A two-plane non-phase near-field antenna measurement method with a coordinate prior physical-driven untrained network

Abstract

This invention discloses a dual-plane phase-free near-field antenna measurement method driven by a coordinate prior physics-based untrained network. Addressing the issues of traditional iterative phase retrieval methods easily getting trapped in local optima and supervised learning relying on training data, this method employs dual-plane amplitude-only measurement. The coordinate prior, consisting of the lateral, longitudinal, and radial coordinates of the first measurement plane, is combined with the initial phase and input into an untrained convolutional neural network to predict the phase of the first measurement plane. The measured amplitude and predicted phase of the first measurement plane are then synthesized into a complex electric field, which is propagated to the second measurement plane via a discretized electromagnetic propagation operator. The error between the predicted and measured amplitudes of the second measurement plane is used as a self-supervised loss to iteratively optimize the network parameters, ultimately recovering the phase of the first measurement plane. This method achieves stable phase retrieval using only dual-plane near-field amplitude measurements, possessing both physical interpretability and good generalization ability, making it suitable for near-field measurement scenarios using phase-free antennas.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic measurement and computational imaging technology, and particularly relates to a method for measuring a dual-plane phaseless near-field antenna using a coordinate prior physics-driven untrained network. Background Technology

[0002] In the field of high-frequency electromagnetic testing and diagnostics, such as antenna radiation characteristic assessment, electromagnetic interference source localization, and aperture field reconstruction, near-field measurement technology is widely used due to its advantages such as controllable testing environment, low space requirements, and support for near-field and far-field transformation. However, in actual near-field testing, it is often very difficult to directly obtain near-field phase information with high accuracy due to factors such as probe positioning error, system thermal drift, cable bending, and environmental reflection.

[0003] To address the aforementioned issues, methods for phase retrieval utilizing only near-field amplitude information have attracted widespread attention. Traditional phase retrieval algorithms, such as the Gerchberg-Saxton algorithm, the Fienup algorithm, and the Wirtinger Flow algorithm, typically recover the phase by iteratively applying amplitude constraints across multiple planes. However, the recovery performance of such methods is sensitive to initial values, easily gets trapped in local optima, and lacks stability under complex field distributions or noisy conditions.

[0004] In recent years, supervised learning-based deep learning methods have been introduced to construct end-to-end mappings from amplitude distributions to phase distributions. However, these methods typically rely on large-scale, task-specific training datasets, resulting in high data preparation costs. More importantly, the model's generalization ability often declines significantly when the type of object being tested, the frequency of operation, or the measurement configuration changes.

[0005] As an emerging paradigm, untrained neural networks, leveraging the structural biases of convolutional networks, can perform single-sample inversion without requiring pre-training datasets, providing a new technical path for phase recovery using only amplitude information. However, existing methods have not yet provided an effective technical solution that can organically combine the physical constraints of electromagnetic propagation with prior information on spatial coordinates to achieve stable self-supervised optimization for phase recovery tasks. This limits their application in practical engineering scenarios, especially in antenna measurement and electromagnetic interference diagnosis. Summary of the Invention

[0006] The purpose of this invention is to provide a method for measuring dual-plane phase-free near-field antennas with coordinate prior physics-driven untrained networks, in order to solve the problems of existing phase recovery methods relying on pre-trained data, being sensitive to initialization, and being prone to getting trapped in local optima.

[0007] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows: A method for measuring a dual-plane phase-free near-field antenna using a coordinate-prior physics-driven untrained network includes the following steps: S1, Obtain near-field amplitude information of the antenna under test on the first and second measurement surfaces; S2, obtain the spatial coordinate information of the first measurement surface, and construct a coordinate prior based on the spatial coordinate information; wherein, the coordinate prior includes the transverse coordinate matrix, the longitudinal coordinate matrix of the sampling grid, and the radial distance matrix constructed from the transverse coordinate matrix and the longitudinal coordinate matrix; S3, the coordinate prior and the initial phase are combined and then input into an untrained convolutional neural network, which predicts the phase distribution of the first measurement surface. S4, combine the measured near-field amplitude of the first measurement surface with the predicted phase to construct the predicted complex electric field of the first measurement surface; S5. Using the electromagnetic propagation operator obtained by discretization of the two-plane electromagnetic propagation model, the predicted complex electric field of the first measurement surface is propagated to the second measurement surface to obtain the predicted complex electric field of the second measurement surface. S6. Based on the error between the predicted complex electric field amplitude of the second measurement surface and the measured near-field amplitude of the second measurement surface, construct a self-supervised loss function; S7. Based on the self-supervised loss function, the parameters of the convolutional neural network are iteratively updated through backpropagation until a preset stopping condition is met, thereby obtaining the recovered phase of the first measurement surface.

[0008] Preferably, coordinate priors are used to explicitly introduce spatial location information into the convolutional neural network to enhance the network's ability to express the spatial structure, fringe features, and radial attenuation characteristics of the near-field distribution, thereby reducing the phase recovery solution space and improving the stability of the optimization process.

[0009] Preferably, the electromagnetic propagation operator is used to describe the electromagnetic field propagation relationship between the first measurement surface and the second measurement surface, so that the predicted complex electric field of the first measurement surface can be mapped to the second measurement surface under physical propagation constraints, thereby giving the entire phase recovery process clear physical constraints and interpretability.

[0010] Preferably, the convolutional neural network performs feature mapping on the coordinate prior through multiple convolutional layers, the hidden layer uses a smooth non-monotonic activation function, and the output layer uses a linear convolutional layer to generate the predicted phase of the first measurement surface.

[0011] Preferably, the smooth non-monotonic activation function is the SiLU function.

[0012] Preferably, the self-supervised loss function is the mean squared error loss function.

[0013] Preferably, the method uses an untrained convolutional neural network for single-sample self-supervised optimization, which does not require pre-constructing a large-scale training dataset for different antenna types, operating frequencies or sampling configurations, and has good generalization ability.

[0014] Preferably, the recovered phase and the measured near-field amplitude of the first measurement surface together constitute the recovered near-field complex electric field, which is used for antenna near-field and far-field transformation, radiation pattern calculation, phase center estimation, or array fault detection.

[0015] The present invention also discloses a coordinate prior physics-driven dual-plane phaseless near-field antenna measurement system for implementing a coordinate prior physics-driven dual-plane phaseless near-field antenna measurement method, comprising one or more processors; and a memory storing computer-readable instructions, which, when executed by one or more processors, cause the system to perform a phase recovery method.

[0016] The present invention also discloses a computer-readable storage medium storing computer-readable instructions, which, when executed by one or more processors, cause the processors to perform a method for measuring a dual-plane phase-free near-field antennas using a coordinate prior physics-driven untrained network. The present invention provides a method for measuring dual-plane phaseless near-field antennas using a coordinate prior physics-driven untrained network, which has the following advantages: 1. By using untrained neural networks and self-supervised learning mechanisms, the dependence on large-scale pre-trained datasets is completely eliminated, significantly reducing data preparation costs; 2. By combining coordinate priors containing spatial coordinate information with an untrained network, the stability and physical plausibility of the phase retrieval results are effectively improved. 3. By constructing strong physical constraints through electromagnetic propagation operators, the entire optimization process has clear physical interpretability; 4. The method has good generalization ability, and stable recovery can be achieved with only dual-plane amplitude information. It can be easily applied to various practical engineering scenarios such as antenna near-field measurement, electromagnetic interference source diagnosis and near-far field transformation. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the physical propagation model for the dual-plane phase recovery of this invention; Figure 2 This is a schematic diagram of the PD-UNN network structure and closed-loop optimization process of the present invention; Figure 3 (a) in the figure is a comparison of the iterative convergence curve in Example 1 with other methods; Figure 3 (b) in the figure is the antenna model used in Example 1; Figure 4 (a) in the figure represents the actual amplitude in Example 1; Figure 4 (b) in the figure represents the magnitude of the reduction in Example 1; Figure 4 (c) in the figure represents the actual phase in Example 1; Figure 4 In this context, (d) represents the phase restored in Example 1; Figure 4 (e) in the figure represents the true and restored far-field radiation pattern of surface E in Example 1; Figure 4 (f) in the figure represents the true and restored far-field radiation pattern of the H plane in Example 1; Figure 5 (a) in the figure represents the 8×8 single-polarization patch array structure in Embodiment 2 of the present invention; Figure 5 (b) in the figure is a schematic diagram of the dual-plane sampling configuration in Embodiment 2 of the present invention; Figure 6 This refers to the training loss in the 8×8 single-polarization patch array example of Embodiment 2 of the present invention; Figure 7 (a) in the figure is the actual amplitude result of the second measurement surface in Embodiment 2 of the present invention; Figure 7 (b) in the figure is the amplitude restoration result of the second measurement surface in Embodiment 2 of the present invention; Figure 8 (a) in the figure is the true phase result diagram of the first measurement surface in Embodiment 2 of the present invention; Figure 8 (b) in the figure is the phase restoration result diagram of the first measurement surface in Embodiment 2 of the present invention; Figure 9 (a) is the far-field reconstruction result of the E-plane in Embodiment 2 of the present invention.

[0018] Figure 9 (b) is the far-field reconstruction result of the H-plane in Embodiment 2 of the present invention. Detailed Implementation

[0019] To better understand the purpose, structure, and function of this invention, the following description, in conjunction with the accompanying drawings, provides a more detailed account of a coordinate-priority physics-driven dual-plane phaseless near-field antenna measurement method for an untrained network.

[0020] A method for measuring a dual-plane phase-free near-field antenna using a coordinate-prior physics-driven untrained network includes the following steps: S1, Obtain near-field amplitude information of the antenna under test on the first and second measurement surfaces; S2, obtain the spatial coordinate information of the first measurement surface, and construct a coordinate prior based on the spatial coordinate information; wherein, the coordinate prior includes the transverse coordinate matrix, the longitudinal coordinate matrix of the sampling grid, and the radial distance matrix constructed from the transverse coordinate matrix and the longitudinal coordinate matrix; S3, the coordinate prior and the initial phase are combined and then input into an untrained convolutional neural network, which predicts the phase distribution of the first measurement surface. S4, combine the measured near-field amplitude of the first measurement surface with the predicted phase to construct the predicted complex electric field of the first measurement surface; S5. Using the electromagnetic propagation operator obtained by discretization of the two-plane electromagnetic propagation model, the predicted complex electric field of the first measurement surface is propagated to the second measurement surface to obtain the predicted complex electric field of the second measurement surface. S6. Based on the error between the predicted complex electric field amplitude of the second measurement surface and the measured near-field amplitude of the second measurement surface, construct a self-supervised loss function; S7. Based on the self-supervised loss function, the parameters of the convolutional neural network are iteratively updated through backpropagation until a preset stopping condition is met, thereby obtaining the recovered phase of the first measurement surface.

[0021] Coordinate priors are used to explicitly introduce spatial location information into convolutional neural networks to enhance the network's ability to express the spatial structure, fringe features, and radial attenuation characteristics of near-field distributions, thereby reducing the phase recovery solution space and improving the stability of the optimization process.

[0022] Electromagnetic propagation operators are used to describe the electromagnetic field propagation relationship between the first and second measurement surfaces, enabling the predicted complex electric field of the first measurement surface to be mapped to the second measurement surface under physical propagation constraints, thereby giving the entire phase recovery process clear physical constraints and interpretability.

[0023] Convolutional neural networks perform feature mapping on coordinate priors through multiple convolutional layers, use smooth non-monotonic activation functions in the hidden layers, and use linear convolutional layers in the output layer to generate the predicted phase of the first measurement surface.

[0024] The smooth, non-monotonic activation function is the SiLU function.

[0025] The self-supervised loss function is the mean squared error loss function.

[0026] The method uses an untrained convolutional neural network for single-sample self-supervised optimization, which does not require pre-constructing a large-scale training dataset for different antenna types, operating frequencies or sampling configurations, and has good generalization ability.

[0027] The recovered phase and the measured near-field amplitude of the first measurement surface together constitute the recovered near-field complex electric field, which is used for antenna near-field and far-field transformation, radiation pattern calculation, phase center estimation, or array fault detection.

[0028] The present invention also discloses a coordinate prior physics-driven dual-plane phaseless near-field antenna measurement system for implementing a coordinate prior physics-driven dual-plane phaseless near-field antenna measurement method, comprising one or more processors; and a memory storing computer-readable instructions, which, when executed by one or more processors, cause the system to perform a phase recovery method.

[0029] The present invention also discloses a computer-readable storage medium storing computer-readable instructions thereon, which, when executed by one or more processors, cause the processors to perform a method for measuring a dual-plane phaseless near-field antenna using a coordinate prior physics-driven untrained network. Example

[0030] This embodiment uses a horn antenna as the object under test to describe in detail the dual-plane near-field phase recovery process of the present invention. In a preferred embodiment, the antenna under test is a standard gain horn antenna with an operating frequency of 15 GHz, such as... Figure 3 (b) in the middle.

[0031] Figure 1 This is a schematic diagram of the physical propagation model for dual-plane phase retrieval. Two parallel measurement surfaces, denoted as the first measurement surface S1 and the second measurement surface S2, are positioned in front of the horn antenna aperture along the propagation direction. The two measurement surfaces are located at distances of 3λ and 5λ from the horn antenna aperture, respectively, where λ is the free-space wavelength corresponding to the operating frequency. Therefore, the interval between the two measurement surfaces is 2λ.

[0032] In this embodiment, both the first measurement surface S1 and the second measurement surface S2 are scanned in the near field using a regular two-dimensional sampling grid. Each measurement surface contains 151×151 sampling points, and the sampling step size in both the x and y directions is 7.5 mm. The near-field electric field amplitude distributions on the two measurement surfaces are obtained through simulation or actual measurement, denoted as A1 and A2, respectively. It is important to emphasize that the input of this method is only the amplitude information on the two measurement surfaces, and does not depend on any phase measurement values.

[0033] Based on the two-dimensional sampling grid of the first measurement surface S1, a horizontal coordinate matrix X, a vertical coordinate matrix Y, and a radial distance matrix R are constructed, where The coordinate matrices X and Y represent the spatial positions of the sampling points in two orthogonal directions, respectively, while the radial distance matrix R represents the radial distribution characteristics of each sampling point relative to the coordinate center. Further, X, Y, and R are compared with the initial phase... Combine to form input tensor It is then fed into an untrained convolutional neural network to output the predicted phase distribution on the first measurement surface S1. .

[0034] In this embodiment, as Figure 2 As shown, the untrained convolutional neural network preferably uses a multi-layer convolutional network structure. Its hidden layers employ the SiLU activation function to enhance gradient propagation capability and optimization stability; the output layer uses a linear convolutional layer to generate a single-channel phase map. This network does not rely on any offline training dataset, and its parameters are optimized online in a self-supervised manner entirely based on the dual-plane near-field amplitude data of the current horn antenna samples.

[0035] Obtain the predicted phase Then, the measured amplitude A1 on the first measurement surface S1 is compared with the predicted phase. By combining the results, the complex electric field on the first measurement surface is obtained: .

[0036] Subsequently, using the electromagnetic propagation operator H obtained by discretization of the two-plane near-field propagation model, the complex electric field E1 is propagated from the first measurement surface S1 to the second measurement surface S2, and the predicted complex electric field on the second measurement surface is obtained: .

[0037] Based on this, the predicted amplitude |E2| on the second measurement surface is calculated and compared with the measured amplitude A2 on the second measurement surface S2 to construct a loss function L. The loss function is preferably the mean square error loss function, i.e.: .

[0038] Then, the backpropagation algorithm is used to calculate the gradient of the network parameters, and the adaptive moment estimation optimization algorithm is used to update the parameters of the untrained convolutional neural network. To suppress abnormal gradients that may occur during the optimization process and improve convergence stability, a gradient clipping threshold can be set to constrain the gradient.

[0039] The iterative process of "phase prediction—complex field construction—physical propagation—amplitude error calculation—network parameter update" is repeated until the maximum number of iterations is reached or the loss function is lower than a preset threshold. After the iteration is completed, the phase distribution on the first measurement surface S1 is output. By combining the recovered phase with the measured amplitude A1 on the first measurement surface, the near-field complex electric field distribution of the horn antenna on the first measurement surface can be reconstructed.

[0040] Based on the recovered near-field complex electric field, the far-field radiation pattern of the horn antenna under test can be calculated by the angular spectrum method or other near-far-field transformation methods, thereby enabling the evaluation of the radiation characteristics of the horn antenna.

[0041] Depend on Figure 3It can be seen that the method of the present invention has good convergence in the simulation examples, and the recovered phase is highly consistent with the true phase, indicating that it can effectively realize near-field phase recovery under the condition of measuring only the amplitude of two planes.

[0042] Depend on Figure 4 As can be seen, the amplitude, phase and far-field radiation pattern recovered by the method of the present invention in the measured data are in good agreement with the reference results, which verifies the effectiveness of the present invention in actual measurement scenarios.

[0043] Example 2: Extension and Application under Different Antenna Types and Operating Frequencies. To verify the generalization ability of the method of this invention, an 8×8 single-polarized patch array was simulated as another type of antenna under test. The antenna structure and dual-plane simulation configuration in Example 2 are as follows: Figure 5 As shown. The array aperture and sampling configuration can be adjusted according to the operating frequency. Dual-plane near-field amplitude data are extracted at 15 GHz, and phase recovery is completed using the same processing procedure as in Example 1.

[0044] For this array case Figure 6 The results show that the method of the present invention can maintain stable loss convergence characteristics under different antenna types. Figure 7 The results show that the method of the present invention can reconstruct the amplitude distribution of the second measurement surface relatively well. Figure 8 and Figure 9 The results show that the method of the present invention can better restore the phase distribution of the first measurement surface and the far-field radiation pattern derived therefrom, indicating that the method of the present invention has good engineering applicability and transferability.

[0045] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A method for measuring a dual-plane phase-free near-field antenna using a coordinate prior physics-driven untrained network, characterized in that, Includes the following steps: Obtain amplitude information of the target object at at least one observation location; Obtain prior information about the spatial coordinates corresponding to the observation location; The coordinate prior information and the initial phase are combined and input into an untrained neural network to obtain the predicted phase at the observation location; The amplitude information is combined with the predicted phase to construct a complex field; Based on the physical propagation characteristics of the target object, the complex field is transformed using a propagation operator to obtain a predicted complex field in another state; A self-supervised loss function is constructed based on the error between the predicted magnitude of the complex field and the actual magnitude information obtained from another state. The parameters of the untrained neural network are iteratively updated based on the self-supervised loss function until a preset condition is met to obtain the recovered phase.

2. The method for measuring a dual-plane phase-free near-field antenna with a coordinate prior physics-driven untrained network according to claim 1, characterized in that, The target object is an electromagnetic interference source, and the amplitude information is the near-field amplitude. The near-field complex field recovered by the antenna measurement method is used for electromagnetic interference detection and location.

3. The method for measuring a dual-plane phase-free near-field antenna with a coordinate prior physics-driven untrained network according to claim 1, characterized in that, The target object is an antenna, the amplitude information is near-field amplitude, and at least one observation position includes a first measurement surface and a second measurement surface within the near-field region.

4. The method for measuring a dual-plane phase-free near-field antenna with a coordinate prior physics-driven untrained network according to claim 1, characterized in that, The physical propagation characteristics include the diffraction propagation of the electromagnetic field between two planes, and the propagation operator is the electromagnetic diffraction matrix obtained by discretizing the two-plane propagation model.

5. The method for measuring a dual-plane phase-free near-field antenna with coordinate prior physics-driven untrained network according to claim 1, characterized in that, The prior information of spatial coordinates includes the horizontal coordinate matrix, the vertical coordinate matrix, and the radial distance matrix constructed from the horizontal and vertical coordinate matrices of the sampling grid.

6. The method for measuring a dual-plane phase-free near-field antenna with a coordinate prior physics-driven untrained network according to claim 1, characterized in that, The neural network is a convolutional neural network, which performs feature mapping on coordinate prior information through multiple convolutional layers, uses a smooth non-monotonic activation function in the hidden layer, and uses a linear convolutional layer in the output layer to generate the predicted phase.

7. The method for measuring a dual-plane phase-free near-field antenna with coordinate prior physics-driven untrained network according to claim 6, characterized in that, The smooth, non-monotonic activation function is the SiLU function.

8. The method for measuring a dual-plane phase-free near-field antenna using a coordinate prior physics-driven untrained network according to claim 1, characterized in that, The self-supervised loss function is the mean squared error loss function.

9. A coordinate-prior physics-driven dual-plane phase-free near-field antenna measurement system for an untrained network, used to implement the coordinate-prior physics-driven dual-plane phase-free near-field antenna measurement method according to any one of claims 1-8, characterized in that, Includes one or more processors; And a memory containing computer-readable instructions that, when executed by one or more processors, cause the system to perform a coordinate prior physics-driven biplane phaseless near-field antenna measurement method for an untrained network.

10. A computer-readable storage medium, characterized in that, It stores computer-readable instructions that, when executed by one or more processors, cause the processors to perform the dual-plane phaseless near-field antenna measurement method for a coordinate prior physics-driven untrained network as described in any one of claims 1 to 8.

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