Millimeter wave imaging method for jointly regulating and controlling reflection intensity and flight time based on metasurface

Abstract

The invention relates to the field of electromagnetic material design and millimeter wave imaging, and discloses a millimeter wave imaging method for jointly regulating and controlling reflection intensity and flight time based on a metasurface, which comprises the following steps: establishing a metasurface equivalent model, and setting target reflectivity and delay distance parameters according to a working frequency band. A hierarchical optimization strategy is adopted, the optimal equivalent impedance and the optimal thickness are calculated based on the transmission line theory, then patterns are screened through a reverse matching algorithm, a full-wave simulation model is established, and geometric parameters are finely adjusted. And then preparing a test sample, performing compensation calibration on the actual dielectric constant of the dielectric substrate layer by measuring group delay peak drift, and correcting the design and completing entity manufacturing based on calibration parameters. And finally, deploying the metasurface on the surface of a measured object. Through joint optimization and closed-loop calibration, synchronous high-precision regulation and control of strength and depth are realized, the problems of difficult design convergence and large low-cost material parameter error are effectively solved, and the millimeter wave imaging camouflage effect is improved.

Description

Technical Field

[0001] This invention relates to the fields of electromagnetic material design and millimeter-wave imaging, specifically a millimeter-wave imaging method based on the joint control of reflection intensity and time of flight using metasurfaces. Background Technology

[0002] Millimeter-wave imaging is a non-ionizing, human-safe electromagnetic detection technology that has been widely used in security systems at airports and various public places. Existing millimeter-wave imaging systems are typically based on broadband signals (such as frequency-modulated continuous waves), characterizing the target material properties by analyzing the reflection intensity of the echo signal, and estimating the target's spatial distance using time-of-flight measurements, thereby forming two-dimensional or three-dimensional imaging results.

[0003] Although millimeter-wave imaging technology boasts high detection efficiency in practical applications, its imaging mechanism relies to some extent on the target's reflection characteristics and range features, making the imaging results highly sensitive to external electromagnetic modulation structures. Existing research has attempted to alter millimeter-wave echo characteristics by introducing absorbing or scattering structures in front of the target, thereby influencing the imaging system's response to the target. However, these methods primarily interfere with imaging by weakening or disrupting the echo signal, making precise and controllable modulation of the imaging results difficult. Furthermore, some studies have focused on adjusting the millimeter-wave imaging system's response to different objects by matching the target's reflection intensity. However, this type of method only operates on the reflection intensity dimension and cannot affect time-of-flight-based range information. Therefore, its imaging modulation capability is limited when facing targets with significant thickness or spatial structures.

[0004] Furthermore, millimeter-wave imaging systems generally employ broadband operating modes, which places higher demands on the consistency of the imaging modulation structure's response within the frequency band. Traditional metasurface design methods often focus on the manipulation of single electromagnetic parameters such as phase or amplitude, lacking the ability to synergistically optimize multi-dimensional parameters, making it difficult to meet the fine modulation targets required for millimeter-wave imaging. Simultaneously, existing design processes typically rely on expensive high-frequency dielectric materials and complex fabrication techniques, making it difficult to balance practical requirements such as performance stability, manufacturing cost, and application scalability. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a millimeter-wave imaging method based on the joint control of reflection intensity and time of flight using metasurfaces. This method solves the problem that traditional metasurface design methods often focus on the control of single electromagnetic parameters such as phase or amplitude, lacking the ability to synergistically optimize multi-dimensional parameters, and thus failing to meet the requirements for fine modulation targets in millimeter-wave imaging scenarios.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a millimeter-wave imaging method based on metasurface-based joint modulation of reflection intensity and time of flight, comprising the following steps:

[0007] First, an equivalent model of a reflective metasurface is established. This model is based on a stacked structure of a top metal patterned layer, an intermediate dielectric substrate layer, and a bottom metal ground layer, and is used to characterize the electromagnetic response characteristics of the metasurface.

[0008] Secondly, the target parameters for imaging control are determined. Based on the equivalent model of a reflective metasurface, and according to the operating frequency band of the millimeter-wave imaging system, the target reflectivity value and the target delay distance value are set; the target reflectivity value corresponds to the preset reflection intensity, and the target delay distance value corresponds to the depth position based on the group delay principle.

[0009] Next, a joint optimization design of the metasurface structure is performed. A hierarchical optimization strategy is adopted to achieve the target parameters for imaging control: The first-level optimization is based on transmission line theory and equivalent circuit model, constructing a joint loss function that includes reflectivity error term and delay distance error term. With the goal of minimizing this joint loss function, the optimal equivalent impedance of the metal pattern layer and the optimal thickness of the dielectric substrate layer are calculated in the complex impedance space. The second-level optimization uses a reverse matching algorithm to select geometric pattern templates that meet the optimal equivalent impedance characteristics from a pre-set pattern library, and establishes a physical simulation model that includes full-wave electromagnetic effects. The geometric parameters of the geometric pattern templates are fine-tuned to generate the metasurface design scheme.

[0010] Next, metasurface prototypes were fabricated and their parameters were calibrated. Test prototypes were prepared, and the actual dielectric constant of the dielectric substrate was compensated and calibrated by measuring the group delay peak of the test prototypes. Based on the calibrated material parameters, the metasurface design scheme was modified, and the final physical prototype was manufactured.

[0011] Finally, a metasurface structure is deployed. The fabricated reflective metasurface structure is then applied to the surface of the object under test, enabling joint modulation of the reflection intensity and time of flight of millimeter-wave echo signals.

[0012] Preferably, in establishing the equivalent model of the reflective metasurface, the metasurface is described using an ABCD transfer matrix. The total transfer matrix is ​​calculated as follows: the transfer matrices of the metal pattern layer, the dielectric substrate layer, and the metal ground layer are sequentially multiplied in cascade according to the signal transmission order; wherein, the transfer matrix of the metal pattern layer is determined by its equivalent impedance, the transfer matrix of the dielectric substrate layer is determined by its characteristic impedance, propagation constant, and thickness, and the transfer matrix of the metal ground layer is determined by the ground layer impedance.

[0013] Preferably, in determining the target parameters for imaging control, the equivalent delay distance corresponding to the target delay distance value is obtained by calculating the frequency derivative of the phase of the reflection coefficient. Specifically, the phase of the reflection coefficient is unwrapped, the negative derivative of the unwrapped phase with respect to the angular frequency is calculated, and this negative derivative is multiplied by half the speed of light to obtain the equivalent delay distance at the corresponding frequency; the reflection coefficient is calculated by transforming the elements of the total transmission matrix.

[0014] Preferably, in the joint optimization design of the metasurface structure, the joint loss function is defined as the weighted sum of the reflectivity error term and the delay distance error term. The reflectivity error term represents the sum of squares of the differences between the calculated reflection coefficient amplitude and the target reflectivity value at each sampling frequency point within the operating frequency band; the delay distance error term represents the sum of squares of the differences between the calculated equivalent delay distance and the target delay distance value at each sampling frequency point within the operating frequency band; the joint loss function is obtained by assigning weight coefficients to the reflectivity error term and the delay distance error term respectively and summing them.

[0015] Preferably, the specific process of using the reverse matching algorithm to screen geometric pattern templates includes: establishing a geometric pattern database containing multiple geometric pattern topologies and their corresponding frequency-dependent impedance data; for each structure in the database, calculating the Euclidean distance between its impedance curve and the optimal equivalent impedance curve calculated in the previous steps, using this as the matching error; and selecting the geometric pattern topology with the smallest matching error and its corresponding initial geometric parameters as the geometric pattern template.

[0016] Preferably, fine-tuning the geometric parameters of the geometric pattern template specifically includes: defining the specific geometric dimensions of the geometric pattern template as a set of optimization variables; using full-wave electromagnetic simulation software to calculate the reflection coefficient amplitude and equivalent delay distance under the current geometric parameters; iteratively updating the geometric parameters with the goal of minimizing the geometric parameter optimization objective function; wherein the geometric parameter optimization objective function is a weighted sum of the reflectivity error term and the delay distance error term calculated based on the full-wave simulation results.

[0017] Preferably, in the fabrication and parameter calibration of metasurface prototypes, the actual dielectric constant compensation calibration method for the dielectric substrate layer is as follows: obtain the theoretical group delay peak frequency obtained by simulation under the nominal dielectric constant, and the actual group delay peak frequency obtained by actual measurement of the test prototype; calculate the compensated dielectric constant based on the physical relationship that the resonant frequency is inversely proportional to the square root of the dielectric constant; the modified metasurface design scheme refers to substituting the compensated dielectric constant into the physical simulation model and readjusting the geometric parameters.

[0018] Preferably, the test sample is prepared using the FR4 substrate etching process.

[0019] Preferably, the deployment of the metasurface solid structure adopts a multi-faceted wrapping strategy, deploying the metasurface solid on the top and side surfaces of the object under test, and maintaining geometric continuity at the connection points.

[0020] This invention provides a millimeter-wave imaging method based on the combined manipulation of reflection intensity and time of flight using metasurfaces. It offers the following advantages: 1. This invention achieves synchronous control of millimeter-wave echo signal reflection intensity and flight time by constructing a joint loss function of reflectivity error term and delay distance error term. It changes the traditional single camouflage mode that can only weaken reflection intensity by absorbing waves. It can simulate the reflection characteristics of specific materials and introduce a preset virtual depth offset in radar line of sight, thereby reconstructing the imaging characteristics of the target in both the intensity map and depth map dimensions, improving the realism and concealment of millimeter-wave imaging control.

[0021] 2. This invention solves the problem of large computational load and difficulty in convergence in the reverse design of broadband metasurfaces by combining transmission line theory with a hierarchical optimization strategy of full-wave electromagnetic simulation. By first using the equivalent circuit model to quickly solve for the optimal solution in the impedance space, and then using the reverse matching algorithm to map the impedance to the geometric structure and make fine adjustments, the hierarchical optimization strategy reduces the parameter search space of the full-wave simulation, reduces the time consumed by iterative calculations while ensuring design accuracy, and improves the efficiency of metasurface structure design.

[0022] 3. This invention introduces a material parameter calibration mechanism based on group delay peak, which reduces the dependence on high-frequency microwave substrate. By measuring the actual group delay peak frequency drift of the test sample, the dielectric constant error of the dielectric substrate is inferred and compensated. This enables low-cost industrial materials such as FR4, which have large dielectric constant dispersion, to meet the requirements of high-precision imaging control, thereby reducing the manufacturing and deployment costs of metasurface solid structures. Attached Figure Description

[0023] Figure 1 This is a schematic diagram illustrating the principle of the reflective metasurface of the present invention; Figure 2 This is a verification experiment showing the effect of using metasurfaces to control imaging reflectivity according to the present invention; Figure 3 This is an example diagram of distance slice imaging of a thick object using a metasurface with optimized reflectivity only, as described in this invention. Figure 4 This is a schematic diagram illustrating the effect of the group delay on the arrival time of the reflected pulse signal according to the present invention. Figure 5 This is an overall flowchart of the directional millimeter-wave imaging modulation design of the present invention; Figure 6 This is an example diagram of the simulation of patterned layer impedance using HFSS software according to the present invention; Figure 7 This is a schematic diagram of the experimental setup and object deployment of the millimeter-wave frequency-modulated continuous wave SAR imaging system of the present invention. Figure 8 The figures show the experimental results of metasurface imaging modulation under different reflectivity requirements of the present invention. Figure 9 The figures show experimental results of metasurface imaging modulation under different group delay requirements according to the present invention. Figure 10 The image shows the imaging modulation experimental results of the metasurface designed using the joint optimization scheme of the present invention. Figure 11 This is a comparison chart of the metasurface imaging modulation capabilities based on Rogers and FR4 in this invention; Figure 12 This is a schematic diagram showing the performance changes of the metasurface imaging modulation experiment under different shapes according to the present invention; Figure 13 The graph shows the performance variation of metasurface imaging modulation experiments at different angles according to the present invention. Figure 14 This is a graph showing the performance variation of metasurface imaging modulation experiments at different distances according to the present invention; Figure 15 This is a graph showing the performance variation of metasurface imaging modulation experiments under different materials according to the present invention; Figure 16 This is an experimental result of metasurface imaging modulation with a human body as the background, based on the present invention. Figure 17 This is a comparison chart of the maximum delay distance under different target reflectivities according to the present invention; Figure 18 This is a simulation diagram of the metasurface imaging modulation experiment based on BP imaging according to the present invention; Figure 19 The image shows the simulation results of the metasurface imaging modulation experiment based on matched filter imaging according to the present invention. Detailed Implementation

[0024] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] Please see the appendix Figure 1 -Appendix Figure 6 This invention provides a millimeter-wave imaging method based on the joint modulation of reflection intensity and time of flight using metasurfaces, comprising the following steps: S101, establish an equivalent model of a reflective metasurface; the model is based on a three-layer stacked structure of metal-dielectric substrate-metal, with the top layer being a metal pattern layer, the middle layer being a dielectric substrate layer, and the bottom layer being a metal grounding layer; the metal grounding layer blocks the electromagnetic coupling between the incident millimeter wave and the object under test, so that the electromagnetic control characteristics mainly depend on the structural parameters of the reflective metasurface itself.

[0026] S102, Determine the target parameters for imaging control; Based on the equivalent model of a reflective metasurface, in order to achieve directional control of the imaging results, it is necessary to set a clear physical target. According to the working frequency band of the millimeter-wave imaging system, set the target reflectivity value and the target delay distance value; The target reflectivity is used to control the echo signal intensity, and the target delay distance is used to control the echo signal flight time based on the group delay principle.

[0027] S103 involves the joint optimization design of the metasurface structure. To simultaneously achieve the imaging control target parameters set in S102, a hierarchical optimization strategy is adopted. First, based on transmission line theory and equivalent circuit models, a joint loss function including reflectivity error and delay distance error terms is constructed. With minimizing the joint loss function as the objective, the optimal equivalent impedance of the metallic pattern layer and the optimal thickness of the dielectric substrate layer are calculated. Subsequently, a reverse matching algorithm is used to select geometric pattern templates from the pattern library that meet the optimal equivalent impedance characteristics. Finally, to compensate for the approximation error of the theoretical model, a physical simulation model incorporating full-wave electromagnetic effects is established, and the geometric parameters of the geometric pattern templates are fine-tuned to generate the metasurface design scheme.

[0028] S104, Metasurface Prototype Fabrication and Parameter Calibration; FR4 substrate etching process or paper-based thermal transfer process is preferred for preparing test samples; the actual dielectric constant of the dielectric material is compensated and calibrated by measuring the group delay peak of the test sample, and the design scheme is modified based on the calibrated material parameters to complete the final physical fabrication.

[0029] S105, Deploy the metasurface solid structure; attach and cover the reflective metasurface solid structure manufactured in step 104 onto the surface of the object under test; in multi-angle imaging scenarios, a multi-faceted wrapping strategy is adopted to deploy the metasurface solid on the top and side surfaces of the object under test, and maintain geometric continuity at the connection points to achieve joint modulation of the reflection intensity and flight time of the millimeter-wave echo signal.

[0030] In establishing the equivalent model of a reflective metasurface, the reflective metasurface, as an artificial electromagnetic material, achieves its electromagnetic properties through a periodically arranged subwavelength unit structure. In the field of view of a millimeter-wave imaging system, the metasurface is considered a linear time-invariant system used to modulate the wavefront of incident electromagnetic waves. When the incident electromagnetic wave irradiates the metasurface, the metallic pattern structure on its surface excites surface currents and magnetic currents. These induced currents act as secondary wave sources, radiating electromagnetic waves outward, thus forming a reflection field with specific amplitude and phase characteristics. (See attached figure.) Figure 1 (In the figure, OutgoingWave: outgoing wave (or reflected wave), IncomingWave: incident wave, Metasurface: metasurface, metal: metal, substrate: dielectric substrate, 3Dviewofmetasurface: 3D view of metasurface, Topview: top view, Bottomview: bottom view, ReflectiveMetasurface: reflective metasurface, Z_air: air impedance, S11: S11 parameter (reflection coefficient), Z_pattern: pattern impedance, Substratelayer: dielectric substrate layer, Metallayer: metal layer, (a) Working principle of MTS: (a) Working principle of metasurface (MTS), (b) Equivalent circuit of the MTS: (b) Equivalent circuit of metasurface (MTS).) To quantitatively analyze the modulation effect of metasurface on millimeter-wave radar signals, a frequency response model of reflective metasurface is established. The frequency response model describes the response characteristics of metasurface to different frequency components within the operating frequency band. The frequency response of metasurface is expressed as a complex function. Its definition is as follows: ; In the formula, Represents angular frequency. Euler's number, which represents the base of the natural logarithm, is a mathematical constant with a value of approximately 2.71828. Represents the imaginary unit. The amplitude portion representing the frequency response corresponds to the metasurface's ability to modulate the intensity of electromagnetic wave reflection. The phase component of the frequency response corresponds to the phase delay of electromagnetic waves generated by the metasurface. This frequency response function characterizes the electromagnetic scattering properties of the metasurface itself, and its specific value depends on the unit geometry of the metasurface, the thickness of the dielectric layer, and the dielectric constant of the material.

[0031] Based on the frequency response model, the interaction process between the incident electromagnetic wave and the metasurface can be described by a frequency domain multiplication relationship. Let the millimeter-wave signal incident on the metasurface be represented in the frequency domain as... The reflected wave signal after metasurface modulation is represented as The relationship between the two can be expressed as: This formula shows that the reflected wave signal is the convolution result of the incident wave signal and the metasurface frequency response (in the time domain), or directly represents a product in the frequency domain. This can be achieved through optimization for specific target scenarios. Amplitude term in and phase term This can directly alter the characteristics of the reflected signal acquired by the receiver. Specifically, millimeter-wave imaging systems typically rely on the intensity of the echo signal to determine the reflectivity of the target material and on the time of flight of the echo signal to calculate the target distance. Therefore, by adjusting... The reflection intensity characteristics in the imaging results can be altered by adjusting... The rate of change of frequency can introduce group delay, thereby altering the range characteristics in the imaging results. This modulation method based on the physical layer signal model provides a theoretical foundation for the directional reconstruction of millimeter-wave imaging results.

[0032] To achieve precise control over reflection intensity, the reflective metasurface in this embodiment employs a layered structure of metal-dielectric substrate-metal. The top layer is a periodic metal pattern layer designed according to specific impedance requirements; the middle layer is a dielectric substrate layer with a fixed dielectric constant and thickness; and the bottom layer is a fully covered metal grounding layer. The bottom metal grounding layer physically serves as electromagnetic shielding and isolation, effectively cutting off the electromagnetic coupling path between the incident millimeter wave and the surface of the covered object. This structural design ensures that the metasurface's reflection characteristics are primarily determined by its own unit structure parameters, and are not affected by the material properties of the covered object (such as dielectric constant and conductivity). This allows the metasurface to maintain stable reflectivity control when facing test objects of different materials (such as metals, plastics, and biological tissues).

[0033] In the specific process of adjusting the reflection intensity, the main objective is to adjust the amplitude-frequency response of the metasurface to match the reflectivity characteristics of a preset background or a specific camouflaged object. Millimeter-wave imaging systems (such as SAR imaging or holographic imaging) typically characterize the reflectivity of a target based on the intensity of the received echo signal. Therefore, this invention optimizes the geometry of the metasurface unit, adjusts its input impedance, and thus changes the amplitude of its scattering parameter (S-parameter).

[0034] Define the operating frequency band range of the millimeter-wave imaging system, and select within that frequency band. A discrete frequency sampling point, denoted as to Assume the average target reflectance of the target background to be simulated within the imaging frequency band is... To ensure that the reflection characteristics of the metasurface approximate the target reflectivity as closely as possible across the entire bandwidth, an optimization objective function based on the least squares method was established. This optimization process aims to minimize the Euclidean distance between the actual reflection coefficient amplitude of the metasurface and the target reflectivity. The optimization objective function is defined as follows: ; In the formula, This indicates that the metasurface at angular frequency The reflection coefficient at that location, This represents the amplitude of the reflection coefficient. This represents the preset target reflectivity value, which is determined based on the measured reflectivity characteristics of the background material to be simulated (such as wood, clothing, human skin, etc.). This represents the total number of sampling points.

[0035] By solving the above objective function, the metasurface structure parameters that meet specific reflectivity requirements can be obtained. We fabricated two metasurface samples using the reflectivity of a wood background as the target and tested their modulation effect on the reflectivity of ceramic knife imaging (see...). Figure 2 (a) Real-world scenario). Among them, MTS1: metasurface 1 is optimized, while MTS2: metasurface 2 is not optimized. Figure 2 (b) No metasurfaces and Figure 2 (c) Imaging results with and without metasurfaces are shown after deploying two metasurfaces.

[0036] For objects with a certain thickness, the aforementioned reflection intensity modulation can eliminate the difference in reflection intensity between the object's surface material and the background material. Based on this, we placed a metasurface with only optimized reflectivity modulation in front of a 5cm thick iron block. Figure 3 (5cm IronCube) and its range slice imaging results were evaluated using a synthetic aperture radar (SAR) imaging system. Slice imaging was used to measure the signal strength distribution at a specific distance.

[0037] like Figure 3 As shown in the image (Background: wood, ReflectiveMTS), on a 15cm imaging slice (see...) Figure 3 (b) Imaging slice at 15 cm): Although the metasurface's reflectivity was modulated to match the wooden background, a significant difference in reflectance intensity still exists between the metasurface, the metal, and the background. This is because at this distance, the imaging background is air, and the imaging information of the wooden board actually located at 20 cm is not captured (see [link to image]. Figure 3(a) Actual scenario: A wooden board 20cm from the radar. Conversely, on the 20cm imaging slice, we observed a square area with weak reflection (see...). Figure 3 (c) An imaging slice at 20 cm shows a significant difference from the background, indicating that the imaging characteristics of thick objects are still preserved in the distance dimension. This result shows that millimeter-wave imaging is not only affected by reflectivity but also closely related to distance response characteristics (i.e., time of flight). Therefore, in order to effectively control the imaging results of thick objects, while maintaining uniform reflectivity modulation, the metasurface needs to further control the time of flight (ToF) to achieve the desired target distance response. In broadband millimeter-wave imaging systems (e.g., frequency-modulated continuous wave radar or stepped-frequency continuous wave radar), the distance resolution of the target object depends on the signal bandwidth, while the absolute distance of the target is calculated by measuring the time delay between the transmitted signal and the echo signal. For a physical distance of... The target, whose theoretical flight time of echo signal is ,in It is the speed of light. Figure 4 (a) shows the time-domain plot of the FMCW pulse and its echo signal (in the figure, Amplitude: amplitude, TXSignal: transmitted signal, RawRXsignal: raw received signal, RXsignalwithgroupdelay: received signal with group delay, Time: time, distance(cm): distance (cm), time(s): time (s), (a) Time-amplitude plot: (a) Time-amplitude plot, (b) Range profile: (b) Range profile (or one-dimensional range profile)). By designing the phase response characteristics of the metasurface, without changing the physical position of the target... Under the premise of introducing additional virtual time delay into the echo signal, the ranging algorithm of the radar system is misled.

[0038] In signal processing theory, group delay Defined as system phase response diagonal frequency The negative derivative of the metasurface. To achieve stable range migration in broadband imaging systems, the metasurface needs to provide an approximately constant group delay across the entire operating frequency band. This implies that the phase response of the metasurface... It should exhibit a linear relationship with frequency, that is, satisfy... ,in It is a constant. In this case, the frequency response function of the metasurface can be expressed as: ; Let the time-domain pulse signal incident on the metasurface be Its frequency domain representation is Frequency domain signal after metasurface reflection The product of the incident signal and the frequency response: ; Performing an inverse Fourier transform on the above equation yields the time-domain reflection signal. : ; To achieve precise control over the virtual distance during the metasurface design phase, a mapping relationship between the reflection coefficient phase and the equivalent delay distance is established. Since the phase is periodic in the frequency domain, direct calculation of the derivative may result in discontinuous jumps. Therefore, the reflection coefficient is first... The phase is unwrapped and denoted as... At this time, the frequency equivalent delay distance at The calculation is as follows: ; During the design process, the target delay distance was set as... , The value is typically determined based on the physical thickness of the occluded object or the relative position of the target and background. To ensure that the metasurface maintains a stable distance modulation effect across the entire bandwidth, an optimization objective function based on distance error is constructed: ; In the formula, These are discrete sampling frequency points within the operating frequency band. Let be the total number of sampling points. By minimizing this objective function, the optimization algorithm can find the optimal unit structure parameters, making the slope of the phase-frequency curve of the metasurface stable at a value corresponding to... Numerically, this method based on physical layer phase slope modulation is applicable not only to frequency-modulated continuous wave radar but also to millimeter-wave imaging systems based on time-domain pulses or other broadband modulation mechanisms. The ranging principle and phase unwrapping algorithm of frequency-modulated continuous wave radar are well-known technologies in this field and will not be elaborated upon here.

[0039] However, simultaneously satisfying specific reflection intensity and flight time delay targets is a complex non-convex optimization problem. Therefore, this embodiment provides a hierarchical joint optimization framework (such as...). Figure 5As shown in the figure, PriorKnowledge, Operatingfrequencyband, Targetdistanceinformation, Targetreflectivityinformation, DesignGoal, Groupdelay, Reflectivity, JointOptimizationScheme, Modeling, GradientDescent, InverseDesign, Fine-tuning, PermittivityCompensation, Fabrication, Supportdifferentsubstrates, FBA-based, Paper-based, Rogers-based, and SuccessfulModulation decompose the complex electromagnetic reverse design process into an equivalent impedance optimization stage based on transmission line theory and a geometric parameter fine-tuning stage based on full-wave simulation. By abstracting the geometric pattern layer into an equivalent impedance sheet, the dimensionality of the initial search space is reduced.

[0040] At the beginning of the design process, the system receives target parameters for imaging control, including target reflectivity. Distance to target To achieve decoupling and collaborative design of these two parameters, this invention constructs a joint loss function that includes a weighted error term. The joint loss function comprehensively measures the deviation of the current design parameters from the target values ​​in both amplitude response and phase slope response. Specifically, the total loss function is defined as follows: The weighted sum of the reflectivity error term and the delay distance error term: ; In the formula, The first one selected within the operating frequency band A discrete sampling angular frequency, This represents the total number of sampling points; It is the amplitude of the reflection coefficient. The preset target reflectivity value; Indicates at angular frequency The equivalent delay distance is calculated based on the phase and frequency derivatives of the reflection coefficient, and this value characterizes the time-of-flight characteristics. The preset target delay distance; and These are the weighting coefficients for the reflectivity error term and the delay distance error term, respectively.

[0041] Weighting coefficient and This is used to balance the importance of the two optimization objectives based on the actual application scenario. For example, in scenarios where the requirement for depth camouflage (stealth) is higher than that for brightness camouflage, the value can be appropriately increased. The numerical value is used to strengthen the constraint on the delay distance. Based on a unified definition of the joint loss function, the optimization process is executed in two levels: the first level is the impedance optimization stage, at which point the loss function... The independent variable is set as the equivalent complex impedance of the patterned layer. and dielectric layer thickness By minimizing The first step involves rapidly searching the complex impedance space to find the ideal impedance curve and dielectric thickness that meet the design requirements, thereby determining the physically feasible theoretical solution space. The second level is the geometric matching and full-wave simulation fine-tuning stage, where the loss function... The independent variable is transformed into specific geometric structural parameters. (e.g., metal linewidth, arm length, etc.). Guided by the previously obtained ideal impedance, a matching geometric topology is selected, and the geometric dimensions are further refined using a loss function to compensate for higher-order electromagnetic effects in the actual physical structure. This hierarchical strategy effectively reduces the curse of dimensionality caused by directly searching the entire space for geometric parameters, ensuring the convergence and accuracy of the design scheme.

[0042] After obtaining the optimal equivalent impedance and dielectric thickness, the process proceeds to the second level: geometric matching and full-wave simulation. This stage involves searching a pre-built database of geometric patterns (containing typical structures such as cross-shaped, circular, and C-ring structures and their corresponding impedance characteristics) and selecting and optimizing the obtained patterns using the Euclidean distance minimization principle. The geometric pattern topology that best matches the curve was determined. Subsequently, a three-dimensional physical model incorporating substrate material loss, edge effects, and higher-order mode coupling effects was established in full-wave electromagnetic simulation software. Using the geometric dimensions of the selected pattern (such as arm length, linewidth, and gap width) as the final optimization variables, the aforementioned joint loss function was applied again. Fine-tuning of the geometric parameters is performed. This process corrects for errors introduced by the transmission line theory model in its approximation, ensuring that the final fabricated metasurface entity can accurately reproduce the expected reflectivity and group delay characteristics in a real electromagnetic environment.

[0043] To support impedance optimization at the first level, a fast analytical model from structural parameters to electromagnetic response needs to be established. Therefore, this implementation establishes an equivalent circuit model based on transmission line theory. This model abstracts the three-layer physical structure of the metasurface—"metal pattern layer, dielectric substrate layer, and metal ground layer"—as a cascaded microwave network composed of lumped parameter elements and distributed parameter elements, and uses an ABCD matrix (also known as a transmission matrix) to analyze the electromagnetic characteristics of each layer.

[0044] In the equivalent circuit model, the periodic metal pattern layer at the top is equivalent to a complex impedance element connected in parallel on the transmission path, denoted as the pattern layer equivalent impedance. This impedance characterizes the scattering properties of the metallic pattern to incident electromagnetic waves, and its value depends on the pattern's geometry (such as linewidth, slots, and topology) and operating frequency. In microwave network analysis, the transmission matrix corresponding to this parallel impedance layer... Represented as: ; The intermediate dielectric substrate layer is modeled as a transmission line with a specific physical length (i.e., dielectric thickness). Let the relative permittivity of the dielectric layer be . Magnetic permeability is Thickness is The characteristic impedance of this transmission line segment is The propagation constant is Among them, characteristic impedance propagation constant , here Free-space wave impedance (approximately 377) ), It is the speed of light. The transmission matrix corresponding to this medium layer. Represented as: ; The bottom-layer, fully-covered metallic grounding layer is approximated as an ideal short-circuit terminator. In practical numerical calculations, to avoid singularities in matrix operations, it is usually equivalent to a very small impedance value. (e.g., 10) -8 The transmission matrix corresponding to this metallic grounding layer. Represented as: ; Based on cascaded network theory, the total transfer matrix of the entire metasurface system It equals the product of the layered matrices in the order of signal transmission (from the incident end to the terminal). That is: ; In the formula, , , , These are the four elements of the cascaded total matrix. After obtaining the total transmission matrix, in order to evaluate the reflection performance of the metasurface, the ABCD matrix is ​​converted into reflection coefficients (i.e., the S-parameters) using the microwave network parameter transformation relationship. For a single-port reflective network, the reflection coefficient at the input port... The calculation formula is as follows: ; Through the above mathematical derivation, a system was established to analyze the design variables (pattern layer impedance). Medium thickness From system response (reflection coefficient) The analytical mapping relationship of ABCD matrix and S-parameter transformation is described. This modeling method allows optimization algorithms to quickly evaluate the reflectivity amplitude and phase delay characteristics under different impedance and thickness combinations without performing time-consuming full-wave electromagnetic field simulations, thus providing accurate theoretical target values ​​for subsequent geometric pattern matching. The basic circuit theory of ABCD matrix and S-parameter transformation is well-known in this field and will not be elaborated here.

[0045] After establishing the equivalent circuit based on the transmission line model, this implementation performs a preliminary impedance-based optimization process. The core of this process lies in directly searching for the optimal solution that simultaneously satisfies the target reflectivity and target delay distance within the complex impedance space, without relying on a specific geometric pattern topology. This determines the ideal electromagnetic response characteristics required for the metasurface metal pattern layer and the physical thickness of the dielectric layer. After determining the equivalent impedance of the pattern layer, the pattern needs to be designed in reverse to achieve this target impedance. For this purpose, we first select several verified metasurface unit patterns (e.g., cross-shaped, C-shaped rings, and concentric ring structures) as candidates. For each candidate pattern, a simulation model containing only the pattern layer is constructed in HFSS, as detailed below. Figure 6As shown in the figure (Candidate: candidate structure, Metalpatterntemplate: metal pattern template, Floquet port: Floquet port, Coupled boundaries: coupled boundaries, Airbox: air domain, Impedance vs. geometric parameters: impedance vs. geometric parameters, AnsysHFSS simulation results with EMFiniteElement Method: AnsysHFSS simulation results based on the electromagnetic finite element method, Metallayer: metal layer). Floquet ports and master / slave boundary conditions were used in the simulation, and the element size was set to half the wavelength at the center frequency of the operating frequency band. Next, the geometric parameters of each candidate pattern were systematically scanned, and the corresponding impedance-frequency response curves were obtained through simulation. Using Euclidean distance as a similarity metric, we selected the pattern template and its parameter combination with the highest impedance matching degree, thereby ensuring that the obtained physical structure can realize the required equivalent impedance characteristics as accurately as possible.

[0046] To efficiently solve the above optimization problem in a multidimensional non-convex solution space, this implementation adopts a combinatorial optimization strategy. For the dielectric layer thickness... This scalar parameter, with a reasonable physical search range (e.g., 0.1mm to 3mm), is used for discretization optimization using hyperparameter search algorithms (such as grid search or random search); for frequency-dependent equivalent impedance... Iterative updates are performed using gradient-based optimization algorithms (such as the Adam optimizer or L-BFGS algorithm). In each iteration, the loss function is calculated. The gradients of the real and imaginary parts of the impedance are applied, and the impedance value is updated along the negative gradient direction until the loss function converges or the preset number of iterations is reached.

[0047] The output of the impedance-based optimization step is an ideal target impedance curve that varies with frequency. and optimal medium thickness Compared to directly scanning the geometry, this impedance-domain optimization method avoids repeatedly calling time-consuming full-wave electromagnetic simulations, significantly shortening the design cycle and enabling the exploration of theoretical performance limits that are difficult to cover with traditional geometric parameter scanning. For example... Figure 17 As shown, the impedance optimization method achieves a larger maximum delay distance compared to the method based solely on fixed pattern scanning, demonstrating the effectiveness of this preliminary optimization step in expanding design freedom.

[0048] Obtain the ideal target impedance curve through the equivalent circuit model. and dielectric layer thickness Subsequently, this implementation performs an inverse mapping from the theoretical impedance space to the physical geometric space, and then performs a final calibration of the structural parameters through full-wave electromagnetic simulation. This process aims to eliminate errors introduced by the approximation of the transmission line model, ensuring that the electromagnetic response of the physical structure accurately meets the design requirements. To achieve impedance-to-geometric conversion, a pre-defined geometric pattern database is established or invoked. This database stores various typical metasurface unit topologies (such as Jerusalem crosses, C-shaped open rings, and square patches) and their corresponding impedance characteristic data. The impedance characteristics of each topology are pre-calculated through parameter scanning, establishing a combination of geometric parameters. With frequency-dependent impedance The mapping relationship between them. In the reverse matching stage, the impedance curves in the database are traversed, and their mapping relationship with the target impedance curve obtained in the previous steps is calculated. The Euclidean distance between them. The evaluation function for the matching process is defined as follows: ; In the formula, Indicates the matching error. For a certain geometric structure in the database at frequency The impedance value at that point, To optimize the obtained ideal target impedance value, a value is selected that minimizes the matching error. Minimal geometric topology and its corresponding initial geometric parameters This serves as the starting point for physical implementation. This search and matching mechanism can quickly determine the unit structure type best suited to current imaging control needs.

[0049] Since the transmission line equivalent circuit model ignores the mutual coupling effect between units, edge field effect, and higher-order mode parasitic effect, it directly uses the initial geometric parameters. The fabricated metasurface may deviate from its expected performance in practice. Therefore, the initial geometric parameters... and the determined dielectric layer thickness Import the model into full-wave electromagnetic simulation software to construct a three-dimensional high-fidelity simulation model that includes detailed physical boundary conditions and excitation sources, such as... Figure 6 As shown. In the full-wave simulation environment, gradient-based fine-grained optimization is performed. The specific dimensional parameters of the geometry (including the metal arm length) are... Line width Gap width (etc.) are defined as the set of optimization variables. The S-parameters of the geometry at different frequencies were calculated using a full-wave solver, and the variables were again adjusted using a joint loss function that included reflectivity error and delay distance error. Iterative fine-tuning is then performed. The final objective function for optimizing the geometric parameters is expressed as: ; In the formula, and These respectively represent the geometric parameters as At that time, the reflection coefficient amplitude and equivalent delay distance were calculated through full-wave simulation. This step, by fine-tuning the geometric dimensions, compensated for the electromagnetic coupling effect in the physical implementation, ensuring that the final metasurface design can accurately reproduce the preset target reflectivity in actual millimeter-wave imaging tests. Delay of target group The specific operation settings and finite element analysis methods of the full-wave electromagnetic simulation software are well-known technologies in this field and will not be elaborated upon here.

[0050] To ensure that the designed metasurface structure can be deployed on a large scale at low cost and adapt to the surface morphology of different objects being tested, this embodiment provides two specific material selection and manufacturing schemes: a printed circuit board scheme based on a rigid substrate and a paper-based thermal transfer scheme based on a flexible substrate.

[0051] In rigid substrate designs, an industry-standard glass fiber reinforced epoxy resin laminate (FR-4) is selected as the dielectric substrate. This material has mature manufacturing process standards and a suitable relative permittivity. Typically between 4.3 and 4.5, the loss tangent is... The value is approximately 0.02. In this scheme, both the metal pattern layer and the metal ground layer are composed of copper foil attached to the surface of a glass fiber reinforced epoxy resin laminate substrate. Excess copper foil is removed using standard printed circuit board photolithography and chemical etching processes, thereby forming a high-precision geometric pattern array on the top layer. Since glass fiber reinforced epoxy resin laminate material has high dielectric loss in the millimeter-wave band, which is generally considered a disadvantage in traditional antenna design, in the reflection control application of this invention, this loss characteristic is incorporated into the resistive parameters of the equivalent circuit model. This helps to achieve attenuation control of the reflected wave amplitude through structural design without the need for additional lumped resistive elements, thereby reducing the system's manufacturing complexity.

[0052] In flexible substrate solutions, to achieve seamless camouflage of curved objects and further reduce costs, cellulose-based materials (such as standard printing paper or photo paper) are selected as the substrate layer. The metallic pattern layer uses hot-stamping foil with a metallic sheen, typically composed of a polyester film carrier, release layer, coloring layer, aluminized layer, and adhesive layer. The metallic grounding layer uses flexible aluminum foil tape or conductive cloth. The manufacturing process is based on electrostatic copying principles and thermal transfer technology: first, a laser printer prints the designed geometric pattern onto a paper substrate in the form of thermoplastic toner; then, the paper substrate covered with hot-stamping foil is passed through a thermal laminator (laminator), where, under high temperature (approximately 160°C) and pressure, the hot-stamping foil adheres only to the areas covered by the toner; finally, the excess foil is peeled off, forming a metasurface pattern composed of an extremely thin metallic layer on the paper substrate.

[0053] In the two material schemes mentioned above, the thickness of the dielectric substrate layer... and dielectric constant These are key physical parameters affecting the phase response of metasurfaces. For glass fiber reinforced epoxy resin laminate substrates, these parameters are provided by the manufacturer and are relatively stable; however, for paper-based materials, the dielectric constant fluctuates due to the influence of paper density and environmental humidity. Therefore, before actual manufacturing, it is necessary to perform high-frequency dielectric property characterization on selected batches of paper material to obtain accurate dielectric constants. The values ​​are then substituted into the aforementioned joint optimization framework for calculation. By employing these widely available commercial off-the-shelf materials, this invention effectively lowers the entry barrier for millimeter-wave stealth and camouflage devices.

[0054] When fabricating metasurfaces using low-cost materials (such as FR-4 or paper substrates), the relative permittivity of the dielectric material is crucial. Material properties often fluctuate between batches or change due to environmental humidity. This uncertainty in material properties can cause a shift in the resonant frequency of the actually processed metasurface, leading to a deviation of its group delay peak from the preset operating frequency band and affecting imaging control. To eliminate this material error, this embodiment proposes a compensation calibration method. This compensation method is based on the inverse physical relationship between the resonant frequency and the dielectric constant of the medium. Given a fixed metasurface unit structure size, its resonant frequency... The group delay response curve is primarily determined by the effective dielectric constant of the dielectric layer. When the actual dielectric constant differs from the nominal value set in the simulation model, the group delay response curve will shift overall on the frequency axis. Specifically, if the actual dielectric constant is higher than the nominal value, the resonant frequency shifts to lower frequencies (red shift); conversely, it shifts to higher frequencies (blue shift). To correct this deviation, the frequency is first determined based on the nominal dielectric constant. Design and fabricate a small batch of standard test specimens, and use a vector network analyzer to measure the reflection coefficient of the specimens in the operating frequency band. Then, the actual group delay response curve can be calculated.

[0055] After acquiring the measured data, the peak frequency in the measured group delay curve is extracted. And compare it with the theoretical peak frequency calculated based on the nominal dielectric constant in the simulation model. A comparison is made. Based on the resonant cavity perturbation theory, the corrected compensation dielectric constant... Calculated using the following calibration formula: ; In the formula, This represents the dielectric constant estimate used to correct the simulation model after calibration. Indicates the nominal dielectric constant of the material used in the initial design; This represents the peak group delay frequency obtained from simulation at the nominal dielectric constant. This represents the peak group delay frequency obtained from actual measurements of the test sample.

[0056] Obtain the compensated dielectric constant Then, this value is substituted back into the full-wave electromagnetic simulation model, replacing the original material parameter settings. Subsequently, keeping the dielectric layer thickness unchanged, the aforementioned geometric parameter fine-tuning process is re-run using the updated dielectric constant as a benchmark to perform secondary optimization of the geometric dimensions of the metal pattern layer (such as arm length, gap width, etc.). The final manufacturing file is then generated. This closed-loop process of "trial production-measurement-correction-remanufacturing" effectively offsets the frequency errors caused by the dispersion of material properties, ensuring that the final mass-produced metasurface entities can accurately produce the expected reflection intensity attenuation and time-of-flight delay at the target operating frequency. The use of the vector network analyzer and the S-parameter measurement operation are testing methods well-known to those skilled in the art and will not be elaborated upon here.

[0057] To systematically verify the effectiveness of the above design method and the feasibility of the manufacturing scheme, this embodiment systematically evaluates the metasurface's reflectivity modulation capability and time-of-flight delay characteristics in a near-real-world planar millimeter-wave imaging scenario. A high-resolution SAR imaging verification system was built, as shown in the attached figure. Figure 7 (Background: background, MagicPatch: metasurface patch (the metasurface designed in this article), IronCube: iron cube).

[0058] The RF front-end of this imaging verification system uses the Texas Instruments IWR1443-Boost millimeter-wave radar board, and the data acquisition module uses a DCA1000EVM. The system is configured in single-transmit, single-receive (SISO) antenna mode, with an operating frequency range of 77.4 GHz to 80.8 GHz, a signal bandwidth of 3.4 GHz, and a frequency modulation slope of 66.7 MHz / μs. To construct a high-precision two-dimensional synthetic aperture, the millimeter-wave radar (mmWaveRadar) is mounted on a precision two-dimensional electric slide rail platform (2DSlideRai). This platform is programmed to perform point-by-point scanning sampling within a 100 mm × 100 mm rectangular area, with a sampling point array of 101 × 101 and a step interval of 1 mm. This high-density spatial sampling ensures that the imaging algorithm can reconstruct target images with millimeter-level resolution. Unless otherwise specified, the metasurface samples in this embodiment are all manufactured using low-cost FR-4 substrates.

[0059] To quantitatively evaluate the effect of metasurfaces on imaging results, an evaluation index system based on slice imaging is introduced. Definition This is the imaging result matrix when the metasurface of the present invention is covered. This is the imaging result matrix when the target object is not included (i.e., only the background is present) (serving as an ideal target reference). Two metrics are used for measurement: cosine similarity and normalized energy difference (NEDM). Cosine similarity (CSM) is used to evaluate the spatial structural similarity of the imaging patterns, and its calculation formula is as follows: ; In the formula, Represents the vector dot product. This represents the Frobenius norm of the matrix. The cosine similarity ranges from 0 to 1; the closer the value is to 1, the more consistent the camouflaged image texture is with the background. The normalized energy difference is used to assess the difference in energy intensity distribution between the two, and its calculation formula is as follows: The closer the normalized energy difference value is to 0, the closer the reflected energy level after adjustment is to the background, and the better the concealment effect.

[0060] To verify the independence and accuracy of reflection intensity modulation, five metasurface samples with different target reflectivities (R≈1) (R=0.1 to R=0.9) but consistent group delay were designed, as shown in the attached figure. Figure 8(a) Imaging results without a metasurface (w / o MagicPatch), (b) Imaging results with MagicPatches of different reflectivities). In the experimental scenario, the metasurface was partially obscured in front of a highly reflective iron cube. In the baseline control group without a metasurface, the high reflectivity of the iron cube resulted in a clear, bright boundary in the imaging results. However, after deploying the metasurface designed in this invention, the reflection intensity of the corresponding region in the imaging results was successfully modulated to a preset level (R=0.1 to R=0.9) through precise attenuation of the reflected signal amplitude. This result confirms that this invention can linearly and controllably reshape the radar cross-section characteristics of an object without changing its physical material through structural design.

[0061] To verify the effectiveness of time-of-flight control, three sets of metasurfaces were designed, as shown in the attached diagram. Figure 9 The preset equivalent delay distances are 0cm, 2cm, and 4cm. In the depth (distance) slices of the imaging results, it was observed that when the group delay is 0 ( Figure 9 Based on a glass fiber reinforced epoxy resin laminate with a metasurface having a delay of 0 cm, the main imaging energy is concentrated at 15 cm and 16 cm (corresponding to the actual physical location of the object); when a group delay corresponding to a distance of 2 cm is introduced ( Figure 9 b, based on a glass fiber reinforced epoxy resin laminate and a metasurface with a delay of 2 cm), the main imaging slices are translated to 17 cm and 18 cm; when a group delay of 4 cm is introduced ( Figure 9 c, Based on a glass fiber reinforced epoxy resin laminate and a metasurface with a delay of 4 cm, the imaging slices were further recessed to 19 cm and 20 cm. This phenomenon indicates that the group delay introduced by the metasurface is accurately resolved as a shift in the distance dimension in a broadband imaging system, thereby enabling virtual control of the depth position of the target object.

[0062] To verify the advantages of the joint optimization framework, a metasurface with target parameters of "delay distance of 4 cm and reflectivity of 0.4" was designed and compared with an absorptive metasurface without a metasurface and one with only adjustable reflectivity. (See attached figure.) Figure 10 (a) Original target imaging, (b) Target imaging with an absorbing metasurface, (c) Target imaging with a MagicPatch. Experimental results show that although traditional absorbing metasurfaces can reduce reflection intensity, they leave a noticeable shape outline loss in the imaging slice. This abnormally low-reflection area actually exposes the object's outline, size, and presence. In contrast, the metasurface using the combined control scheme of this invention not only adjusts the reflection intensity but also shifts the reflected signal to the background plane, filling in the shape outline loss. This allows the imaging result to perfectly blend with the background in both intensity and distance dimensions, achieving deep stealth camouflage.

[0063] To evaluate the feasibility of a low-cost manufacturing approach, metasurfaces with the same parameters (design targets: (a) delay 0 cm / reflectivity 0.9 and (b) delay 4 cm / reflectivity 0.6) manufactured using industrial-grade FR-4 substrates (low cost) and RF-grade Rogers substrates (high cost) were compared, with reference to Appendix Figure 11 Experimental results show that although the reflection intensity within the imaging slice of the FR-4 substrate fluctuates slightly due to its high dielectric loss, its overall average reflectivity and group delay modulation effect are highly consistent with those of the Rogers substrate. This demonstrates that the optimization method proposed in this invention has strong robustness and can effectively overcome the non-ideal characteristics of low-cost materials through structural compensation, providing technical support for large-scale industrial deployment.

[0064] To verify the versatility of the metasurface design provided by this invention in handling objects with different materials, geometries, and thicknesses, eight representative test objects were selected for verification, as shown in the attached figure. Figure 12 These objects include: plant leaves (A), plant seeds (B), powdered substances (C), liquid alcohol containers (D), matchboxes (E), pills (F), toy guns (G), and ceramic products (H). The physical thickness of objects A to G ranges from 1 cm to 5 cm, while the thickness of object H is approximately 0.2 cm. Using the aforementioned joint optimization framework, five metasurface prototypes based on FR-4 substrates were designed and fabricated for these objects. Their time-of-flight delay parameters cover the range of 0 cm to 5 cm, and their reflectivity parameters were optimized to match their respective background environments.

[0065] In the experiment, a background image slice without an object was used as a reference to calculate a quantitative index between the imaging result after covering the metasurface and the background reference. Experimental data show that the average cosine similarity between the modulated imaging result and the background pattern for all test objects is approximately 0.97. This indicates that the metasurface successfully erases the original outline of the object in the imaging structural features, making it highly fit the background texture. Simultaneously, the average normalized energy difference remains at a low level of approximately 0.11, demonstrating that the difference in energy distribution between the two is minimal. These results fully demonstrate that the imaging modulation capability of this invention does not depend on the specific geometric or dielectric properties of the tested object, and has broad applicability.

[0066] To evaluate the system's robustness under non-ideal observation conditions, angle sensitivity tests and distance sensitivity tests were conducted, as shown in the appendix. Figure 13 and attached Figure 14In the angle experiment, the object was placed 15cm away from the transceiver, with the metasurface in close contact with the front of the object. The angle of incidence varied from -30° to 30° (with 0° as perpendicular incidence). Experimental results showed that within the angle of incidence range of -20° to 20°, the metasurface maintained stable imaging modulation, with minimal fluctuations in the cosine similarity (CSM) and normalized energy difference (NEDM) indices. When the angle of incidence exceeded ±30°, the modulation performance decreased to some extent. This is mainly because, under oblique incidence conditions, the reflected wave primarily follows the specular reflection path, causing the echo energy to deviate from the receiving aperture of the monostatic radar, resulting in a reduction in effective received energy. This physical phenomenon is an inherent law of electromagnetic scattering, but under typical small-angle radar detection scenarios, this invention still exhibits reliable performance. In the distance experiment, with the angle of incidence fixed at 0°, the distance between the object and the transceiver was adjusted within the range of 10cm to 40cm. The results show that within this distance range, the metasurface can always maintain the expected delay and reflectivity response, proving that its modulation mechanism is based on physical wavefront modulation, rather than a lens effect dependent on a specific focal length.

[0067] Considering the diversity of materials used to disguise targets in practical applications, six solid cubes were selected as test subjects, made of glass (A), ceramic (F), paraffin wax (D), metal (C), sponge (B), and plastic (E). (See attached document.) Figure 15 These materials encompass a wide range of electromagnetic response characteristics, from low to high dielectric constants and from insulators to conductors. Four FR-4-based metasurfaces were fabricated for these materials, configured with matched reflectivities and time-of-flight delays of 0 cm, 3 cm, 4 cm, and 5 cm, respectively. Experimental results show that on all tested materials, the modulated imaging achieved a CSM value higher than 0.98 and an NEDM value of approximately 0.12. This indicates that the reflective metasurface design of this invention can effectively shield against material differences in objects behind it, providing a consistent camouflage effect.

[0068] To verify its application potential on complex biological surfaces, a flexible metasurface was fabricated using a paper-based thermal transfer process, and a human chest imaging scene was constructed. (See attached image.) Figure 16In this scenario, an attempt was made to conceal metal scissors and pliers placed under the clothing on a person's chest. Without the metasurface covering, millimeter-wave imaging clearly showed the outlines of the scissors and pliers, and due to the high reflectivity of the metal, their brightness was much higher than the human background. When the paper-based metasurface designed in this invention was applied, by jointly controlling the reflection intensity (to match the reflectivity of human skin) and group delay (to compensate for the tool thickness), the tool features in the imaging results disappeared, and slices at different depths all showed features matching the human background. This experiment confirms the feasibility of this invention in the fields of wearable devices and human security and privacy protection.

[0069] To investigate the theoretical performance limits of the joint optimization framework proposed in this invention, large-scale numerical simulation experiments were conducted. (See attached diagram.) Figure 17 In the simulation settings, the hyperparameter search space is defined as follows: the number of metasurface layers is 1 to 4, the thickness of the dielectric layer is 0.1 mm to 1.2 mm, the upper limit of the number of optimization iterations is 20,000, and the number of hyperparameter search experiments is 500.

[0070] First, the performance of three typical frequency bands—24-30GHz, 30-40GHz, and 77-81GHz—was compared. For example... Figure 17 (a) As shown in the impedance-based optimization at different frequency bands, the 77-81 GHz band exhibits the best delay performance, with a maximum achievable delay distance approximately 3 to 6 cm higher than the other two lower frequency bands. This result aligns with the physical principle that maintaining a larger group delay flatness is easier within a relatively narrow bandwidth, while lower frequency bands, due to their wider relative bandwidth, present greater challenges in dispersion control. Furthermore, the performance of the "impedance-based optimization" and "geometric pattern scanning-based optimization" schemes in the 77-81 GHz band is compared. Figure 17 (b) Different optimization methods in the 77–81 GHz band are shown. Taking a typical cross-shaped pattern as an example, the impedance-based optimization method can achieve a maximum delay distance of up to 13 cm, while the traditional fixed-pattern scanning method can only reach a maximum of about 9 cm. This is attributed to the fact that the impedance-based optimization method performs a continuous search in the complex impedance space, without being limited by the parameter constraints of a specific geometric topology, thus enabling it to explore the theoretically optimal solution with a more dramatic phase change rate.

[0071] To verify the universality of metasurface manipulation effects across different imaging algorithms, a spatial domain SAR back-projection algorithm and a frequency domain-based matched filtering algorithm were implemented. (See attached...) Figure 18 and attached Figure 19In the simulation setup, an iron plate was placed at 15cm, and the metasurface (MTS) was configured to introduce an additional group delay of 2cm and modulate the reflectivity to 0.3. Simulation results show that regardless of the imaging algorithm used, the metal plate covered with the metasurface was reconstructed at a position of 17cm (i.e., a physical position of 15cm ± 2cm), and the reflection intensity was reduced. This indicates that the modulation effect of the present invention occurs at the physical layer of electromagnetic wave propagation, directly altering the amplitude and time-of-flight information of the echo signal. Therefore, it has equivalent deception or modulation capabilities for all millimeter-wave imaging algorithms that rely on these physical quantities for image reconstruction.

Claims

1. A millimeter-wave imaging method based on metasurface joint modulation of reflection intensity and time of flight, characterized in that, Includes the following steps: An equivalent model of a reflective metasurface is established, which is based on a stacked structure of a top metal pattern layer, an intermediate dielectric substrate layer, and a bottom metal ground layer. The target parameters for imaging control are determined based on the equivalent model of a reflective metasurface and the target reflectivity and delay distance values ​​are set according to the operating frequency band of the millimeter-wave imaging system. The joint optimization design of metasurface structure is carried out, and the imaging control target parameters are achieved by adopting a hierarchical optimization strategy. First, the joint loss function of reflectivity and delay distance is constructed based on the equivalent circuit model, the optimal equivalent impedance and substrate thickness are calculated, then the geometric pattern template that meets the impedance is selected, and the geometric parameters are fine-tuned using the full-wave electromagnetic simulation model to generate the design scheme. Metasurface prototype fabrication and parameter calibration: Prepare test samples, compensate and calibrate the actual dielectric constant of the dielectric substrate by measuring the group delay peak, modify the design scheme based on the calibration parameters, and complete the physical fabrication. Deploy metasurface solid structures to cover the surface of the object under test, and jointly modulate the reflection intensity and flight time of millimeter-wave echo signals.

2. The millimeter-wave imaging method based on metasurface joint modulation of reflection intensity and time of flight according to claim 1, characterized in that, In establishing the equivalent model of the reflective metasurface, the equivalent model of the reflective metasurface is described using an ABCD transmission matrix. The total transmission matrix is ​​calculated as follows: according to the signal transmission order, the transmission matrix of the metal pattern layer, the transmission matrix of the dielectric substrate layer, and the transmission matrix of the metal ground layer are cascaded and multiplied in sequence. The transmission matrix of the metal pattern layer is determined by the equivalent impedance of the metal pattern layer, the transmission matrix of the dielectric substrate layer is determined by the characteristic impedance, propagation constant, and thickness of the dielectric substrate layer, and the transmission matrix of the metal ground layer is determined by the impedance of the ground layer.

3. The millimeter-wave imaging method based on metasurface joint modulation of reflection intensity and time of flight according to claim 2, characterized in that, In determining the target parameters for imaging control, the equivalent delay distance corresponding to the target delay distance value is obtained by calculating the frequency derivative of the phase of the reflection coefficient. Specifically, the phase of the reflection coefficient is unwrapped, the negative derivative of the unwrapped phase with respect to the angular frequency is calculated, and the negative derivative is multiplied by half the speed of light to obtain the equivalent delay distance at the corresponding frequency. The reflection coefficient is obtained by transforming the elements of the total transmission matrix.

4. The millimeter-wave imaging method based on metasurface joint modulation of reflection intensity and time of flight according to claim 3, characterized in that, In the joint optimization of metasurface structures, the joint loss function is defined as a weighted sum of a reflectivity error term and a delay distance error term. The reflectivity error term represents the sum of squares of the differences between the calculated reflection coefficient amplitude and the target reflectivity value at each sampling frequency point within the operating frequency band. The delay distance error term represents the sum of squares of the differences between the calculated equivalent delay distance and the target delay distance value at each sampling frequency point within the operating frequency band. The weighted sum is obtained by assigning weight coefficients to the reflectivity error term and the delay distance error term respectively and then summing them.

5. The millimeter-wave imaging method based on metasurface joint modulation of reflection intensity and time of flight according to claim 1, characterized in that, In the joint optimization design of metasurface structures, the step of using a reverse matching algorithm to select geometric pattern templates from a pattern library that conform to the optimal equivalent impedance characteristics specifically includes: Establish a geometric pattern database containing various geometric pattern topologies and their corresponding frequency-dependent impedance data. For each structure in the geometric pattern database, the Euclidean distance between its impedance curve and the optimal equivalent impedance curve calculated in the joint optimization design of metasurface structures is used as the matching error. The geometric pattern topology with the smallest matching error and its corresponding initial geometric parameters are selected as the geometric pattern template.

6. The millimeter-wave imaging method based on metasurface joint modulation of reflection intensity and time of flight according to claim 4, characterized in that, In the joint optimization design of metasurface structures, the fine-tuning of the geometric parameters of the geometric pattern template specifically includes: Define the specific geometric dimension parameters of the geometric pattern template as a set of optimization variables; The reflection coefficient amplitude and equivalent delay distance under the current geometric parameters were calculated using full-wave electromagnetic simulation software. The geometric parameters are iteratively updated with the objective of minimizing the geometric parameter optimization objective function; the geometric parameter optimization objective function is a weighted sum of the reflectivity error term and the delay distance error term calculated based on the full-wave simulation results.

7. The millimeter-wave imaging method based on metasurface joint modulation of reflection intensity and time of flight according to claim 1, characterized in that, In the fabrication and parameter calibration of metasurface prototypes, the actual dielectric constant of the dielectric substrate is compensated and calibrated by measuring the group delay peak value of the test prototype. The specific calibration method is as follows: Obtain the theoretical peak group delay frequency obtained by simulation under the nominal dielectric constant, and the actual peak group delay frequency obtained by actual measurement of the test sample; Based on the physical relationship that the resonant frequency is inversely proportional to the square root of the dielectric constant, calculate the square of the ratio of the nominal dielectric constant multiplied by the theoretical group delay peak frequency to the actual group delay peak frequency. Modifying the metasurface design scheme means substituting the compensated dielectric constant into the physical simulation model and then fine-tuning the geometric parameters.

8. The millimeter-wave imaging method based on metasurface joint modulation of reflection intensity and time of flight according to claim 1, characterized in that, In the prototype fabrication and parameter calibration of metasurfaces, the test samples were prepared using the FR4 substrate etching process.

9. A millimeter-wave imaging method based on metasurface joint modulation of reflection intensity and time of flight according to claim 1, characterized in that, In the deployment of metasurface solid structures, a multi-faceted wrapping strategy is adopted, in which the metasurface solid is deployed on the top and side surfaces of the object under test, and geometric continuity is maintained at the connection points.

10. A millimeter-wave imaging control device, characterized in that, A millimeter-wave imaging method based on metasurface joint modulation of reflection intensity and time of flight, applicable to any one of claims 1-9, comprises: a processor and a memory, wherein the memory stores a computer program, and the computer program is executed by the processor.

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