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

Abstract

The invention relates to a vortex electromagnetic wave target high-frequency scattering calculation method based on equivalent edge electromagnetic current correction, and belongs to the field of electromagnetic calculation. The method comprises the following steps: constructing a target triangulation model and extracting a convex split edge; decomposing the Bessel vortex wave into planar wavelets for superposition; calculating a main scattering field under wavelet irradiation by adopting a physical optical method PO; calculating a diffraction field of the wavelet on the convex split edge based on a physical diffraction theory equivalent edge electromagnetic current PTDEEC model; and superposing the main scattering field and the edge diffraction field to obtain a corrected total field, and calculating a radar cross section (RCS). According to the method, the diffraction error of a traditional PO method on the edge of the target is effectively corrected through the equivalent edge electromagnetic current, the scattering calculation precision of the electrically large-size edge target under the irradiation of the complex vortex beam is remarkably improved, and a more reliable high-frequency algorithm is provided for radar target recognition and stealth design.

Description

Technical Field

[0001] The present invention relates to a method for calculating scattering characteristics of electrically large targets irradiated by Bessel vortex electromagnetic waves, and in particular to a scattering field algorithm for high-frequency PO approximation of vortex beams corrected by equivalent edge electromagnetic current. Background Art

[0002] Calculation of electromagnetic scattering characteristics has important application value in fields such as radar target identification, stealth technology design, and remote sensing detection. Traditional methods for calculating electromagnetic scattering from electrically large targets typically employ high-frequency approximation methods such as physical optics (PO) and geometric optics (GO). These methods significantly reduce computational complexity by simplifying the propagation and scattering of electromagnetic waves, making them suitable for rapid calculations of electrically large targets. However, the traditional PO method ignores the diffraction effects at the edges of the target during calculation, resulting in large errors in the calculation results at the edge regions. This problem is particularly prominent under complex beam illumination.

[0003] In recent years, Bessel beams have attracted extensive attention in electromagnetic scattering research due to their unique non-diffraction and self-recovery properties. Bessel beams can maintain their beam shape unchanged during propagation and have strong penetration capabilities against obstructions. Therefore, they have potential advantages in analyzing the scattering characteristics of electrically large targets. The vortex scattering field of electrically large targets can be effectively obtained by combining angular spectrum expansion with high-frequency PO approximation. However, the edge diffraction effect of complex targets with edges fails to fully reveal their scattering performance. Existing methods still have the problem of insufficient accuracy when calculating the high-frequency scattering of vortex targets.

[0004] Traditional PO methods only consider specular reflection from the target surface and ignore edge diffraction effects, resulting in significant errors in the calculated results at the edges. This error is particularly amplified when irradiated by complex beams, such as those with large electromagnetic vortex beam divergence or high topological charge. Furthermore, existing high-frequency approximation methods (such as GO and UTD) have limited processing capabilities for complex beams, making it difficult to accurately describe the interaction between Bessel beams and the target. This is particularly true at the edges of the target and in areas with significant curvature variations, where the calculated results often deviate from reality. Summary of the Invention

[0005] The purpose of the present invention is to provide an equivalent edge electromagnetic current scattering correction method for electrically large targets under Bessel vortex beam illumination, so as to solve the problem that the traditional physical optics PO method ignores the edge diffraction effect and has insufficient calculation accuracy when calculating the scattering characteristics of electrically large targets under complex beam illumination.

[0006] In order to achieve the above objectives, the present invention is implemented through the following technical solutions: A method for calculating electromagnetic scattering characteristics of an electrically large target under Bessel beam illumination comprises the following steps: S1, constructing the geometric model of the electrically large-scale target, using FEKO software to generate the three-dimensional model of the target and triangulate the target surface, discretizing it into a series of triangular facets; S2, extracting the geometric edge information of the target from the triangulated model; by traversing the common edges of the triangles, identifying the geometric edges of the target and extracting the convex edges; S3, based on the theoretical model of Bessel beam, establish a mathematical representation model of its angular spectrum expansion, set the parameters of Bessel beam, including wavelength, topological charge, half cone angle, etc., and use plane wave angular spectrum expansion to expand the Bessel beam into a superposition of a series of plane waves; S4, using the physical optics method to calculate the current distribution on the target surface under the illumination of the decomposed Bessel beam and the main scattered field generated by it; according to the PO theory, the current distribution on the target surface is calculated, and the integral calculation is performed on each triangular facet, and the sub-spectral scattering solution is superimposed to output the main scattered field calculated by the PO method; S5, to correct for 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 decomposed plane wave diffraction field. The piecewise integrals of all decomposed plane waves for each edge are superimposed to obtain its diffraction field. The diffraction coefficient is calculated using the PTDEEC model to correct the field error of the traditional PO in the edge area. S6: Superimpose the main scattered field calculated by the PO method and the edge diffraction field calculated by the EEC method to obtain the corrected total scattered field. Calculate the radar cross section (RCS) of the target and output the final electromagnetic scattering characteristics calculation results.

[0007] Compared with the prior art, the present invention has the following advantages: By introducing EEC, the present invention effectively corrects the edge diffraction effect ignored by the traditional PO method, significantly improving the calculation accuracy of the high-frequency electromagnetic scattering characteristics of electrically large targets under the irradiation of Bessel vortex beams, especially in areas with large changes in target edges and curvature, and can better handle the scattering problems of complex vortex electromagnetic waves such as Bessel beams; significantly improves the RCS calculation accuracy of edge targets, and is particularly suitable for high topological charge vortex beams. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 This is a schematic diagram of the overall flow of a method for calculating electromagnetic scattering characteristics of an electrically large target under Bessel beam illumination according to the present invention; Figure 2 It is the triangular facet decomposition diagram of the target model.

[0009] Figure 3 It is a schematic diagram of the edges of the concave and convex parts of a geometric body.

[0010] Figure 4This is the edge extraction result diagram.

[0011] Figure 5 It is a schematic diagram of the scattering of the scatterer at the observation point.

[0012] Figure 6 It is a schematic diagram of the diffraction angle of the wedge edge.

[0013] Figure 7 This is the scattering result diagram of Bessel beam in the single-station case. DETAILED DESCRIPTION

[0014] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0015] S1, construct the geometric model of the electrically large-scale target, use FEKO software to generate the three-dimensional model of the target and triangulate the target surface, discretizing it into a series of triangular facets.

[0016] In the embodiment of the present application, the electrically large-scale geometric model is a cylinder with a height of 0.36m and a diameter of 0.24m. The frequency of the incident electromagnetic wave is 10GHz. FEKO is used to model the electrically large-scale object, and the surface of the model is meshed with triangular elements. The triangular element mesh data is derived, such as Figure 2 shown.

[0017] S2, extracts the target's geometric edge information from the triangulated model. By traversing the common edges of the triangles, the target's geometric edges are identified and the convex edges are extracted.

[0018] In the embodiment of the present application, the obtained triangulated facet data is imported into MATLAB for processing, the coordinate information of each facet is extracted and the normal vector of each facet is calculated. After that, the edges of the model need to be identified and the convex edges are extracted, while the unnecessary concave edges are removed.

[0019] Edges are divided into concave and convex edges. In EEC applications, only convex edges are required. Figure 3 (a) and (c) show the cases of concave edges and convex edges respectively. In order to distinguish convex edges from concave edges, we first need to traverse all triangular face elements and find the adjacent triangular face elements (1) and (2). Use the normal vectors of (1) and (2) to calculate the angle. If the angle ψ=0°, it is a plane. If ψ≠0°, it is an edge. In actual practice, if ψ is less than a small amount, it can be regarded as a plane.

[0020] After obtaining the edge, it is necessary to remove some concave edges that are useless for subsequent calculations. After obtaining the adjacent triangle facet pairs (1) and (2) on the edge, as shown in Figure 3As shown in (b) and (d) above, their unit normals are used to find their sum vector n. Next, the midpoint A of the edge contained in the face pair is moved a short distance d in the direction of the sum vector n to obtain a new coordinate point B, where d can be expressed as 1 / 10 of the minimum edge length of the triangle. Point B is connected to the center of the triangle and its opposite vertex to determine the included angle θ. Next, point B is moved a distance d in the direction of the sum vector n to obtain a new coordinate point C. Point C is connected to the center of the triangle and its opposite vertex to determine the new included angle θ1. At this point, it can be determined that when θ1 < θ, θ tends to decrease, indicating that the edge is convex and should be retained. When θ1 > θ, θ tends to increase, indicating that the edge is concave and should be ignored. Figure 4 The edge extraction result diagram of the model used in this embodiment is given.

[0021] S3, based on the theoretical model of Bessel beam, establishes its mathematical representation model, sets the parameters of Bessel beam, including wavelength, topological charge, half-cone angle, etc., and uses plane wave angular spectrum expansion to expand the Bessel beam into a superposition of a series of plane waves.

[0022] A Bessel beam is a special form of light beam with a non-diffraction characteristic, meaning that its lateral distribution remains unchanged during propagation. l The electric field distribution of the first-order Bessel beam is described in cylindrical coordinates as in J l (·) is the Bessel function of the first kind, l is the topological charge, k ri = k sin α 0, k zi = k cos α 0, , φ i = arctan (y i / x i ) , φ i is the azimuth, α 0 is the half cone angle.

[0023] Based on the vector angular spectrum decomposition, the incident electric field can be expressed as In the formula is the scalar amplitude, and in this implementation case, xLinearly polarized incident Bessel vortex beam.

[0024] S4 uses physical optics to calculate the current distribution on the target surface under Bessel beam illumination and the resulting primary scattered field. Based on the PO theory, the current distribution on the target surface is calculated and integrated for each triangular patch, outputting the primary scattered field calculated by the PO method.

[0025] like Figure 5 As shown, Any plane wavelet decomposition of the Bessel wave p The incident vector, is the field point unit vector, r ′ is the coordinate vector of the infinitesimal element ds, and R is the distance from ds to the field point P. The far-field scattering field of the physical optics method can be expressed as follows: Where, is the unit normal vector at r′, E T =E i + E s and H T =H i + H s Arbitrary decomposition of plane waves at the bins p The total electric and magnetic fields.

[0026] At this point, the scattering field of any plane wavelet decomposed by the Bessel beam 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: in S5, in order to correct the edge diffraction effect ignored by traditional PO, EEC is introduced to calculate the diffraction field contribution of the target edge. Each edge is segmented and superimposed to obtain its diffraction field; For any plane wavelet p , the formula for calculating the scattered field of a target illuminated by a Bessel beam using EEC is: in in 、 and is the PTDEEC diffraction coefficient, k is the wave number of the incident wave, is the direction of scattered wave; The tangent line for the splitting edge; is the characteristic impedance of free space, The position vector of a fixed point on the splitting edge; is the position of the observation point, .

[0027] Therefore, it is necessary to obtain the diffraction coefficient of the target edge, which depends only on the diffraction angle. According to the geometric diffraction theory, the incident direction and the scattering direction have two angles with the target edge, which are recorded as β i 、 β s , φ 'and φ ,like Figure 6 As shown in the figure. β i is the angle between the incident wave and the positive direction of the edge tangent, β s is the angle between the scattered wave and the positive direction of the edge tangent, which can be expressed as , Calculation, diffraction angle φ 'and φ It can be written as therefore , similarly we can get .

[0028] The expression for the diffraction coefficient is in The above formula shows an intermediate variable, defined as μ =cos α , can be obtained according to the following expression in At this point, the diffraction field of any plane wavelet decomposed by Bessel beam decomposition has been obtained using EEC. The diffraction field of the entire Bessel beam on the target can be expressed by integrating the scattering results of all plane wavelets: S6: Superimpose the main scattered field calculated by the PO method and the edge diffraction field calculated by the EEC method to obtain the corrected total scattered field. Calculate the RCS of the target and output the final electromagnetic scattering characteristic calculation results.

[0029] Perform vector superposition of the obtained PO field and EEC field: According to the definition of radar cross section, the RCS of the scattered field can be calculated by the following formula: like Figure 7 Figure 2 shows the normalized RCS results of a Bessel beam for a typical edge target model in a single-station scenario using an embodiment of the present invention. The results demonstrate that while the traditional PO and the modified algorithm are highly consistent in the specular reflection region of planar structures, edge diffraction from the target at edges also contributes to the total scattered RCS of the vortex electromagnetic wave target. This invention improves the accuracy of the scattering solution for typical edge targets using Bessel beams and other vortex electromagnetic waves, providing solid theoretical support for orbital angular momentum radar target detection and recognition technology based on vortex electromagnetic waves.

[0030] Although the present invention has been described in detail through preferred embodiments, the foregoing description is merely illustrative of specific embodiments and does not limit the scope of protection of the present invention. Any obvious modifications or substitutions within the technical scope disclosed in this application by a person skilled in the art fall within the scope of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

Claims

1. A method for calculating high-frequency scattering of vortex electromagnetic waves by targets based on equivalent edge electromagnetic flow correction, characterized in that: The following steps are involved: S1. Construct a geometric model of an electrically large target, triangulate the target surface, and discretize it into multiple triangular patches; S2, extracting the convex edge information of the target from the triangulation model; S3, establishing an angular spectrum expansion model of the Bessel vortex electromagnetic wave, setting the wavelength, topological charge and half-cone angle parameters of the beam, and decomposing the Bessel vortex electromagnetic wave into a superposition of multiple plane wavelets; S4. Use the physical optics method PO to calculate the current distribution on the target surface under the illumination of each plane wavelet, and integrate to obtain the main scattered field ; S5. Use the equivalent edge electromagnetic current (EEC) method to calculate the diffraction field contribution of each plane wavelet generated by the target convex edge: Perform segmented integration on each convex edge to calculate the diffraction coefficient and , the diffraction coefficient is determined by the incident angle β i , scattering angle β s and diffraction angle φ 'and φ Determine; superimpose the diffraction fields of all plane wavelets on the edge to obtain the total edge diffraction field ; The diffraction coefficient is calculated using the physical diffraction theory equivalent edge electromagnetic flow PTDEEC model; S6, the main scattered field With the edge diffraction field Vector superposition to obtain the corrected total scattered field , and calculate the radar cross section RCS of the target.

2. The method according to claim 1, characterized in that The method for extracting the convex edge in step S2 includes: - Traverse the common edges of adjacent triangles and calculate the angle β between the two normals; - If β is greater than the threshold, it is determined to be an edge; - Move the midpoint of the edge and calculate the angle change trend, retaining the convex edge with θ1<θ.

3. The method according to claim 1, characterized in that The electric field distribution of the Bessel vortex electromagnetic wave in step S3 is expressed as: in J l (·) is the Bessel function of the first kind, l is the topological charge, k ri = k sin α 0 ，k zi = k cos α 0, , φ i = arctan (y i / x i ) , φ i is the azimuth, α 0 is the half cone angle.

4. The method according to claim 1, wherein The diffraction coefficient in step S5 and The calculation formula is: in is an intermediate variable defined as μ =cos α , can be obtained according to the following expression in cosγ1=sin β i without β s cos φ + cos β i cos β s Cart γ 2= ​​sin β i my β s basket( N π - φ ) + basket β i Cart β s 。 5. The method according to claim 1, wherein The total scattered field in step S6 The calculation formula of RCS is: The total scattered field vector superposition calculation formula is: The formula for calculating RCS is: .

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