A method for electromagnetic scattering SBR calculation of a distributed material mapping target
By constructing a distributed material mapping scheme and caching reusable path parameters, ray tracing and material electromagnetic calculations are decoupled, thus solving the efficiency bottleneck of the traditional SBR method in distributed material mapping targets and achieving rapid optimization design and efficient computation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANJING UNIV OF INFORMATION SCI & TECH
- Filing Date
- 2026-04-01
- Publication Date
- 2026-06-26
AI Technical Summary
Traditional bouncing ray tracing has an efficiency bottleneck when dealing with distributed material mapping targets, requiring the re-execution of time-consuming ray tracing processes, resulting in wasted computational resources and slow iteration speed.
A distributed material mapping scheme is constructed by dividing the region and conformal mapping. Scattering parameters are calculated using the periodic moment method, reusable path parameters are cached, ray tracing and material electromagnetic calculations are decoupled, and the reflection field is updated only when the material changes.
When the target geometry is fixed, repeated ray tracing is avoided, significantly improving computational efficiency and supporting rapid optimization design and engineering evaluation of distributed stealth materials.
Smart Images
Figure CN122287115A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of electromagnetic simulation technology, specifically to a method for calculating electromagnetic scattering SBR of a distributed material mapping target. Background Technology
[0002] The Shooting and Bouncing Rays (SBR) method is one of the mainstream algorithms for studying the electromagnetic scattering characteristics of electrically large targets with complex geometries. In modern intelligent stealth design, to achieve better electromagnetic characteristic control, researchers often need to apply different material schemes (such as radar-absorbing materials or frequency-selective surfaces) to different parts of a fixed aircraft or ship platform, and achieve the optimal solution for overall stealth performance through refined distributed material mapping. Because such engineering usually has the characteristics of maintaining constant geometry while frequently changing surface electromagnetic parameters, it is called the Partial Modification Problem (PMP).
[0003] However, the traditional SBR method suffers from a severe efficiency bottleneck when dealing with PMP problems. Whenever the surface material changes, the traditional algorithm must re-execute the entire ray tracing process, including time-consuming intersection tests of rays with a massive number of triangular facets, multi-hop reflection path tracing, and complex spatial geometry calculations. Since the computational time of the ray tracing process typically accounts for more than 70% of the total electromagnetic simulation time, this repetitive tracing operation for fixed geometries leads to a huge waste of computational resources, severely limiting the iterative speed of coating design and optimization. Summary of the Invention
[0004] Purpose of the invention: The purpose of this invention is to provide a method for calculating electromagnetic scattering SBR that decouples ray tracing for distributed material mapping targets.
[0005] Technical solution: A method for calculating electromagnetic scattering SBR of a distributed material mapping target, comprising the following steps:
[0006] S1. Divide the target surface into regions based on its electromagnetic properties and assign different materials to each region. Then, adjust the corresponding regions by conformal mapping based on the local shape features of the target surface to construct a distributed material mapping scheme for the target.
[0007] S2. Calculate the scattering parameters of different materials used in the distributed material mapping scheme of the target at different incident angles using the periodic moment method, and construct a discrete scattering parameter database.
[0008] S3. Use the bouncing ray method to perform the first ray tracing of the target and obtain reusable path parameter information;
[0009] S4. Based on the target's distributed material mapping scheme, calculate the corresponding scattering parameters using the discrete scattering parameter database, and then solve for the reflection field vector by combining the corresponding reusable path parameter information.
[0010] S5. Solve the far-field scattering electric field of a single effective ray tube using the reflection field vector. Summate the far-field scattering electric fields of all effective ray tubes to obtain the total scattering electric field. Calculate the scattering cross-section of the target using the total scattering field.
[0011] Specifically, the scattering parameters include the reflection coefficient and the transmission coefficient. The formula for calculating the reflection coefficient is:
[0012]
[0013] In the formula: The reflection coefficient, The pitch angle, It is the azimuth angle. The amplitude coefficients of the mode components of the incident wave are... The amplitude coefficients of the mode components of the reflected wave are... The reflected electric field vector, Horizontal vector characteristic function conjugate, Let be the propagation constant. The spatial position coordinates on the z-axis, Characteristic impedance, This is the reference surface for calculating the reflection coefficient.
[0014] Specifically, step S3 includes:
[0015] The initial ray tracing process for the target is performed, and reusable path parameters are calculated. These reusable path parameters include reflection direction, vertical polarization basis vector, parallel basis vector, intersection coordinates, local incident angle, and intersection surface element information. The obtained reusable path parameters are stored in the form of a multi-dimensional vector.
[0016] Specifically, the reflection direction is derived from the incident vector and the surface normal vector using Snell's law:
[0017]
[0018] In the formula: The direction of reflection, Let be the incident vector. It is the surface normal vector;
[0019] The formula for calculating the vertical polarization basis vector is:
[0020]
[0021] In the formula: It is the vertical polarization basis vector;
[0022] The formula for calculating the parallel basis vector is:
[0023]
[0024] In the formula: These are parallel basis vectors.
[0025] Specifically, step S4 includes:
[0026] S41. Based on the target's distributed material mapping scheme, locate the adjacent angle index from the discrete scattering parameter database and calculate the corresponding reflection coefficient using bilinear interpolation.
[0027] S42. Read the stored vertical polarization basis vector and decompose the incident field vector of each reflection into two scalar components projected onto the direction of the vertical polarization basis vector and the direction of the parallel polarization basis vector.
[0028] S43. Solve for the reflection field vector using the reflection coefficient and vertical polarization basis vector obtained in step S41.
[0029] Specifically, the calculation of the corresponding reflection coefficient using bilinear interpolation includes:
[0030] make Indicates that at the angle index is The pre-calculated reflection coefficient, for points falling on... Index is and between, Index is and Target angle between Calculate the interpolation weights for bilinear interpolation:
[0031]
[0032] In the formula: , For interpolation weights, , The angle sampling step size;
[0033] Using the obtained interpolation weights, the formula for calculating the interpolated reflection coefficient is as follows:
[0034]
[0035] In the formula: This is the interpolated reflection coefficient.
[0036] Specifically, step S42 includes: converting the incident field vector... Projecting onto the incident basis vector, the incident field components are calculated using the buffered vertical polarization basis vector:
[0037]
[0038]
[0039] In the formula: The incident field vector The vertical polarization scalar component, The incident field vector Parallel polarization scalar components; It is the vertical polarization basis vector. These are parallel basis vectors.
[0040] Specifically, step S43 includes:
[0041] Using the angle of the target ray Indexing, calculating the reflection coefficient matrix:
[0042]
[0043] In the formula: For the parallel polarization scalar component of the reflected electric field vector, For the vertical polarization scalar component of the reflected electric field vector, The reflection coefficient is in the TM polarization state. The reflection coefficient is in the TE polarization state. This represents the TM polarization scattering coefficient induced when the incident wave is TE polarized. This represents the TE polarization scattering coefficient induced when the incident wave is TM polarized;
[0044] Then calculate the reflection parallel basis vectors:
[0045]
[0046] In the formula: These are the reflection parallel basis vectors. The direction of reflection;
[0047] The updated scalar components are recombinated with the orthogonal basis of reflection to synthesize the reflection field vector:
[0048]
[0049] In the formula: is the reflection field vector.
[0050] Specifically, the formula for calculating the far-field scattered electric field of a single effective ray tube is as follows:
[0051]
[0052] In the formula: For observation point Far-field scattered electric field at that location Distance from the observation point It is the free space wavenumber. Let be a unit vector in spherical coordinates. represent The far-field amplitude of polarization, represent The far-field amplitude of polarization;
[0053] The formula for calculating the total scattered electric field is:
[0054]
[0055] In the formula: Angle of incidence The total scattered electric field, The total number of effective X-ray tubes participating in far-field synthesis. Represented by the equivalent aperture field The first The far-field contribution of the X-ray tube, The phase factor accumulated along this ray path. This is the phase shift.
[0056] Specifically, the formula for calculating the scattering cross-section is:
[0057]
[0058] In the formula: This represents the scattering cross-section.
[0059] Beneficial Effects: Compared with existing technologies, the significant advantage of this invention is that by decoupling geometric ray tracing from material electromagnetic calculations, and under the premise of a fixed target geometry, reusable path parameters are cached after the initial complete tracing. Subsequent changes in material layout only require updating the reflection field calculation, thus completely avoiding the drawback of traditional SBR methods that repeatedly perform time-consuming ray tracing due to changes in surface materials. This method, while ensuring computational accuracy, improves computational efficiency in multi-scheme iteration scenarios to near constant time, effectively supporting the rapid optimization design and engineering evaluation of distributed stealth materials. Attached Figure Description
[0060] Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention.
[0061] Figure 2 This is a schematic diagram of the target surface distributed mapping scheme in Embodiment 1 of the present invention.
[0062] Figure 3 This is a schematic diagram of multiple reflections of the X-ray tube at the dihedral angle in Embodiment 1 of the present invention.
[0063] Figure 4 This is a comparison chart of the RCS calculation results in Embodiment 1 of the present invention.
[0064] Figure 5 This is a comparison chart of calculation time in Embodiment 1 of the present invention. Detailed Implementation
[0065] A preferred embodiment of the present invention will be further described below with reference to the accompanying drawings.
[0066] Example 1
[0067] This embodiment provides a method for calculating the electromagnetic scattering SBR of a distributed material mapping target, including the following steps:
[0068] Step 1: Divide the target surface into regions based on its electromagnetic properties and assign different materials to each region. Then, adjust the corresponding regions according to the local shape features of the target surface to construct a distributed material mapping scheme for the target.
[0069] Please refer to Figure 2 As shown, the two colors of the target surface represent two regions obtained by dividing the target ship surface and two different coating materials. The main basis for dividing the region is the geometric features of the target surface and the strength of electromagnetic scattering in each part. Different electromagnetic materials or periodic units are selected to meet the electromagnetic characteristic requirements of different functional areas.
[0070] Meanwhile, for local areas with complex shapes and curvature variations within the region, in order to enable the coating units to adhere more precisely to the surface, the periodic coating units are adaptively adjusted by rotation based on their local spatial location, surface curvature change rate, normal vector, and polarization information, and a circumferential laying method is adopted (see reference). Figure 2 (As illustrated by the red curve in the middle), this method of allocating different units to the overall region and performing conformal mapping in local regions constructs the distributed material mapping scheme required for subsequent calculations.
[0071] Step 2: Calculate the scattering parameters (S-parameters) of different materials used in the target distributed material mapping scheme at different incident angles using the periodic moment method, and construct a discrete scattering parameter database.
[0072] For distributed coating materials, including absorbing materials (RAM) or periodic frequency selective surfaces (FSS), the periodic method of moments (FSS) is used for characterization. By utilizing the periodic Green's function and periodic boundary conditions, the solution domain of the periodic structure is reduced to a single periodic cell; and the Ewald transform method is used to combine the spectral and spatial domain forms of the periodic Green's function, thereby accelerating its processing; the plane wave is set to travel at an arbitrary angle. Incident, according to Floquet theory, the electromagnetic field can be represented by a transverse vector eigenfunction in any plane perpendicular to the z-axis within a periodic structure, using the Floquet model. Expanded in the following form:
[0073]
[0074]
[0075] In the formula: For electric field strength, The magnetic field strength, The horizontal vector component is perpendicular to the z-axis. Floquet mode index for spatial harmonics, , These are the energy coefficients transmitted in the positive and negative directions of the z-axis, respectively. The transmission constant, Characteristic impedance, is the spatial coordinate on the z-axis.
[0076] When the incident wave is TE polarized, the characteristic impedance value is:
[0077]
[0078] When the incident wave is TM polarized, the characteristic impedance value is:
[0079]
[0080] In the formula: Angular frequency, Permeability, is the dielectric constant.
[0081] Secondly, assuming the incident plane wave propagating from the negative z-axis corresponds to the p-th Floquet mode, let... In calculating the reflection coefficient The reference surface of the plane, let To find the transmission coefficient ( The reference surface of the plane. The total electric field on the surface includes the incident field propagating in the positive z-direction and the scattered field from the metal body propagating in the negative z-direction. Expanding its transverse component using Floquet's theorem, we get:
[0082]
[0083] definition for The conjugate form of the above equation is obtained by multiplying both sides by . and to Integrating on the surface, based on the orthogonality of Floquet modes, the reflection coefficient of the p-th layer mode can be expressed as: Format:
[0084]
[0085] In the formula: The reflection coefficient, The pitch angle, It is the azimuth angle. and These are the amplitude coefficients of the mode components of the incident wave and the reflected wave, respectively. The reflected electric field vector, Horizontal vector characteristic function conjugate, Characteristic impedance, This is the reference surface for calculating the reflection coefficient.
[0086] Since subsequent steps primarily utilize the reflection coefficient for calculations, this embodiment only demonstrates the calculation method for the reflection coefficient among the scattering parameters. The periodic moment method described above is used in electromagnetic simulation software to calculate the different materials used in the distributed material mapping scheme at different incident angles. Based on the scattering parameters, a discrete scattering parameter database is constructed.
[0087] Step 3: Use the bouncing ray method to perform the first ray tracing of the target and obtain reusable path parameter information.
[0088] Please refer to Figure 3 As shown, the ray tube undergoes multiple reflections on the dihedral surface, intersecting with triangular facets on different surfaces. The initial ray tracing calculation is as follows: the coordinates of the intersection point between the ray and the facet are determined by solving the ray propagation equation and the triangle parametric equation. Based on the principles of geometrical optics (GO), the reflection direction is determined. Based on the incident vector and surface normal vector Using Snell's law, we can derive the following:
[0089]
[0090] Simultaneously, the angle between the incident ray and the intersecting surface element is calculated and defined as the local incident angle. And the vertical polarization basis vector used for polarization decomposition Defined as:
[0091]
[0092] The parallel basis vector of the incident ray is:
[0093]
[0094] Finally, the reusable path parameter information obtained from the first ray tracing (reflection direction, vertical polarization base vector, intersection coordinates, local incident direction, intersection element information, etc.) is cached in the form of a multi-dimensional vector with angle, ray tube number, and reflection count.
[0095] Step 4: Based on the target's distributed material mapping scheme, calculate the corresponding scattering parameters using the discrete scattering parameter database, and then solve for the reflection field vector by combining the corresponding reusable path parameter information.
[0096] In this invention, when the surface material changes, the redundant ray tracing process is skipped; the electromagnetic field is updated only by retrieving reusable path parameters and reflection coefficients. Because PMM calculates the incident angle at... When calculating the scattering parameters at a given time, there exists an angular step size; therefore, based on the local incident angle... When indexing scattering parameters, bilinear interpolation is required to obtain accurate reflection coefficients.
[0097] make Indicates that at the angle index is The pre-calculated reflection coefficient, for points falling on... Index is and between, Index is and Target ray angle between Interpolation weights and The calculation is as follows:
[0098]
[0099] In the formula: , The angle sampling step size.
[0100] Using the obtained interpolation weights, the interpolated reflection coefficient The derivation is as follows:
[0101]
[0102] Furthermore, the incident field vector Projecting onto the incident basis vector, the incident field components are calculated using the buffered vertical polarization basis vector:
[0103]
[0104]
[0105] In the formula: The incident field vector The vertical polarization scalar component, The incident field vector The parallel polarization scalar components.
[0106] Then, using the intersecting surface information from the cache, the region where it is located is obtained, along with the current distributed material mapping scheme and the coating material (corresponding scattering parameters) used by the target at that location. The local incident angle from the cache is then used. Index the reflection coefficient matrix to further calculate the reflected field components:
[0107]
[0108] In the formula: For the parallel polarization scalar component of the reflected electric field vector, For the vertical polarization scalar component of the reflected electric field vector, The reflection coefficient is in the TM polarization state. The reflection coefficient is in the TE polarization state. This represents the TM polarization scattering coefficient induced when the incident wave is TE polarized. This represents the TE polarization scattering coefficient induced when the incident wave is TM polarized.
[0109] Reflection parallel basis vectors It is relative to the direction of reflection. Defined:
[0110]
[0111] Finally, the reflection field vector is synthesized by recombinating the updated scalar components with the orthogonal reflection basis. :
[0112]
[0113] Please see Figure 1As shown, without repeating ray tracing, it is only necessary to input the target mesh file, frequency, wave direction and scattering parameters to be calculated into the electromagnetic simulation software, and the target reflection field vector can be updated by searching for the corresponding reusable path parameters. If no corresponding reusable path parameters are found, steps one to three are executed to obtain the corresponding reusable path parameters.
[0114] Step 5: Use the reflection field vector to solve for the far-field scattering electric field of a single effective X-ray tube. After summing the far-field scattering electric fields of all effective X-ray tubes, the total scattering electric field is obtained. The scattering cross-section of the target is then calculated using the total scattering field.
[0115] At the observation point Far-field scattered electric field This is obtained by summing the contributions of all effective X-ray tubes; therefore, the contribution of a single X-ray tube is calculated first, using the following formula:
[0116]
[0117] In the formula: Distance from the observation point It is the free space wavenumber. It is a unit vector in spherical coordinates. and Represent and The amplitude of polarization in the far field.
[0118] and By exiting the surface The above integral derivation of the aperture field yields the following formula:
[0119]
[0120] In the formula: It is the unit vector of the direction of the observation point. It is the position vector on the exit aperture of the ray tube. It is the unit normal vector of the integral surface. and This corresponds to the electromagnetic field at the exit aperture of the ray tube after multiple reflections. The free-space wave impedance; the integral term in the above equation is expressed as a scalar shape function defined by the aperture geometry. :
[0121]
[0122] In the formula: It is the direction of ray scattering. This represents the cross-sectional area at the exit aperture. Let be the center vector of the aperture surface; this integral term is solved analytically using Gordon's formula.
[0123] Then, through the method obtained in step four... The final reflection field vector of the ray tube ,use Substitute the solved reflection field into the equation to solve for the far-field amplitude, and then further obtain the far-field scattering electric field of the current ray tube. .
[0124] Finally, through calculation The far-field scattered electric fields of each effective ray tube are summed to obtain the total scattered electric field. :
[0125]
[0126] In the formula: Represented by the equivalent aperture field The first Far-field contribution of a single X-ray tube The phase factor accumulated along this ray path; This represents the phase shift accumulated along the ray path.
[0127] Calculate the scattering cross section (RCS) using the total scattered electric field:
[0128]
[0129] In the formula: This represents the scattering cross-section.
[0130] Therefore, by decoupling time-consuming geometric ray tracing from material electromagnetic calculation, this invention eliminates the need for repeated geometric ray tracing when processing distributed material layout optimization or modification design, thus significantly improving the computational efficiency of electromagnetic scattering characteristics of complex stealth targets.
[0131] Please refer to Figure 4 As shown, Figure 4 The above describes the RCS calculation results obtained by simulation using the scheme of this invention and the traditional SBR method. The scheme of this invention is used to simulate four mapping schemes: ideal conductor (PEC), single material A, single material B, and a combination of materials A and B. As a comparison, the traditional SBR method is used to simulate the mapping scheme of material A+B. Figure 4 As can be seen, the simulation calculation of the material A+B combination mapping scheme using the scheme of the present invention is highly consistent with the simulation calculation results obtained by the traditional SBR method, proving the feasibility of the ray tracing decoupling of the present invention.
[0132] Please refer to Figure 5 As shown, Figure 5 By comparing the computation time required for simulation using the scheme of this invention with that of the traditional SBR method, it can be clearly seen that, due to the adoption of the ray tracing decoupling scheme, the computation time of this invention remains almost constant when facing mapping schemes with different material types and different combinations of material quantities. Compared with the traditional SBR, it achieves an order-of-magnitude reduction in time consumption and significantly shortens the design cycle.
Claims
1. A method of electromagnetic scattering SBR computation of a distributed material-mapped object, characterized in that, Includes the following steps: S1. Divide the target surface into regions based on its electromagnetic properties and assign different materials to each region. Then, adjust the corresponding regions by conformal mapping based on the local shape features of the target surface to construct a distributed material mapping scheme for the target. S2. Calculate the scattering parameters of different materials used in the distributed material mapping scheme of the target at different incident angles using the periodic moment method, and construct a discrete scattering parameter database. S3. Use the bouncing ray method to perform the first ray tracing of the target and obtain reusable path parameter information; S4. Based on the target's distributed material mapping scheme, calculate the corresponding scattering parameters using the discrete scattering parameter database, and then solve for the reflection field vector by combining the corresponding reusable path parameter information. S5. Solve the far-field scattering electric field of a single effective ray tube using the reflection field vector. Summate the far-field scattering electric fields of all effective ray tubes to obtain the total scattering electric field. Calculate the scattering cross-section of the target using the total scattering field.
2. The method of claim 1, wherein: The scattering parameters include the reflection coefficient and the transmission coefficient, and the formula for calculating the reflection coefficient is as follows: where: is the reflection coefficient, is the elevation angle, is the azimuth angle, is the mode component amplitude coefficient of the incident wave, is the mode component amplitude coefficient of the reflected wave, is the reflected electric field vector, is the transverse vector eigenfunction is the conjugate of the transverse vector eigenfunction is the propagation constant, is the spatial position coordinate on the z-axis, is the characteristic impedance, is the reference surface for calculating the reflection coefficient.
3. The electromagnetic scattering SBR calculation method for distributed material mapping targets according to claim 1, characterized in that, Step S3 includes: The initial ray tracing process for the target is performed, and reusable path parameters are calculated. These reusable path parameters include reflection direction, vertical polarization basis vector, parallel basis vector, intersection coordinates, local incident angle, and intersection surface element information. The obtained reusable path parameters are stored in the form of a multi-dimensional vector.
4. The electromagnetic scattering SBR calculation method for distributed material mapping targets according to claim 3, characterized in that: The reflection direction is derived from the incident vector and the surface normal vector using Snell's law: In the formula: The direction of reflection, Let be the incident vector. It is the surface normal vector; The formula for calculating the vertical polarization basis vector is: In the formula: It is the vertical polarization basis vector; The formula for calculating the parallel basis vector is: In the formula: These are parallel basis vectors.
5. The electromagnetic scattering SBR calculation method for distributed material mapping targets according to claim 3, characterized in that, Step S4 includes: S41. Based on the target's distributed material mapping scheme, locate the adjacent angle index from the discrete scattering parameter database and calculate the corresponding reflection coefficient using bilinear interpolation. S42. Read the stored vertical polarization basis vector and decompose the incident field vector of each reflection into two scalar components projected onto the direction of the vertical polarization basis vector and the direction of the parallel polarization basis vector. S43. Solve for the reflection field vector using the reflection coefficient and vertical polarization basis vector obtained in step S41.
6. The electromagnetic scattering SBR calculation method for distributed material mapping targets according to claim 5, characterized in that, The calculation of the corresponding reflection coefficient using bilinear interpolation includes: make Indicates that at the angle index is The pre-calculated reflection coefficient, for points falling on... Index is and between, Index is and Target angle between Calculate the interpolation weights for bilinear interpolation: In the formula: , For interpolation weights, , The angle sampling step size; Using the obtained interpolation weights, the formula for calculating the interpolated reflection coefficient is as follows: In the formula: This is the interpolated reflection coefficient.
7. The electromagnetic scattering SBR calculation method for distributed material mapping targets according to claim 6, characterized in that, Step S42 includes: converting the incident field vector Projecting onto the incident basis vector, the incident field components are calculated using the buffered vertical polarization basis vector: In the formula: The incident field vector The vertical polarization scalar component, The incident field vector Parallel polarization scalar components; It is the vertical polarization basis vector. These are parallel basis vectors.
8. The electromagnetic scattering SBR calculation method for distributed material mapping targets according to claim 7, characterized in that, Step S43 includes: Using the angle of the target ray Indexing, calculating the reflection coefficient matrix: In the formula: For the parallel polarization scalar component of the reflected electric field vector, For the vertical polarization scalar component of the reflected electric field vector, The reflection coefficient is in the TM polarization state. The reflection coefficient is in the TE polarization state. This represents the TM polarization scattering coefficient induced when the incident wave is TE polarized. This represents the TE polarization scattering coefficient induced when the incident wave is TM polarized; Then calculate the reflection parallel basis vectors: In the formula: These are the reflection parallel basis vectors. The direction of reflection; The updated scalar components are recombinated with the orthogonal basis of reflection to synthesize the reflection field vector: In the formula: is the reflection field vector.
9. The electromagnetic scattering SBR calculation method for distributed material mapping targets according to claim 1, characterized in that, The formula for calculating the far-field scattering electric field of a single effective ray tube is as follows: In the formula: For observation point Far-field scattered electric field at that location Distance from the observation point It is the free space wavenumber. Let be a unit vector in spherical coordinates. represent The far-field amplitude of polarization, represent The far-field amplitude of polarization; The formula for calculating the total scattered electric field is: In the formula: Angle of incidence The total scattered electric field, The total number of effective X-ray tubes participating in far-field synthesis. Represented by the equivalent aperture field The first The far-field contribution of the X-ray tube, The phase factor accumulated along this ray path. This is the phase shift.
10. The electromagnetic scattering SBR calculation method for distributed material mapping targets according to claim 9, characterized in that: The formula for calculating the scattering cross-section is: In the formula: This represents the scattering cross-section.