Loongbour lens reverse engineering method based on electromagnetic inverse scattering

Abstract

The invention discloses a Longboer lens reverse engineering method based on electromagnetic inverse scattering, and relates to the technical field of detection imaging of a Longboer lens, and the method comprises the following steps: S1, data collection: arranging an electromagnetic wave transmitter and a receiver outside a lens, obtaining electromagnetic information of the lens through transmitting and receiving, and obtaining the electromagnetic information of the lens; the target area is divided into a plurality of grids, a predicted scattered field is obtained through calculation and accumulation, electromagnetic wave scattering measurement and implicit neural network modeling are combined, high-precision reconstruction of the three-dimensional structure in the luneberg lens is achieved, lens scattered field data are obtained through multi-angle and multi-frequency electromagnetic wave excitation and receiving, and the reconstruction precision of the three-dimensional structure in the luneberg lens is improved. The continuous dielectric constant distribution in the lens is modeled by means of the implicit neural network, the three-dimensional structure information of the lens can be obtained more freely and accurately, and compared with analysis of a traditional Longbour lens structure, the method is more convenient and accurate.

Description

Technical Field

[0001] This invention relates to the field of Luneburg lens detection and imaging technology, specifically to a Luneburg lens reverse engineering method based on electromagnetic backscattering. Background Technology

[0002] Lenses, due to their unique omnidirectional focusing characteristics, low aberrations, and wide bandwidth applicability, have shown great promise in various fields such as optical imaging, communication antennas, and space optics. This optical element places extremely high demands on the three-dimensional continuous distribution of the refractive index within the material. In traditional non-destructive testing techniques… X-ray imaging is a widely used technique. The physical mechanism of the interaction between X-rays and materials involves only the attenuation and absorption of X-rays. The imaging information it provides essentially reflects the macroscopic mass distribution characteristics of the material and cannot directly reveal the electromagnetic properties of the material. Reconstructing the internal structure of the scattering body requires solving the problem of electromagnetic wave inverse scattering imaging. Existing inverse scattering imaging methods are generally based on numerical methods such as finite difference, finite element or integral equations to solve the forward model. In order to ensure numerical stability, the continuous space must be discretized into voxels or meshes. Spatial discretization inevitably leads to resolution loss, which forces the continuous change of dielectric constant to be represented by discrete points.

[0003] Existing Optical imaging cannot provide the true refractive index variation and optical working mechanism when studying the internal structure of gradient refractive index optical elements. In scenarios with large refractive index gradients or complex internal material structures, multiple scattering is significantly enhanced, further increasing the difficulty of inversion and making traditional linearization methods or weak scattering approximations difficult to apply. In contrast, the coarse discretization of inverse scattering imaging methods will destroy the natural spherical or radial symmetry structure of Luneburg lenses, causing the estimated refractive index curve to jitter or be discontinuous, affecting the fitting of theoretical models and the verification of manufacturing quality.

[0004] To avoid the aforementioned technical problems, it is indeed necessary to provide a Luneburg lens reverse engineering method based on electromagnetic backscattering to overcome the deficiencies in the prior art. Summary of the Invention

[0005] This invention provides a Luneburg lens reverse engineering method based on electromagnetic backscattering, which can effectively solve the problems mentioned in the background art. Optical imaging cannot provide the true refractive index variation and optical working mechanism when studying the internal structure of gradient refractive index optical elements. In scenarios with large refractive index gradients or complex internal material structures, multiple scattering is significantly enhanced, further increasing the difficulty of inversion. This makes traditional linearization methods or weak scattering approximations difficult to apply. Inverse scattering imaging methods, coarse discretization can destroy the natural spherical or radial symmetry structure of Luneburg lenses, causing the estimated refractive index curve to fluctuate or become discontinuous, affecting the fitting of theoretical models and the verification of manufacturing quality.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a Luneburg lens reverse engineering method based on electromagnetic backscattering, comprising the following steps:

[0007] S1. Data Acquisition: Electromagnetic wave transmitters and receivers are placed outside the lens to acquire electromagnetic information from the lens through transmission and reception.

[0008] S2. Discretization: The target area is divided into several grids, and the predicted scattering field is obtained by calculation and accumulation.

[0009] S3. Network Construction: Construct a mapping network from spatial points to induced current, construct a mapping network from induced current to dielectric constant, and train them jointly.

[0010] S4. Network Model Testing: Input the spatial location vector to the dielectric constant prediction network and output the dielectric constant value at the corresponding location.

[0011] In step S1, an electromagnetic wave transmitter and a receiver are used. Both are precisely controlled by a robotic arm in terms of their spatial position and orientation. The robotic arm moves outside the imaging area according to a preset trajectory. The transmitter radiates electromagnetic waves to the lens under different spatial orientations and different incident angles. At the same time, another set of robotic arms carrying receivers are deployed at various observation angles outside the lens and receive the scattered echo signals, thereby achieving full circumferential coverage of the lens's scattering information.

[0012] According to the above technical solution, in step S1, two measurement processes are performed under the control of a robotic arm to obtain high-precision scattered field data. The steps are as follows:

[0013] First, without placing the lens, the background field is acquired following the same robotic arm trajectory;

[0014] Subsequently, the lens is placed in the area, and the robotic arm repeats the same measurement path to obtain the total field containing the lens effect. By subtracting the total field from the background field point by point, the pure scattering field data caused by the lens is extracted.

[0015] Finally, the scattering values ​​obtained from all the transmitter-receiver combinations under the control of the robotic arms are constructed into a scattering field measurement matrix according to the transmitter number, receiver number and frequency index, which describes the electromagnetic scattering characteristics of the lens under multiple angles and multiple frequency bands.

[0016] According to the above technical solution, in step S2, during training, the scene is divided into a grid, the induced current is calculated at discrete points, and an approximately continuous integral is accumulated. Specifically, the target area is... The system is divided into several small cubic grids. Several points are randomly sampled at the center of each grid. The induced current is calculated for these discrete points, and the predicted scattering field is obtained by accumulating and integrating approximately continuously.

[0017] According to the above technical solution, in S3, a mapping network from spatial points to induced current is constructed, namely the first network, to approximate the induced current at each point in space. This network takes the coordinates of any three-dimensional spatial point in the target area and the coordinates of the transmitter as input, and outputs the induced current corresponding to the point by training and fitting the interaction relationship between electromagnetic waves and the medium.

[0018] During training, the induced currents of all spatial points in the entire scene are summed to form a complete predicted scattering field. This predicted scattering field is compared with the scattering field actually measured by the receiver, the loss function is calculated, and the network parameters are optimized through backpropagation so that it can accurately predict the induced current generated at each spatial point under different emitter illumination. The design of this network allows it to automatically capture multiple scattering phenomena and the complex response of high-contrast media.

[0019] According to the above technical solution, in S3, a mapping network from induced current to dielectric constant is constructed, namely the second network, which maps the induced current to the dielectric constant of the corresponding spatial point. The network takes the three-dimensional coordinates of each spatial point as input and outputs the dielectric constant of that point, thus directly obtaining the dielectric distribution of any spatial point.

[0020] During training, the network uses the dielectric constant predicted by the network itself to calculate the predicted induced current, and uses the induced current output by the first network as a reference to calculate the loss. The network parameters are optimized through backpropagation. The second network learns the nonlinear mapping relationship between the induced current and the dielectric constant to predict the dielectric constant at any location in space.

[0021] By jointly training the first and second networks, the first network generates the induced current distribution, and the second network maps it to the dielectric constant. The parameters of the two networks are optimized simultaneously through backpropagation, and the three-dimensional structure inside the lens is reconstructed with high accuracy, thus predicting the continuous dielectric constant distribution.

[0022] According to the above technical solution, in S4, after the model training is completed, the three-dimensional spatial coordinates in the region are used as continuous query points and input to the trained dielectric constant prediction network. The network is a differentiable implicit field representation model, whose input is a spatial position vector and whose output is the dielectric constant value at the corresponding position.

[0023] In the actual reconstruction process, by traversing and sampling continuous coordinates within the region according to a set spatial resolution, a series of discrete coordinate-dielectric constant pairs are obtained. These data points constitute a three-dimensional point cloud representation of the dielectric constant inside the target.

[0024] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0025] 1. This invention obtains information by utilizing the interaction between electromagnetic waves and the distribution of dielectric constant inside an object. Under electromagnetic wave irradiation, changes in the dielectric constant inside a material cause the incident electromagnetic waves to produce effects such as scattering, refraction, and reflection. These effects leave information about the dielectric properties of the material in the scattered field. By measuring and acquiring the scattered field from multiple angles and frequencies, and combining it with an appropriate inversion algorithm, the three-dimensional distribution of the dielectric constant inside the material can be reconstructed. This method can not only reflect the internal structure of the material, but also directly reveal the refractive index distribution law of gradient refractive index optical elements, thereby reflecting their optical function and working mechanism.

[0026] 2. This invention constructs a mapping network from spatial points to induced current and a mapping network from induced current to dielectric constant, and jointly trains the two networks to achieve an end-to-end forward optimization process. It can reconstruct the three-dimensional structure inside the lens with high precision and predict the continuous dielectric constant distribution. Inputting continuous query points into the trained dielectric constant prediction network is a differentiable implicit field representation model. Since the network achieves implicit continuous modeling of the dielectric parameters of the entire region, it does not need to rely on regular grids or preset discrete structures. It overcomes the difficulty of directly solving the inverse matrix transformation in traditional methods and can perform high-precision prediction at any position while maintaining physical consistency.

[0027] In summary, this invention utilizes a combination of electromagnetic wave scattering measurement and implicit neural network modeling to achieve high-precision reconstruction of the internal three-dimensional structure of a Luneburg lens. This method acquires lens scattering field data through multi-angle and multi-frequency electromagnetic wave excitation and reception, and uses an implicit neural network to model the continuous dielectric constant distribution inside the lens. This allows for more free and accurate acquisition of the lens's three-dimensional structural information. Compared to traditional Luneburg lens structure analysis, this method is more convenient and accurate, and is suitable for application in optical lenses that require internal structure detection. Attached Figure Description

[0028] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0029] In the attached diagram:

[0030] Figure 1 This is a schematic diagram of the overall process of the present invention;

[0031] Figure 2 This is a schematic diagram of the overall physical structure of the Luneburg lens data acquisition device of the present invention;

[0032] Figure 3 This is a spatial arrangement diagram of the electromagnetic wave transmission and reception of the present invention;

[0033] Figure 4 This is a schematic diagram of the network structure of the present invention. Detailed Implementation

[0034] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0035] Example 1:

[0036] like Figure 1-4 As shown, the present invention provides a technical solution, a Luneburg lens reverse engineering method based on electromagnetic backscattering, comprising the following steps:

[0037] S1. Data Collection

[0038] An electromagnetic wave transmitter and a receiver are used, both of which are precisely controlled in space by a robotic arm. The robotic arm moves outside the imaging area according to a preset trajectory, enabling the transmitter to radiate a single frequency electromagnetic wave to the lens under different spatial orientations and different incident angles, thereby fully exciting the electromagnetic response at various locations inside the lens. At the same time, another set of robotic arms carrying receivers are deployed at various observation angles outside the lens and receive the scattered echo signals, thereby achieving full coverage of the lens's circumferential scattering information.

[0039] Inspired by the basic idea of ​​the traditional free-space method of "deriving the electromagnetic parameters of materials by comparing the unloaded field and the loaded field", but breaking through the limitation of the free-space method that can only handle flat materials and unidirectional transmission / reflection, the full-space scattering field measurement of three-dimensional complex structures is realized by controlling the multi-angle motion of the transmitter and receiver with a robotic arm. Therefore, it can be used for the reconstruction of the three-dimensional dielectric constant of non-uniform optical devices such as gradient refractive index lenses.

[0040] To obtain high-precision scattered field data, two measurement processes were implemented under the control of a robotic arm. First, without the lens in place, background field data was collected along the same robotic arm trajectory, as shown in Table 2. Then, the lens was placed in the area, and the robotic arm repeated the same measurement path to obtain the total field data including the lens effect, as shown in Table 1. By subtracting the total field from the background field point by point, the pure scattered field data caused by the lens was extracted. Finally, the scattered values ​​obtained by the transmitter-receiver combination under the control of all robotic arms were constructed into a scattered field measurement matrix according to the transmitter number, receiver number, and frequency index. This matrix is ​​used to fully describe the electromagnetic scattering characteristics of the lens under multiple angles and frequency bands.

[0041] Table 1 Total field data after lens placement

[0042]

[0043] Table 2 Background Field Data

[0044]

[0045] S2, Discretization processing:

[0046] While the ultimate goal is to obtain the integral accumulation in continuous space for accurate calculation of the scattered field, directly processing continuous integrals is clearly impossible. Approximate calculations can only be performed using discrete points. Therefore, during training, the scene is divided into a grid. This invention calculates the induced current at discrete points and accumulates an approximate continuous integral. Specifically, the target area... The system is divided into several small cubic grids. Several points are randomly sampled at the center of each grid. The induced current is calculated for these discrete points, and the predicted scattering field is obtained by accumulating and integrating approximately continuously.

[0047] The advantages of this division are: first, it transforms continuous problems into computable matrix or vector operations, improving the feasibility and efficiency of numerical computation;

[0048] Secondly, it facilitates visualization; grid colors and heatmaps can intuitively represent the distribution of induced current intensity.

[0049] Third, it allows for flexible allocation of sampling density, enabling more detailed sampling of regions with large amounts of information and improving integration accuracy. In short, spatial partitioning serves as a bridge to achieve numerical solutions and visualization, allowing continuous electromagnetic responses to be effectively represented and processed on a computer.

[0050] S3, Network Construction:

[0051] The three-dimensional electromagnetic scattering imaging problem is divided into two network modules, corresponding to two key aspects of the electromagnetic scattering process: the mapping from a spatial point to the induced current, and the mapping from the induced current to the dielectric constant.

[0052] 1. Mapping network from spatial point to induced current:

[0053] A first neural network is constructed to approximate the induced current at each point in space. This network takes the coordinates of any three-dimensional point in the target area and the coordinates of the transmitter as input, and through training, it fits the interaction relationship between the electromagnetic wave and the medium, outputting the induced current corresponding to that point.

[0054] During training, the induced currents of all spatial points in the entire scene are accumulated to form a complete predicted scattering field. This predicted scattering field is compared with the scattering field actually measured by the receiver, the loss function is calculated, and the network parameters are optimized through backpropagation so that it can accurately predict the induced current generated at each spatial point under different transmitter illumination. The design of this network allows it to automatically capture multiple scattering phenomena and complex responses of high-contrast media, thus maintaining good prediction capabilities even in highly complex environments.

[0055] 2. Mapping network from induced current to dielectric constant:

[0056] A second neural network is further constructed to map the induced current to the dielectric constant of the corresponding spatial point. This network takes the three-dimensional coordinates of each spatial point as input and outputs the dielectric constant of that point. Through this mapping, the dielectric distribution of any spatial point can be obtained directly, achieving high-precision three-dimensional structure prediction.

[0057] During training, the network uses the dielectric constant predicted by the network itself to calculate the predicted induced current, and uses the induced current output by the first network as a reference to calculate the loss. The network parameters are optimized through backpropagation. In this way, the second network can accurately learn the nonlinear mapping relationship between the induced current and the dielectric constant, overcoming the difficulty of directly solving the inverse matrix transformation in traditional methods. It can achieve the prediction of the dielectric constant at any location in space while maintaining physical consistency.

[0058] By jointly training the two networks mentioned above, an end-to-end forward optimization process is achieved. The first network generates the induced current distribution, and the second network maps it to the dielectric constant. The parameters of the two networks are optimized simultaneously through backpropagation. This method can reconstruct the three-dimensional structure inside the lens with high accuracy and predict the continuous dielectric constant distribution.

[0059] S4. Network Model Testing:

[0060] After the model training is completed, the three-dimensional spatial coordinates within the region are input as continuous query points into the trained dielectric constant prediction network. This network is a differentiable implicit field representation model. Its input is a spatial position vector, and its output is the dielectric constant value at the corresponding position. Since the network achieves implicit continuous modeling of the dielectric parameters of the entire region, it can make high-precision predictions for any query point without relying on regular grids or preset discrete structures. In the actual reconstruction process, by traversing and sampling the continuous coordinates within the region according to the set spatial resolution, a series of discrete coordinate-dielectric constant pairs are obtained. These data points constitute a three-dimensional point cloud representation of the dielectric constant inside the target, thereby realizing a continuous-discrete mapping from the scattered field measurement data to the distribution of the dielectric constant inside the target.

[0061] Example 2:

[0062] like Figure 1-4 As shown, a Luneburg lens reverse engineering method based on electromagnetic backscattering is used to acquire 360° omnidirectional scattering field data of a target sample. The target sample is placed as an unknown scatterer within the imaging region, which is denoted as . A three-dimensional coordinate system is established within this area and used as a reference coordinate system for the transmitter, receiver, and sample positions. To ensure accurate representation of the robot arm and sample coordinates in a unified coordinate system, the robot arm base and sample center point are calibrated. The coordinates of the sample center point in the unified coordinate system are defined as follows: The coordinates of the robotic arm base in a unified coordinate system are: , ;

[0063] Install the transmitter at the end of the first robotic arm A receiver is installed at the end of the second robotic arm. The joint angle vector is read through the robotic arm control system. and arm segment length parameters The spatial position of the end effector in the robot arm's base coordinate system is calculated using the robot arm's forward kinematics model. :

[0064]

[0065] in, This represents the positive kinematic mapping function of the robotic arm, and then the coordinates are transformed to a pre-defined coordinate system. Down:

[0066]

[0067] in, The coordinates of the two robotic arms are respectively in a unified coordinate system. , ;

[0068] In measuring the geometric information of the sample Next, calculate the minimum axis-aligned rectangle of the packaged sample. Assuming the center of the rectangle coincides with the center of the sample, then the vertex coordinates of the rectangle in a unified coordinate system are... for:

[0069]

[0070] This rectangle serves as a spatial reference for scattered field acquisition and for robotic arm positioning; the center point of the rectangle... It can serve as the rotation center for the robotic arm's motion trajectory, enabling omnidirectional data collection around the sample;

[0071] The robotic arm control system operates according to a preset rotation angle. With pitch angle Plan the spatial trajectory of the transmitter and receiver around the sample for each acquisition angle. The robotic arm controls the end effector to move to the planned position. and It also reads its spatial coordinates in a unified coordinate system in real time, and its position can be represented by the relationship between spherical coordinates and the center of the rectangular frame as follows:

[0072]

[0073]

[0074] in, and These are the radii from the transmitter and receiver to the center of the sample, respectively.

[0075] Notice, and The actual positions of the transmitter and receiver, which are planned for the motion trajectory of this invention, still need to be calculated using the kinematic model of the robotic arm.

[0076] In this embodiment, the propagation and scattering of electromagnetic waves can be divided into two stages. The first stage is the interaction stage between electromagnetic waves and scatterers. When the incident wave from the transmitter irradiates different positions inside the scatterer, an induced current will be generated inside the scatterer.

[0077] At this point, the radiation field received by the receiver can be denoted as:

[0078]

[0079] in, The spatial coordinates of the receiver;

[0080] The coordinates of the three-dimensional point in the query;

[0081] The spatial coordinates of the transmitter;

[0082] The incident electric field of the transmitter;

[0083] The total electric field;

[0084] Green's function in free space;

[0085]

[0086] in, The distance between two points For free space wavenumber;

[0087]

[0088] in, The operating frequency of electromagnetic waves, The speed at which light travels in free space;

[0089] The induced current satisfies the following relationship with the total electric field:

[0090]

[0091] in, For dielectric contrast, This represents the relative permittivity of the scattering body;

[0092] Assume the surface where the receiver is located is Scattered field It can be represented as:

[0093]

[0094] Since continuous integrals cannot be directly solved on a computer, this embodiment divides the space into... A small cubic grid, assuming its center point is... Within each grid, actual training points are generated through random sampling, and their coordinates are represented as follows:

[0095]

[0096] in, Indicates The mean, A Gaussian distribution with standard deviation, It is a hyperparameter used to control the dispersion of sampling points around the center of the grid;

[0097] This probabilistic sampling method can cover different locations within the grid, enabling the network to perceive more spatial location changes during training, thereby alleviating the problem that fixed discrete points may miss specific spatial location information.

[0098] Correspondingly, the discretized scattering field integral equation is applied in each partitioned unit. Using basis functions To expand the induced current :

[0099]

[0100] in, No. The coefficients of the basis functions (essentially the first basis function) (the magnitude of the current on each discrete unit);

[0101] Let the number of receiver locations be . , in the One receiving point Substitute the scattering field at that location. From the formula, we can obtain:

[0102]

[0103] definition

[0104]

[0105] This embodiment uses the pulse basis as the basis function, therefore the above equation can be approximated as:

[0106]

[0107] For the first One receiver location, For the first One sampling point, For the corresponding mesh volume;

[0108] The simplified scattering field express:

[0109]

[0110] in:

[0111]

[0112] Similarly, the main field It can be represented as:

[0113]

[0114] at the same time, After discretization, it can be represented in the format of vector product;

[0115]

[0116] Combining the above equations, we can obtain:

[0117]

[0118] in, It is the identity matrix. Measurements can be taken via a receiver after the object is removed in the second stage.

[0119] The ultimate goal of this embodiment is to obtain the dielectric constant distribution at a specified spatial location. Observation shows that if the incident field and the received scattered field are directly used as the input / output of a single network for fitting, the mapping implicitly involves a complex global matrix inverse transformation (equivalent to solving the inverse problem of the volume integral equation), which is difficult to train stably. Therefore, this embodiment decomposes the problem into two learnable modules, so that each module only needs to fit the "forward mapping", thereby avoiding the direct solution of the inverse transformation and improving trainability and robustness. In this embodiment, in order to approximate the distribution of induced current in continuous space, a first neural network is constructed.

[0120] Let the spatial coordinates of the transmitter be... Discrete three-dimensional spatial coordinates are Position encoding of coordinates enhances high-frequency performance:

[0121]

[0122] in, It is a hyperparameter that controls the spectral bandwidth;

[0123] The encoded vector is fed into a network for processing; the network employs a multilayer perceptron. The structure outputs the induced current at a given grid point under a specific transmitter. :

[0124]

[0125] Subsequently, using the discrete Green's function matrix The discrete induced current is projected onto the receiver location to generate the predicted scattered field. :

[0126]

[0127] in, For the first Discrete induced current corresponding to each transmitter To predict the scattering field;

[0128] The predicted scattered field is compared with the actual scattered field measured by the receiver, and a loss function is defined. for:

[0129]

[0130] in, Total number of transmitters;

[0131] This embodiment further constructs a second neural network. By establishing a correspondence between the induced current at a spatial point and its dielectric constant, a continuous representation of the spatial dielectric constant distribution is formed. Similarly, to achieve a relationship between the dielectric constant and the dielectric constant... High-resolution continuous representation of spatial distribution, with input using coordinate point location encoding:

[0132]

[0133] Dielectric constant and induced current

[0134] The following conditions must be met:

[0135]

[0136]

[0137] The induced current output by network one. Based on the predicted dielectric constant The obtained contrast ratio;

[0138] By minimizing and The difference between them is used to train a second neural network;

[0139]

[0140] and These are hyperparameters used to balance the loss function;

[0141] To further constrain the smoothness of the spatial distribution of the dielectric constant, this embodiment introduces a method in the joint loss function. The regularization term penalizes drastic spatial variations in the dielectric constant, making the reconstruction result more continuous and smooth, while avoiding excessive oscillations. Let the continuous field of the dielectric constant output by the neural network be denoted as... ;

[0142] This embodiment employs isotropic three-dimensional total variational regularization terms. :

[0143]

[0144] in, , , These represent the first-order gradients of the dielectric constant in each coordinate direction, and the final joint training objective is... :

[0145]

[0146] After the training phase, the present invention enters the dielectric constant field reconstruction phase. First, based on the imaging area... Within a spatial range, samples are taken at a preset resolution to construct a three-dimensional coordinate sampling set. Subsequently, each 3D coordinate point is sequentially input into the trained dielectric constant prediction network. The network then performs inference calculations on all sampled points, outputting a series of dielectric constant values ​​for each query coordinate. To obtain the corresponding prediction results This forms a coordinate-dielectric constant pair:

[0147]

[0148] After completing the reasoning of all spatial points, the above data set constitutes a three-dimensional point cloud of the dielectric constant inside the lens. Each data point contains its position in three-dimensional space and the magnitude of the local dielectric constant predicted by the network, thus forming a three-dimensional discrete representation of the internal structure of the lens. The dielectric constant can be mapped to color information for visualization.

[0149] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A reverse engineering method for Luneburg lenses based on electromagnetic backscattering, characterized in that: Includes the following steps: S1. Data Acquisition: Electromagnetic wave transmitters and receivers are placed outside the lens to acquire electromagnetic information from the lens through transmission and reception. S2. Discretization: The target area is divided into several grids, and the predicted scattering field is obtained by calculation and accumulation. S3. Network Construction: Construct a mapping network from spatial points to induced current, construct a mapping network from induced current to dielectric constant, and train them jointly. S4. Network Model Testing: Input the spatial location vector to the dielectric constant prediction network and output the dielectric constant value at the corresponding location. In step S1, an electromagnetic wave transmitter and a receiver are used. Both are precisely controlled by a robotic arm in terms of their spatial position and orientation. The robotic arm moves outside the imaging area according to a preset trajectory. The transmitter radiates electromagnetic waves to the lens under different spatial orientations and different incident angles. At the same time, another set of robotic arms carrying receivers are deployed at various observation angles outside the lens and receive the scattered echo signals, thereby achieving full circumferential coverage of the lens's scattering information.

2. The Luneburg lens reverse engineering method based on electromagnetic backscattering according to claim 1, characterized in that: In step S1, two measurement processes are performed under the control of a robotic arm to obtain high-precision scattered field data. The steps are as follows: First, without placing the lens, the background field is acquired following the same robotic arm trajectory; Subsequently, the lens is placed in the area, and the robotic arm repeats the same measurement path to obtain the total field containing the lens effect. By subtracting the total field from the background field point by point, the pure scattering field data caused by the lens is extracted. Finally, the scattering values ​​obtained from all the transmitter-receiver combinations under the control of the robotic arms are constructed into a scattering field measurement matrix according to the transmitter number, receiver number and frequency index, which describes the electromagnetic scattering characteristics of the lens under multiple angles and multiple frequency bands.

3. The Luneburg lens reverse engineering method based on electromagnetic backscattering according to claim 1, characterized in that: In S2, during training, the scene is divided into grids, the induced current is calculated at discrete points and the approximate continuous integral is accumulated. Specifically, the target region ROI is divided into several small cubic grids, several points are randomly sampled at the center of each grid, the induced current is calculated at these discrete points, and the predicted scattering field is obtained by accumulating the approximate continuous integral.

4. The Luneburg lens reverse engineering method based on electromagnetic backscattering according to claim 1, characterized in that: In S3, a mapping network from spatial points to induced currents is constructed, namely the first network, which approximates the induced current at each point in space. This network takes the coordinates of any three-dimensional spatial point in the target area and the coordinates of the transmitter as input, and through training, fits the interaction relationship between electromagnetic waves and the medium to output the induced current corresponding to that point. During training, the induced currents of all spatial points in the entire scene are summed to form a complete predicted scattering field. This predicted scattering field is compared with the scattering field actually measured by the receiver, the loss function is calculated, and the network parameters are optimized through backpropagation so that it can accurately predict the induced current generated at each spatial point under different emitter illumination. The design of this network allows it to automatically capture multiple scattering phenomena and the complex response of high-contrast media.

5. The Luneburg lens reverse engineering method based on electromagnetic backscattering according to claim 4, characterized in that: In S3, a mapping network from induced current to dielectric constant is constructed, namely the second network, which maps the induced current to the dielectric constant of the corresponding spatial point. This network takes the three-dimensional coordinates of each spatial point as input and outputs the dielectric constant of that point, thus directly obtaining the dielectric distribution of any spatial point. During training, the network uses the dielectric constant predicted by the network itself to calculate the predicted induced current, and uses the induced current output by the first network as a reference to calculate the loss. The network parameters are optimized through backpropagation. The second network learns the nonlinear mapping relationship between the induced current and the dielectric constant to predict the dielectric constant at any location in space. By jointly training the first and second networks, the first network generates the induced current distribution, and the second network maps it to the dielectric constant. The parameters of the two networks are optimized simultaneously through backpropagation, and the three-dimensional structure inside the lens is reconstructed with high accuracy, thus predicting the continuous dielectric constant distribution.

6. The Luneburg lens reverse engineering method based on electromagnetic backscattering according to claim 5, characterized in that: In S4, after the model training is completed, the three-dimensional spatial coordinates in the region are input as continuous query points to the trained dielectric constant prediction network. The network is a differentiable implicit field representation model, whose input is a spatial position vector and whose output is the dielectric constant value at the corresponding position. In the actual reconstruction process, by traversing and sampling continuous coordinates within the region according to a set spatial resolution, a series of discrete coordinate-dielectric constant pairs are obtained. These data points constitute a three-dimensional point cloud representation of the dielectric constant inside the target.

Images