A method for physical optics scattering field computation based on pixelated projection

Abstract

The present application relates to a kind of physical optical scattering field calculation methods based on pixel projection, belong to the field of computational electromagnetics, and the calculation method includes: after obtaining target three-dimensional CAD model, corresponding setting parameter is carried out, and target is carried out surface projection and generates projection area;Projection area is pixelated and is dispersed and is carried out curvature constraint, the radiation function of pixel point is calculated and radiation image is constructed;Each pixel point is calculated by closed expression formula, and total scattering field is calculated by GPU parallel architecture and is exported after output.This application is based on the basic theory of physical optics (PO), under the premise of meeting the applicable conditions of PO, it can guarantee higher calculation accuracy.Pixilated projection mode can more finely describe the geometric details and surface characteristics of the target, so as to more accurately simulate the scattering behavior of complex shape, edge effect and non-uniform material surface, improve the applicability of the method to actual engineering target and the reliability of calculation result.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of computational electromagnetics, and in particular to a physical optics scattering field calculation method based on pixelated projection. BACKGROUND

[0002] Radar cross section (RCS) analysis has important application value in key fields such as radar system design, target recognition, electromagnetic compatibility, etc. With the complexification of modern target geometry and the increase of electrical size, the high-precision and fast calculation of the electromagnetic scattering characteristics of the target has become a core challenge in the field of computational electromagnetics. The traditional design stage relies on RCS prediction to build a target database, optimize the scattering field, and replace high-cost measurement, so it is urgent to break through the efficiency bottleneck of the existing method.

[0003] The current mainstream method has the following significant limitations: 1. The full-wave method (such as the method of moments MOM, multi-layer fast multipole method MLFMA) has high accuracy, but the calculation resource consumption increases exponentially with the frequency, and it is difficult to handle large-size targets due to the limitation of computer memory; 2. In the high-frequency approximation method, the shooting and bouncing ray method (SBR) needs to perform large-scale ray-patch intersection tests, and the computational complexity is of the order of the square of the number of patches (O(N²)), which is inefficient for complex targets; 3. The physical optics method (PO) is suitable for large-size problems, but the core radiation integral usually has no theoretical closed-form solution. The existing discretization scheme (triangular / quadrilateral patches or quadratic surfaces) relies on numerical integration or asymptotic approximation, which has a heavy computational burden. The stationary phase method, saddle point method and other asymptotic methods have inherent defects such as difficulty in locating stationary points, sensitivity to curvature (failure when curvature tends to zero), and multiple stationary point path solving, which makes it difficult to guarantee the generality and accuracy of the scattering field of complex curved surfaces. 4. Graph electromagnetic computation (GRECO) Although the blanking and patch segmentation are accelerated by using graphics hardware, it is limited by the screen resolution of early GPUs, and the pixelated field value lacks physical intuition, and it fails to deeply integrate the advantages of computer graphics.

[0004] In recent years, the breakthrough development of GPU technology has provided a new way to solve the above problems: Modern image processing units (GPUs) have shown significant acceleration potential in computational electromagnetics by taking advantage of large-scale parallel architecture and high memory bandwidth, combined with general-purpose computing frameworks such as CUDA. However, the existing GPU acceleration scheme still has three shortcomings: 1. The discretization model of the complex curved surface PO integral does not fully utilize the parallel characteristics of the GPU; 2. The hardware mapping of the surface radiation function lacks efficient implementation; 3. The pixel-level processing of the traditional GRECO is not deeply coupled with the physical optics theory. SUMMARY

[0005] The present application aims to overcome the shortcomings of the prior art and provides a physical optics scattering field calculation method based on pixelated projection, which solves the problems existing in the prior art.

[0006] The purpose of the present application is achieved by the following technical solutions: a physical optical scattering field calculation method based on pixel projection, the calculation method comprising:

[0007] Step one, after obtaining the target three-dimensional CAD model, the corresponding setting parameters are performed, and the target is projected to generate a projection area;

[0008] Step two, the projection area is pixelated and discretized and curvature constraint is performed, the radiation function of the pixel point is calculated and the radiation image is constructed;

[0009] Step three, the oscillation integral of each pixel point is calculated through the closed expression, and the total scattering field is calculated through the GPU parallel architecture and outputted.

[0010] The step one specifically includes the following contents:

[0011] A1, obtaining a target three-dimensional CAD model;

[0012] A2, setting the incident wave parameters, including frequency f, wavelength λ, incident direction , polarization mode;

[0013] A3, setting the projection parameters, including defining the projection plane along the scattering observation direction ;

[0014] A4, orthogonally projecting the target surface along the direction to the XOY plane to generate a projection area ;

[0015] A5, using Z-buffer algorithm to retain visible surface points and discard the occluded area;

[0016] A6, recording the boundary size L and H of the projection area, L represents the length and H represents the width.

[0017] The step two specifically includes the following contents:

[0018] B1, dividing each into m*n rectangular pixels to obtain the length ΔL=L / m and the width ΔH=H / n of each pixel;

[0019] B2, calculating the corresponding surface gradient of each pixel center point , if , directly associating the surface point coordinates ( ) and the normal vector , if If the curvature constraint is not satisfied, the local surface region is subdivided and projected.

[0020] The step three specifically includes the following contents:

[0021] C1, calculate the radiation function of the pixel point by the formula , wherein, is an imaginary unit, is a wave number, represents a spherical wave phase factor, is the distance from the observation point to the origin, is a projection plane normal unit vector, is a unit vector in the direction of incident wave propagation, is the value of the incident electric field at the curved surface point , represents a z-direction phase modulation term;

[0022] C2, calculate the vertical polarization and the horizontal polarization respectively;

[0023] C3, radiation image construction: mapping generates the amplitude / phase image of R;

[0024] C4, for each pixel point , calculate the oscillation integral by the closed-form expression to obtain wherein, , is the difference component of the scattering wave vector and the incident wave vector in the x and y directions, respectively represent the length and width of the pixel, is a Bessel function, represents the coordinates of the th pixel center point on the projection plane, represents the center point phase term;

[0025] C5, thread mapping: allocate m×n pixels to the GPU thread grid, and each thread processes one pixel;

[0026] C6, kernel function execution: calculate the contribution value of each pixel to the far-field scattering field by threads and store the result in shared memory;

[0027] C7, hierarchical reduction summation: use parallel reduction summation within the thread block to obtain the total scattering field as ;

[0028] C8, output the dual-polarized scattering field components as​ and wherein, is the vertical polarization scattered field component; is the horizontal polarization scattered field component, j denotes the jth pixel, denotes the vertical polarization component of the radiation function of the jth pixel, denotes the horizontal polarization component of the radiation function of the jth pixel, denotes the shape function of the jth pixel.

[0029] The present application has the following advantages:

[0030] 1. Significant improvement in computational efficiency: The core method discretizes the target surface into pixel units and uses pixelated projection technology to handle the interaction of light waves with the target, converting complex continuous integrals into discrete pixel superposition calculations. This discretization processing method is naturally suitable for parallel computing architecture (such as GPU), which can fully utilize hardware acceleration capabilities. Compared with traditional direct integration methods or partial numerical methods, the calculation speed can be improved by orders of magnitude when dealing with large size and complex structure targets, greatly shortening the simulation time.

[0031] 2. Enhanced computational accuracy and applicability: Based on the basic theory of physical optics (PO), the method can ensure high computational accuracy under the premise of meeting the PO applicability conditions (such as the target size being much larger than the wavelength, the observation point being in the far field or the local smooth area). The pixelated projection method can more accurately describe the geometric details and surface characteristics of the target (such as assigning different attributes to pixels), thus more accurately simulating the scattering behavior of complex shapes, edge effects, and non-uniform material surfaces, improving the applicability of the method to actual engineering targets and the reliability of the calculation results.

[0032] 3. Optimization of complex target and multiple scattering processing capability: The pixelated data structure facilitates efficient handling of occlusion judgment and visibility calculation, which is crucial for analyzing complex targets with occlusion relationships (such as cavities, gap structures). Although mainly based on single scattering PO, the framework of this method (especially the pixel-based spatial relationship management) provides a convenient foundation for efficiently integrating multiple scattering calculation models (such as iterative PO, some ideas of the SBR bounce ray method), expanding its potential in dealing with strongly coupled, multiple reflection scattering problems.

[0033] 4. Strong generality and engineering practicability of the algorithm: the method has clear principles and relatively standardized processes (target discretization, pixel projection, local field calculation, far-field integration), which are easy to program and integrate into existing electromagnetic simulation software platforms. Its high efficiency makes it very suitable for engineering application scenarios that require a large number of parameter scans, optimization design (such as antenna RCS optimization and stealth shape design), or near real-time simulation (such as some dynamic scene simulation), providing a powerful practical calculation tool for radar cross section (RCS) analysis, optical device design, target recognition, and other fields. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 is a curved surface projection and pixelation schematic diagram;

[0035] Figure 2 is a projection area Sampling and rectangular area discretization schematic diagram. DETAILED DESCRIPTION

[0036] To make the purposes, technical solutions, and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, not all. The components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in conjunction with the drawings herein is not intended to limit the scope of protection of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present application. The present application will be further described below with reference to the drawings.

[0037] One of the embodiments of the present application specifically relates to a high-efficiency physical optics scattering field calculation method based on pixelated projection and radiation images, which is suitable for fast simulation of the radar cross section (RCS) of large-size electric targets such as aircraft and ships. The method innovatively combines pixelated projection technology and physical optics principles to achieve significant breakthroughs in efficiency, accuracy, ability to process complex targets, and engineering practicability, providing key technical support for efficient and accurate electromagnetic / optical scattering simulation.

[0038] Specifically includes the following content:

[0039] S1, input preparation and parameter setting;

[0040] S11, obtaining a three-dimensional CAD model of a target (such as curved surface mesh data of an aircraft or a ship);

[0041] S12, Set incident wave parameters: frequency f, wavelength λ, incident direction , polarization mode (horizontal / vertical polarization);

[0042] S13, Set projection parameters: projection plane (usually XOY plane), projection direction Define projection plane (usually XOY plane);

[0043] S2, Surface projection and region generation;

[0044] S21, Orthogonal project the target surface along direction to XOY plane, generate projection region ( Figure 1 schematic), where the surface represents the three-dimensional object surface whose scattering field is to be calculated, represents the two-dimensional region covered by the projection of the three-dimensional target surface Σ on XOY plane;

[0045] S22, Occlusion processing: use Z-buffer algorithm to retain visible surface points and discard occluded regions;

[0046] S23, Record the boundary size L (length) and H (width) of the projection region.

[0047] S3, Pixelization and curvature constraint;

[0048] S31, Divide the projection region uniformly into m×n rectangular pixels Figure 2 (schematic), get the length ΔL=L / m and width ΔH=H / n of each pixel;

[0049] S32, Key constraint: calculate the surface gradient at the center point of each pixel:

[0050] S33, If , directly associate the surface point coordinates and normal vector ;

[0051] S34, If (not satisfying the curvature constraint), subdivide and project the local surface region (recursively execute S2-S3 operations to recalculate the sub-pixel gradient until the constraint is satisfied).

[0052] S4, Radiation function calculation and image generation;

[0053] S41, Calculate the radiation function of the pixel point :

[0054] ,

[0055] where, is the imaginary unit, used to assist complex number operation; is the wave number, denotes the spherical wave phase factor, is the distance from the observation point to the origin, is the projection plane normal unit vector, is the incident wave propagation direction unit vector, is the incident electric field value at the curved surface point , denotes the z-direction phase modulation term.

[0056] S42, Polarization decomposition: calculate (VH), (VH), respectively, (VH), (VH), respectively,

[0057] ,

[0058] ,

[0059] where, is the vertical polarization unit vector, perpendicular to the scattering direction , is the horizontal polarization unit vector, perpendicular to and .

[0060] S43, Radiated image construction: map the amplitude / phase image of R, as shown in Figure 1 , visually display the strong scattering area (such as corner reflector, cavity opening), in the figure, denotes the incident electric field value, denotes the total scattered field value; is the observation point position vector; denotes the spherical wave phase factor of the incident wave propagation direction; denotes the spherical wave phase factor perpendicular to the scattering direction; and denote the vector area element on the projection plane and the vector area element on the curved surface , respectively.

[0061] S5, Shape function analytical integration, for each pixel point , calculate the oscillation integral through the closed-form expression to obtain:

[0062] ,

[0063] where, , is the difference between the scattering wave vector and the incident wave vector in x and y directions, represents the i-th pixel region, represents the i-th pixel region, represents the high frequency oscillation phase function, represents the actual physical size (length and width) of the pixel, is the sinc function used to analytically handle the high frequency oscillation integral, represents the i-th pixel region, represents the i-th pixel region, represents the i-th pixel region.

[0064] S6, GPU parallel architecture design;

[0065] S61, thread mapping: m x n pixels are allocated to the GPU thread grid, and each thread processes one pixel;

[0066] S62, kernel function execution: each pixel's contribution to the far-field scattering field is calculated by threads and the results are stored in shared memory.

[0067] S63, hierarchical reduction summation: parallel reduction (Parallel Reduction) is used within the thread block to sum up the total scattering field:

[0068] .

[0069] S7, far-field scattering field output, output the dual-polarized scattering field components:

[0070] ,

[0071] ,

[0072] where, is the vertical polarization scattering field component; is the horizontal polarization scattering field component, subscript j represents the j-th pixel, and the summation is performed on all pixels (from j = 1 to m x n), represents the vertical polarization component of the radiation function of the j-th pixel, represents the horizontal polarization component of the radiation function of the j-th pixel, represents the shape function of the j-th pixel.

[0073] ​The foregoing is considered as merely a preferred embodiment of the present application and it is understood that the present application is not limited to the forms described herein, should not be considered as excluding other embodiments, and can be used in various other combinations, modifications and improvements, and can be changed within the scope of the concept described herein, by the above teachings or related art or knowledge. Any changes and variations made by those skilled in the art without departing from the spirit and scope of the present application should be within the scope of the claims of the present application.

Claims

1. A method for calculating physical optical scattering fields based on pixelated projection, characterized in that: The calculation method includes: Step 1: After obtaining the target 3D CAD model, set the corresponding parameters and perform surface projection on the target to generate a projection area; Step 2: Discretize the projection area into pixels and apply curvature constraints, calculate the radiation function of each pixel and construct a radiation image; Step 3: Calculate the oscillation integral for each pixel using a closed-form expression, and then output the total scattering field after calculating it using a GPU parallel architecture. Step two specifically includes the following: B1, will The pixels are evenly divided into m×n rectangular pixels, resulting in a length of ΔL=L / m and a height of ΔH=H / n for each pixel. B2. Calculate the center point of each pixel. Corresponding surface gradient ,like Then the coordinates of the points on the surface are directly associated ( and normal vector ,like Then, the local surface region that does not meet the curvature constraint condition is subdivided and projected. Step three specifically includes the following: C1. Through formula Calculate pixels radiation function ,in, The imaginary unit, For wave number, Represents the phase factor of a spherical wave. The distance from the observation point to the origin. The normal vector of the projection plane is the unit vector. Let be the unit vector in the direction of incident wave propagation. For the incident electric field at a point on the curved surface The value at that location, This represents the z-axis phase modulation term; C2. Calculate the vertical polarization respectively. and horizontal polarization ; C3. Radiation image construction: Mapping to generate amplitude / phase image of R; C4. For each pixel The oscillation integral is obtained by calculating the closed-form expression. ,in, , These are the difference components between the scattered wave vector and the incident wave vector in the x and y directions. These represent the length and width of a pixel, respectively. It is the Singer function. Indicates the first The coordinates of the center point of each pixel on the projection plane Indicates the phase term at the center point; C5, Thread Mapping: Assigns m×n pixels to the GPU thread grid, with each thread processing one pixel; C6. Kernel function execution: computation via threads The contribution of each pixel to the far-field scattering field is obtained and the results are stored in shared memory; C7. Layered Reduction Summation: Parallel reduction summation is used within the thread block to obtain the total scattered field. ； C8, Output dual-polarization scattering field components are and ,in, This represents the vertically polarized scattering field component; Let j represent the horizontally polarized scattering field component, and j denote the j-th pixel. Let represent the vertical polarization component of the radiation function of the j-th pixel. This represents the horizontal polarization component of the radiation function of the j-th pixel. The shape function representing the j-th pixel.

2. The method for calculating physical optical scattering fields based on pixelated projection according to claim 1, characterized in that: Step one specifically includes the following: A1. Obtain the target 3D CAD model; A2. Set the incident wave parameters, including frequency f, wavelength λ, and incident direction. Polarization mode; A3. Set projection parameters, including those along the scattering observation direction. Define the projection plane; A4. Target surface along The direction is orthogonally projected onto the XOY plane to generate the projection area. ; A5. Use the Z-buffer algorithm to retain visible surface points and discard occluded areas; A6. Record the boundary dimensions L and H of the projection area, where L represents the length and H represents the width.

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