplexing have been designed to further improve the information-carrying capacity [24,25].
However, from the very beginning of the design, the capabilities of the abovementioned metasurfaces have been limited, which of course has been removed gradually with the advent of real-time reconfigurable metasurface. Active elements (loaded with varactors and diodes) [26–28], thermal-sensitive phase-transition materials [29,30], liquid metal [31], and applied-voltage sensitive graphene [32] have been investigated to realize a dynamic metasurface. Compared with the optical frequency band, there are few studies on the real-time MH in the microwave frequency due to the limitation of wavelength range, application range, and active loss. Therefore, it is an arduous task to realize a low loss, broadband, real-time reconfigurable metasurface, and arbitrary holography with high data and high SNR.
In this paper, an RTFDMM has been designed in the microwave frequency band. Regardless of the achievement in the low loss of metasurfaces, their phase-distribution can be set according to the target interested owing to the ON-OFF state of the PIN diode and the shunting effect of the capacitor. Therefore, the RTFDMM can be employed in the holographic imaging system. In combination with the MGS algorithm, the holography system that adopts the RTFDMM technology can achieve a roll over the previous imaging devices. The imaging results have demonstrated that the real-time reconfigurable metasurface could promote the advancement of the microwave imaging technology.
2. Design of reprogrammable metasurface holography
The full view of the RTFDMM holographic imaging system is shown in Fig. 1. At first, the preset image information is subject to the MGS algorithm through the input port. Subsequently, the phase distribution, which is generated by the MGS algorithm, is written to the reconfigurable metasurface connected to the MGS algorithm by field-programmable gate array (FPGA). Finally, the holographic imaging is generated by reconfigurable metasurface in the output port.
Fig. 1. The full view of RTFDMM holographic imaging system. (a) The target image. (b) The MGS algorithm flowchart. (c) The phase distribution of diffraction surface. (d) The designed metasurface. (e) The holographic imaging.
The target image is the input parameter of the RTFDMM imaging system, as shown in Fig. 1(a). The MGS algorithm evolves from the conventional GS algorithm [33]. During the execution of the algorithm, the Rayleigh-Sommerfeld formula is adopted to replace the Fourier transform based on the Fraunhofer diffraction formula in the near field [34,35], as shown in the Eq. (1). Where, complex amplitudes Eq and Es represent the target point and source point, respectively. And a is a constant, only depends on the frequency. In the Equation, k represents the wave vector of free space, r represents the diffraction distance, and cosθ represents the directivity of Es.
The algorithm flowchart is shown in Fig. 1(b), with the initial phase-distribution matrix φm° and weight matrix wn° provided at the beginning. The Eq. (1) is approximately written as Eq. (2) under the condations of discrete metasurface source and the linear influence of a. The complex amplitude Enp of imaging surface is formed by integrating the phase φmp-1 into the input amplitude (the amplitudes are set to be one), which can be considered the p-th Green's function transform of diffraction metasurface. In which, M represents the number of metasurface elements, rmn represents the distance between the m-th element and the n-th hologram pixel,and z represents the distance between the imaging surface and the metasurface. The next phase distribution φmp is derived from the inverse Green's function transform of the Enp-1, as shown in Eqs. (3)and(4), where, Es represents the amplitudes of the target field, and N represents the number of pixels of imaging surface. The next iteration begins until certain conditions are satisfied.
The final phase distribution matrix φm is shown in Fig. 1(c). After the execution of the MGS algorithm, the φm is written into the reconfigurable metasurface, as shown in Fig. 1(d), which contains an array of 32×32 active elements, with the size of element being 10 mm. Under the vertically polarized EM wave, a PIN diode and a capacitor are loaded into the active element, which alters a phase difference of 180°±30° from 8.45 GHz to 12.60 GHz when the PIN diode is converted into ON or OFF, as shown in Fig. 2(a). Moreover, it is an effective way to achieve the low loss of the element that loads shunt capacitor into anisotropic microstrip patch with the aim of reducing the induced current through the PIN diode. The asymmetries of electronic device placement and patch shape are also designed to obtain appropriate phase state and low loss, resulting in losses below 0.75 dB within operating bands in Fig. 2(b). The design details of the active element can be seen in a paper [36].
The energy reflection efficiency can routinely reach to 0.846 under the incidence of vertically polarized plane waves from Fig. 2(b). Therefore, it can be assumed that the amplitudes are identical. The phase of the metasurface is determined by the PIN diode state. The ON is 0, while the OFF is π. Therefore, the final calculated phase φm needs to be quantified to 0 and π. The following Equation is employed:
There are two prominent indicators for evaluating the quality of metasurface holographic imaging, including root-mean-square error (RMSE) and SNR, among which the former is introduced to measure the difference between the energy intensity ratio of the holographic image and the preset, as shown in Eq. (6); while the latter is defined as the intensity in the image to the standard deviation of the background noise, from Eq. (7). Where, MAX is number of pixels of 8 bit.
When the metasurface is completed, there are some main factors that affect the imaging quality, as shown in Fig. 3. The distance between the diffraction metasurface and the imaging surface is set as z. The resolution ratio, defined by the number of pixels of imaging surface, is N. The size of the pixel is x*λ. It is worthwhile noting that the GS algorithm can generate different phase distributions by changing the input parameters z, N = u*v, and x. The ANSYS HFSS software is employed to simulate the RTFDMM, with the results shown in Fig. 4 and Fig. 5. In the near field imaging, the placement of the image surface can exert a significant impact on the quality of the holographic imaging, which is especially obvious for fixed metasurface imaging on account of the unchanged phase distribution.
Fig. 4. The real-time quantified phase-distribution φm|1bit and near-field energy distribution as z changes.
Figure 4 presents the real-time near-field energy distribution varying with z. Energy distribution of EM waves meets vector superposition principle. According to Eq. (2), the amplitude and phase of each pixel are related to the change of z. Besides, the amplitude difference between the center and the edge of the imaging surface can be affected by the change of z. However, the RTFDMM imaging system can compensate for the influence on phase, amplitude, and amplitude difference through adaptively reprogramming the phase distribution. In the RTFDMM hologram, the imaging area expands from one surface to one space with the real-time changes of the phase distribution. The RMSE and SNR of the RTFDMM holographic image would vary with imaging distance z, as shown in Fig. 5(a), which clearly demonstrates that the high-quality imaging can be maintained for different z (3λ to 8λ) with adaptive tuning.
As shown in Fig. 5(b), under the condition that z and N remain unchanged, x is changed for the observation of changes in SNR and RMSE. For the pixel size x, the microwave diffraction phenomenon also meets the diffraction limit. However, due to the aggregation and arrangement of the metasurface elements, the evanescent wave in the near field will be converted into a transmission wave for imaging. Thereby, the super-resolution imaging can be realized. When x is between 0.4 and 0.55, the SNR and RMSE have optimal performance by adaptively reprogramming the phase distribution. With the consideration of the diffraction limit θ, the information of EM wave at the edge of the imaging surface would reduce, which results in a decline in the imaging quality. As shown in Fig. 5(c), the SNR and RMSE can achieve better values when the size of the imaging surface is not more than the range of the diffraction limit at the corresponding z0. In addition, there is an inverse correlation change in the relationship between N and SNR. Under the conditions that the total energy is reflected by metasurfaces and the size of pixel remains the same, the more pixels there are, the less energy is concentrated in each pixel, or conversely, the higher the energy is. Therefore, the imaging with low N has more energy than their original size, as shown in Fig. 6.
3. RTFDMM holographic imaging
The color brightness of the target image, which is indicated by the gray value, is characterized by the intensity of electric field in traditional microwave imaging. However, as for the target image with rich colors, such as Olympic rings in Figs. 7(a) and 7(b), the closer the gray value is to the background, the worse the imaging effect will be, e.g. the yellow ring. In contrast, the greater the difference from the background, the better the imaging effect, e.g. the black ring. In the RTFDMM holographic imaging system, the GS algorithm is further modified with a view to recognizing the color of the target image automatically. Therefore, in order to obtain a better imaging effect, the target images are divided into five sub-images according to their colors, which means each sub-image contains partial information of the original image. The gray value of each sub-images is quantized as 0 to get the maximum difference from the background, as shown in Fig. 7(c). When the gray value of all sub-images is quantized as 0, the color information of the image cannot be characterized by the electric field intensity. The operating band of the RTFDMM imaging system ranges from 8.45 GHz to 12.60 GHz, which can be divided into many operating frequency bands. When the phase distribution of the metasurface is under the condition shown in Fig. 8(a), the electric field distribution shown in Fig. 8(f) can be obtained at 8.8 GHz. Approximately, when the phase distribution is under the conditions shown in Figs. 8(b), 8(c), 8(d) and 8(e), the electric field distribution at 9.5 GHz, 10.4 GHz, 11.2 GHz and 12.0 GHz is shown in Figs. 8(f), 8(g), 8(h) and 8(i), respectively. In order to ensure the quality of imaging, it is necessary to ensure that there is no difference in the electric field intensity of each sub-image. However, there are numerous operating frequency points, which means that the frequency would be employed to characterize the color information of the image. Figures 8(j), 8(k), 8(l), 8(m) and 8(n) present the measured results of frequencies characterizing different colors. The entire imaging can be obtained by accumulating five sub-images with different frequencies. With the adoption of the frequency division multiplexing technology, the metasurface can possess multiple imaging channels. Therefore, the loading of high data can be achieved in the RTFDMM imaging system.
Fig. 8. The results of frequency characterizing different colors. The electric field distribution at (a)8.8 GHz, (b)9.5 GHz, (c)10.4 GHz, (d)11.2 GHz and (e)12.0 GHz. The simulation electric field distribution (f)8.8 GHz, (g)9.5 GHz, (h)10.4 GHz, (i)11.2 GHz and (j)12.0 GHz. The measurement electric field distribution (k)8.8 GHz, (l)9.5 GHz, (m)10.4 GHz, (n)11.2 GHz and (o)12.0 GHz.
As per the above analysis, the imaging effect of the target images with low pixels is better in the microwave field. In Table 1, there are 258 pixels in the entire imaging, and the peak energy intensity at 10 GHz is 0.74. Compared with the entire imaging, the number of pixels in each sub-image decreases by 1/5 approximately. It can be noted that the peak energy intensity of the holographic imaging increases by at least 1/3 of the original image. And the measured results also verify this change. The SNRs are presented in row five of Table 1. Besides, the SNR of final imaging, which is defined as the smallest among all sub-images, is 14.3 dB. Obviously, reprogrammable metasurface can provide higher quality images flexibly.
Table 1. The SNR and RESM of sub-imagings.
With the adoption of the RTFDMM technology, not only can high data of holographic imaging be achieved, but also the SNR of imaging would be increased. However, the cost is an expansion in the time domain. Fortunately, the reconfigurable metasurface inherently has the ability to expand the time domain. Each sub-holographic image can be completed by one-time adjustment of the phase distribution, namely that the holographic imaging is not completely generated until the metasurface traverses those phase distributions corresponding to all the above frequency points. The phase distribution depends on the state of PIN diode. According to the datasheet of the PIN diode (SMP1340-040LF), the switching speed is 2-3 ns. The FPGA clock rate controlling the switching of PIN diode state is 100 MHz, and the corresponding operation cycle time is 10 ns. The one-time writing phase-state number of the upper antenna software is a quarter of all elements, with each instruction cycle being 40 ns. Moreover, a total of 40 instructions are required to change the state of a PIN diode after the shift register, that is, 1.6µs. A shift register can control 8 diodes, and a total of 32 parallel operations are required. Therefore, it takes about 51.2µs to change the phase distribution of metasurface at a time. Therefore, the metasurface can achieve a stable electric field distribution within 51.2µs. With regarding the time of five-phase reconstruction as a period T, which is 256µs, the same sub-image appears once every 256µs, as shown in Fig. 9. In a continuous and stable periodic cycle, the electric field probe is 1s, which indicates that the corresponding time of the probe is much longer than the switching time of period T. In this case, it would appear as complete holographic imaging. The RTFDMM imaging technology has been fully implemented for high-quality imaging.
4. Experimental section
A prototype, which is composed of 32*32 elements with 320*320mm2 in size, has been fabricated, as shown in Fig. 10. The FPGA control system is plugged into the back of the model and connected with the computer through a wire. The physical model is characterized experimentally in an anechoic chamber with an Agilent 8722ES network analyzer and Programmable DC Power Supply RIGOL DP831, which is employed to supply a DC 1.37 V voltage to each column. A feed antenna working in X-band is adopted to generate linear-polarized plane wave to illuminate reconfigurable diffraction metasurface. Besides, a standard probe is employed to scan the image surface with a resolution of 1mm2 with the aim of obtaining holographic images.
Refer to Fig. 11 for the results of simulation and measurement. Although the measurement results are in good agreement with the simulation results in the image contour, there are some differences in the image details. The inhomogeneity of ring width and the deviation of ring position are caused by fabrication losses and the measurement environment. Under the condition of 8.8 GHz and 10.4 GHz, the resolution ratio of the measurement ring is at a low level, which is caused by anomalous scattering of metasurface edge.
Fig. 11. The simulation results of near-field scanning (a)with RTFDMM technology and (b)without RTFDMM technology. The measurement results of near-field scanning (c)with RTFDMM technology and (d)without RTFDMM technology.
5. Conclusion
To sum up, in this paper, a real-time reconfigurable metasurface holographic imaging system has been designed. In addition, the reconfigurable metasurface based on PIN diode and capacitor has the real-time 1-bit phase adjustment capability. As a result, it can rapidly regulate and control the distribution of the near-field EM energy. In combination with the MGS algorithm, the metasurface can be regarded as an optimal alternative to traditional imaging devices to achieve real-time imaging. Benefiting from the shunting effect of the capacitor and the ingenious structure design, the metasurface in this study has an operating band of 8.45GHz-12.6 GHz. Therefore, the RTFDMM has been employed to address such problems as low SNR, low flexibility, and large RMSE. As per the results of simulation and measurement, the RTFDMM technology can achieve a better imaging effect in the holographic imaging system, with the SNR increased to 14.3 dB and the RMSE being 1.496%. The RTFDMM technology has forward-working significance in the research on microwave detection and imaging. Therefore, there are great opportunities for this technology to be employed in all-weather and all-terrain military exploration equipment in the future.
Funding
National Postdoctoral Program for Innovative Talents (2019M653960, BX20180375); Natural Science Basic Research Program of Shaanxi Province (2019JQ-103, 20200108, 2020022, 2020JM-350); National Natural Science Foundation of China (No.61671464, No.61701523, No.61801508).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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