A vortex electromagnetic wave target high-frequency scattering correction algorithm based on equivalent edge electromagnetic current

Abstract

The present application relates to a kind of vortex electromagnetic wave target high-frequency scattering calculation method based on equivalent edge electromagnetic current correction, belong to electromagnetic calculation field.Method includes: constructing target triangulation model and extracting convex split edge;Bessel vortex wave is decomposed into plane subwave superposition;The main scattering field under the irradiation of subwave is calculated using physical optics PO;Based on physical diffraction theory, the diffraction field of subwave in convex split edge is calculated using PTDEEC model of equivalent edge electromagnetic current;The main scattering field and edge diffraction field are superposed to obtain the modified total field, and the radar cross section (RCS) is calculated.The present application effectively corrects the diffraction error of traditional PO method at the edge of target by equivalent edge electromagnetic current, significantly improves the scattering calculation precision of large-size edge target under complex vortex beam irradiation, and provides more reliable high-frequency algorithm for radar target recognition and stealth design.

Description

Technical Field

[0001] This invention relates to a method for calculating the scattering characteristics of electrically large targets irradiated by Bessel vortex electromagnetic waves, specifically to a scattering field algorithm for high-frequency PO approximation of vortex beams corrected by equivalent edge electromagnetic current. Background Technology

[0002] Electromagnetic scattering characteristic calculations have significant application value in radar target identification, stealth technology design, and remote sensing. For electromagnetic scattering calculations of electrically large targets, traditional methods typically employ high-frequency approximations such as Physical Optics (PO) and Geometric Optics (GO). These methods significantly reduce computational complexity by simplifying the propagation and scattering processes of electromagnetic waves, making them suitable for rapid calculations of electrically large targets. However, the traditional PO method neglects the diffraction effect at the target edges during the calculation, leading to significant errors in the calculation results in the edge regions, especially under complex beam illumination.

[0003] In recent years, Bessel beams have attracted widespread attention in electromagnetic scattering research due to their unique non-diffraction and self-restoring properties. Bessel beams can maintain their shape during propagation and possess strong penetrating power through obstructions, thus offering potential advantages in analyzing the scattering characteristics of electrically large targets. While angular spectral expansion combined with the high-frequency PO approximation can effectively obtain the vortex scattering field of electrically large targets, it fails to fully reveal the scattering performance of complex targets with edges and diffraction effects.

[0004] Existing methods still suffer from insufficient accuracy when calculating high-frequency scattering of vortex targets.

[0005] Traditional PO methods only consider specular reflection from the target surface, neglecting edge diffraction effects. This leads to significant errors in the calculation results in edge regions, especially under complex beam illumination conditions such as large divergence angles of electromagnetic vortex beams or high topological charges, where the errors are further amplified. Furthermore, existing high-frequency approximation methods (such as GO and UTD) have limited ability to handle complex beams and struggle to accurately describe the interaction between Bessel beams and targets, particularly at target edges and in regions with significant curvature changes, where the calculation results often deviate from reality. Summary of the Invention

[0006] The purpose of this invention is to provide an equivalent edge electromagnetic current scattering correction method for electrically large targets under Bessel vortex beam illumination, in order to solve the problem that the traditional physical optics PO method neglects the edge diffraction effect and has insufficient calculation accuracy when calculating the scattering characteristics of electrically large targets under complex beam illumination.

[0007] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0008] A method for calculating the electromagnetic scattering characteristics of electrically large targets under Bessel beam illumination includes the following steps:

[0009] S1. Construct a geometric model of an electrically large target, use FEKO software to generate a three-dimensional model of the target and triangulate the target surface to discretize it into a series of triangular patches.

[0010] S2, extract the geometric edge information of the target from the triangulated model; identify the geometric edges of the target by traversing the common edges of the triangular facets, and extract the convex edges;

[0011] S3. Based on the theoretical model of the Bessel beam, establish a mathematical representation model for its angular spectrum expansion, set the parameters of the Bessel beam, including wavelength, topological charge number, half-cone angle, etc., and use plane wave angular spectrum expansion to expand the Bessel beam into a series of plane wave superpositions.

[0012] S4. The current distribution on the target surface under the decomposed Bessel beam illumination and the resulting main scattering field are calculated using the physical optics method. Based on the PO theory, the current distribution on the target surface is calculated, and the integral calculation is performed for each triangular facet. The sub-wavelength scattering solution is superimposed to output the main scattering field calculated by the PO method.

[0013] S5. In order to correct the edge diffraction effect ignored by the traditional PO method, the equivalent edge electromagnetic current (EEC) is introduced to calculate the contribution of the target edge to the diffraction field of the decomposed plane wave. The piecewise integral of all the decomposed plane waves over each edge is superimposed to obtain its diffraction field. The diffraction coefficient is calculated by the PTDEEC model to correct the field error of the traditional PO in the edge region.

[0014] S6. The main scattering field calculated by the PO method is superimposed with the edge diffraction field calculated by the EEC method to obtain the corrected total scattering field. The radar cross section (RCS) of the target is calculated, and the final electromagnetic scattering characteristic calculation results are output.

[0015] Compared with the prior art, the present invention has the following advantages:

[0016] This invention effectively corrects the edge diffraction effect neglected by the traditional PO method by introducing EEC, and significantly improves the calculation accuracy of high-frequency electromagnetic scattering characteristics of electrically large targets under Bessel vortex beam illumination. In particular, it can better handle the scattering problem of complex vortex electromagnetic waves such as Bessel beams at the target edge and in areas with large curvature changes. It also significantly improves the RCS calculation accuracy of edge targets, and is especially suitable for high topological charge vortex beams. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the overall process for calculating the electromagnetic scattering characteristics of electrically large targets under Bessel beam illumination according to the present invention.

[0018] Figure 2 This is a triangular mesh diagram of the target model.

[0019] Figure 3 It is a schematic diagram of the concave and convex parts of a geometric shape.

[0020] Figure 4 This is the result of edge extraction.

[0021] Figure 5 This is a schematic diagram of scattering by the scatterer at the observation point.

[0022] Figure 6 This is a schematic diagram of the diffraction angle at the edge of the wedge.

[0023] Figure 7 This is a diagram showing the scattering results of the Bessel beam in a single-station scenario. Detailed Implementation

[0024] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0025] S1. Construct a geometric model of the electrically large target, use FEKO software to generate a three-dimensional model of the target and triangulate the target surface, discretizing it into a series of triangular patches.

[0026] In this embodiment, the electrically large geometric model is a cylinder with a height of 0.36m and a diameter of 0.24m. The incident electromagnetic wave frequency is 10GHz. FEKO is used to model the electrically large object, and the surface of the model is meshed using triangular elements. The triangular mesh data is then exported, as shown below. Figure 2 As shown.

[0027] S2 extracts the geometric edge information of the target from the triangulated model. By traversing the common edges of the triangular facets, the geometric edges of the target are identified, and the convex edges are extracted.

[0028] In this embodiment, the obtained triangular facet mesh data is imported into MATLAB for processing, the coordinate information of each facet is extracted, and the normal vector of each facet is calculated. Then, the edges of the model need to be identified, convex edges are extracted, and unwanted concave edges are removed.

[0029] Edges are divided into concave edges and convex edges; only convex edges are needed in EEC applications. For example... Figure 3 As shown in (a) and (c), the cases of concave and convex edges are respectively shown. In order to distinguish between convex and concave edges, it is necessary to first traverse all triangular elements and find adjacent triangular elements (1) and (2). Use the normal vectors of (1) and (2) to find the included angle. If the included angle ψ=0°, it is a plane. If ψ≠0°, it is an edge. In reality, ψ is less than a small quantity and can be regarded as a plane.

[0030] After obtaining the edge, it is necessary to remove a portion of the concave edges that are useless for subsequent calculations. After obtaining the adjacent triangular facet pairs (1) and (2) on the edge, as follows: Figure 3 As shown in (b) and (d), their unit normal vectors are used to calculate their sum vector n. Then, the midpoint A of the edges contained in the facet pair is moved a small distance d along the direction of the sum vector n to obtain a new coordinate point B, where d can be represented by 1 / 10 of the smallest side length of the triangular facet. Point B is connected to the opposite vertex of the triangular facet pair to obtain the included angle θ. Next, point B is moved a distance d along the direction of the sum vector n to obtain a new coordinate point C. Point C is connected to the opposite vertex of the triangular facet pair to obtain a new included angle θ1. At this point, it can be determined that when θ1 < θ, θ tends to decrease, indicating that the edge is a convex part and should be retained; when θ1 > θ, θ tends to increase, indicating that the edge is a concave part and should be ignored. Figure 4 The edge extraction results of the model used in this embodiment are shown in the figure.

[0031] S3. Based on the theoretical model of the Bessel beam, establish its mathematical representation model, set the parameters of the Bessel beam, including wavelength, topological charge, half-cone angle, etc., and use plane wave angular spectrum expansion to expand the Bessel beam into a series of plane wave superpositions.

[0032] A Bessel beam is a special type of light beam that has no diffraction characteristics, meaning that its lateral distribution remains unchanged during propagation. l The electric field distribution of a Bessel beam is described using cylindrical coordinates.

[0033]

[0034] in J l (·) represents the Bessel function of the first kind. l For topological charge, k ri = k sin α 0, k zi = k cos α 0, , φ i = arctan (y i / x i ) , φ i It is the azimuth angle. α 0 represents a semi-cone angle.

[0035] Based on vector angular spectrum decomposition, the incident electric field can be expressed as:

[0036] In the formula For scalar amplitude, this implementation case adopts... x Linearly polarized incident Bessel vortex beam.

[0037] S4 uses physical optics to calculate the current distribution on the target surface under Bessel beam illumination and the resulting principal scattered field. Based on the Poisson-Pierre (PO) theory, the current distribution on the target surface is calculated, and integration is performed on each triangular facet to output the principal scattered field calculated using the PO method.

[0038] like Figure 5 As shown, For any plane wavelet of Bessel wave decomposition p The incident vector, The field point unit vector, r Let ′ be the coordinate vector of the infinitesimal element ds, and R be the distance from ds to the field point P. The far-field scattering field in physical optics can be described as follows:

[0039]

[0040] In the formula, Let E be the unit outward normal vector at point r′. T =E i + E s and H T =H i + H s Decompose plane waves at any surface element. p The total electric field and the total magnetic field.

[0041] Thus, the scattering field of any plane wavelet from the Bessel beam decomposition has been obtained. The scattering effect of the entire Bessel beam on the target can be expressed by integrating the scattering results of all plane wavelets as follows:

[0042]

[0043] in

[0044]

[0045] S5. To correct the edge diffraction effect neglected by traditional PO, EEC is introduced to calculate the diffraction field contribution of the target edge. Piecewise integration is performed on each edge and the results are superimposed to obtain its diffraction field.

[0046] For any plane wavelet p The formula for calculating the scattered field of a target illuminated by a Bessel beam using EEC is:

[0047]

[0048] in

[0049]

[0050] in , and For PTDEEC, the diffraction coefficient is... k It is the wave number of the incident wave. The direction of the scattered wave; Tangent to the split edge; The characteristic impedance in free space, The position vector of a fixed point on the cleft edge; The position of the observation point. .

[0051] Therefore, it is necessary to obtain the diffraction coefficient of the target edge, and the diffraction coefficient depends only on the diffraction angle. According to the geometric diffraction theory, the incident direction and the scattering direction each have two angles with the target edge, denoted as . β i , β s , φ 'and φ ,like Figure 6 As shown in the figure. β i It is the angle between the incident wave and the positive direction of the edge tangent. β s It is the angle between the scattered wave and the positive tangential direction of the edge, which can be expressed as... , Calculate the diffraction angle. φ 'and φ It can be written as

[0052]

[0053] therefore Similarly, we can obtain .

[0054] The expression for the diffraction coefficient is:

[0055]

[0056]

[0057] in

[0058]

[0059] The above formula contains an intermediate variable, defined as follows: μ =cos α It can be obtained using the following expression.

[0060]

[0061] in

[0062]

[0063]

[0064] At this point, the diffraction field of any plane wavelet decomposed by EEC has been obtained. The diffraction field of the entire Bessel beam at the target can be expressed by integrating the scattering results of all plane wavelets, as follows:

[0065]

[0066] S6. The main scattering field calculated by the PO method is superimposed with the edge diffraction field calculated by the EEC method to obtain the corrected total scattering field. The RCS of the target is calculated, and the final electromagnetic scattering characteristic calculation results are output.

[0067] The obtained PO field and EEC field are then vector-superimposed:

[0068]

[0069] According to the definition of radar cross section, the RCS of the scattered field can be obtained by the following formula:

[0070]

[0071] like Figure 7 The figure shows the normalized RCS results of a typical edge-shaped target model using a Bessel beam in a single-station scenario according to an embodiment of this application. The results show that the traditional PO and modified algorithms are highly compatible in the specular reflection region of a planar structure. However, edge diffraction of the target at the edge also contributes to the total scattering RCS of vortex electromagnetic wave targets. This invention improves the accuracy of the scattering solution of vortex electromagnetic waves such as Bessel beams on typical edge-shaped targets to a certain extent, providing solid theoretical support for orbital angular momentum radar target detection and identification technology based on vortex electromagnetic waves.

[0072] Although the present invention has been described in detail through preferred embodiments, the above description is merely an example of specific implementation and does not constitute a limitation on the scope of protection of the present invention. For those skilled in the art, any obvious modifications or substitutions within the scope of the technology disclosed in this application fall within the scope of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A method for calculating high-frequency scattering of a target of a vortex electromagnetic wave based on equivalent edge current correction, characterized in that, The method comprises the following steps: S1, constructing a geometric model of an electrically large target, performing triangular partitioning on the target surface, and discretizing the target surface into a plurality of triangular patches; S2, extracting convex edge information of the target from the triangular partitioning model; S3, establishing an angular spectrum expansion model of a Bessel vortex electromagnetic wave, setting wavelength, topological charge number, and half-cone angle parameters of the wave beam, and decomposing the Bessel vortex electromagnetic wave into a superposition of a plurality of planar sub-waves; S4, calculate the current distribution on the target surface under the illumination of each plane wave by physical optics (PO) method, and integrate to obtain the main scattering field ; S5, calculating the diffraction field contribution of each plane wave on the target convex edge by using the equivalent edge current (EEC) method: segmenting each convex edge and integrating to calculate the diffraction coefficient , and , which is determined by the incident angle , the scattering angle and the diffraction angle and ; superimposing the diffraction fields of all plane waves on the edge to obtain the total edge diffraction field ; is the angle of incidence of the incident wave with the positive direction of the tangent to the edge, is the angle of scattering of the scattered wave with the positive direction of the tangent to the edge, , , , ; S6、the main scattering field with the edge diffraction field Vectorial superposition, resulting in the modified total scattering field and calculate the radar cross section, RCS, of the target.

2. The method of claim 1, wherein, The extraction method of the convex edge in step S2 comprises: traversing the common edge of adjacent triangular patches, calculating the normal angle β of the two patches, and determining the edge if β is greater than a threshold value; moving the edge midpoint and calculating the angle change trend, and retaining the convex edge with θ1< θ; The edge midpoint A is moved by a distance d along the direction of the sum vector n of the unit normal vectors of the adjacent triangular patches to obtain coordinate point B, the point B is connected with the vertex opposite to it in the triangular patch pair, and the included angle θ is obtained; then the point B is moved by a distance d along the direction of the sum vector n to obtain coordinate point C, the point C is connected with the vertex opposite to it in the triangular patch pair, and the included angle θ1 is obtained, and d is 1 / 10 of the minimum edge length of the triangular patch.

3. The method of claim 1, wherein, The electric field distribution of the Bessel vortex electromagnetic wave in step S3 is represented as: where J l (·) is the first kind Bessel function, l is the topological charge, k ri = k sin a0, k zi = k cos a0, , φ i = arctan(y i / x i ), φ i is the azimuthal angle, a0is the half-cone angle, and k is the wave number of the incident wave.

4. The method of claim 1, wherein, The diffraction coefficient in step S5 and The calculation formula is: wherein is an intermediate variable defined as may be obtained according to the following expression wherein ， 。 5. The method of claim 1, wherein, The total scattering field in step S6 The formula for calculating the RCS is: Total scattered field Vector superposition formula: The formula for calculating RCS is: .

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