A high-order RCM24 electromagnetic scattering calculation method for fast generation of SAR image data

Abstract

The application provides a high-order RCM24 electromagnetic scattering calculation method for fast generation of SAR image data, and relates to the technical field of electric digital data processing and computer simulation, and the method comprises the following steps: step 1, an electromagnetic scattering calculation model of a rough ground surface and a target above the rough ground surface is established, and a calculation region, a spatial grid size, electromagnetic parameters and an electromagnetic wave incidence direction and a polarization mode are set. The application relaxes the time step restriction under the premise of keeping high phase precision, so as to improve the electromagnetic scattering calculation efficiency; secondly, the corresponding numerical wave number is calculated according to the incidence angle, and is substituted into an analytical plane wave expression, so that the incidence wave accurate loading suitable for the RCM24 algorithm is realized; meanwhile, a convolutional perfectly matched layer (CPML) absorbing boundary is constructed, so that the electromagnetic wave at the boundary of the calculation region can be effectively absorbed, the electromagnetic scattering echo data of the rough ground surface and the target above the rough ground surface can be quickly generated, and the electromagnetic scattering echo data can be used for SAR image data generation.

Description

Technical Field

[0001] This invention relates to the field of electronic digital data processing and computer simulation technology, and in particular to a high-order RCM24 electromagnetic scattering calculation method for rapid generation of SAR image data. Background Technology

[0002] Synthetic Aperture Radar (SAR) imaging technology has significant applications in Earth observation, surface parameter inversion, and target detection. To study the electromagnetic wave scattering characteristics of rough surface structures and targets above them, and to generate high-precision SAR echo data, it is typically necessary to establish a numerical model of electromagnetic scattering and perform time-domain calculations of the electromagnetic field. The Finite-Difference Time-Domain (FDTD) method is widely used for simulation analysis of complex surface and target electromagnetic scattering problems due to its advantages such as direct solution of Maxwell's equations, broadband time-domain characteristics, and strong modeling capabilities. However, traditional FDTD methods usually employ second-order time and second-order spatial precision difference schemes, and their time steps are strictly limited by the Courant–Friedrichs–Lewy (CFL) stability condition. To ensure numerical stability, the time step must be less than the stability threshold determined by the spatial grid size. When performing SAR electromagnetic scattering simulations on rough surfaces and targets above them, the traditional FDTD method requires a large number of time step iterations due to the large computational area and long simulation time, resulting in low computational efficiency and difficulty in quickly obtaining high-precision electromagnetic scattering echo data.

[0003] To address the limitation of time steps in traditional FDTD methods, several improved methods have been proposed. For example, implicit FDTD methods (such as ADI-FDTD and CN-FDTD) relax the CFL stability condition to some extent by introducing implicit time discretization schemes, thus allowing for larger time steps. However, these methods typically require solving matrix equations or performing iterative solutions at each time step, resulting in high computational complexity and increased memory consumption and computational overhead. Another type of method reduces numerical dispersion error by increasing the spatial difference order or introducing improved difference operators, such as higher-order FDTD methods, non-standard FDTD methods, and difference methods based on dispersion relation preservation (DRP). These methods can improve the phase accuracy of electromagnetic wave propagation, but in many cases, their stability conditions remain relatively strict, and the improvement in time steps is limited. In recent years, some studies have improved numerical dispersion characteristics and relaxed stability conditions to some extent by introducing higher-order spatial difference terms into the traditional FDTD update equations, thereby improving computational efficiency. However, existing methods may be insufficient in balancing numerical stability, phase accuracy, and computational efficiency, especially in electromagnetic scattering simulations of complex and rough surfaces and SAR imaging, where it is still difficult to achieve both high accuracy and high efficiency in electromagnetic scattering calculations. Summary of the Invention

[0004] This invention provides a high-order RCM24 electromagnetic scattering calculation method for rapid generation of SAR image data. Based on the CM24 framework, a high-order RCM24 difference scheme is constructed by introducing a second-order accurate third-order spatial difference structure into the update equation. While ensuring high phase accuracy, the time step limit is relaxed, thereby improving the efficiency of electromagnetic scattering calculation. At the same time, for the complex incident conditions and open area calculation requirements in SAR simulation, this method can efficiently and accurately establish the electromagnetic scattering model of rough surfaces and targets above them, providing a reliable electromagnetic scattering calculation foundation for the rapid generation of SAR image data.

[0005] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows:

[0006] A high-order RCM24 electromagnetic scattering calculation method for rapid generation of SAR image data, the method comprising:

[0007] Step 1: Establish an electromagnetic scattering calculation model for the rough surface and the target above the rough surface, and set the calculation area, spatial grid size, electromagnetic parameters, electromagnetic wave incident direction and polarization mode.

[0008] Step 2: Based on the electromagnetic scattering calculation model, construct the high-order RCM24 electromagnetic field update equation;

[0009] Step 3: Based on the higher-order RCM24 electromagnetic field update equation and the incident direction of the electromagnetic wave, construct the RCM24 total field-scattered field connection boundary, calculate the corresponding numerical wavenumber according to the incident direction of the electromagnetic wave, substitute the numerical wavenumber into the analytical plane wave expression, and realize the loading of the incident wave in the calculation region.

[0010] Step 4: Based on the high-order RCM24 electromagnetic field update equation, construct a convolution fully matched layer absorbing boundary suitable for the RCM24 algorithm at the boundary of the computational region.

[0011] Step 5: Based on the high-order RCM24 electromagnetic field update equation, incident wave, and convolution fully matched layer absorption boundary, perform time-domain iterative calculation to obtain electromagnetic scattering echo data of the rough surface and the target above the rough surface; output electromagnetic scattering echo data for SAR image data generation.

[0012] The above-described solution of the present invention has at least the following beneficial effects:

[0013] The high-order RCM24 electromagnetic field update equation proposed in this invention relaxes the time step limit while maintaining high phase accuracy, thereby reducing the number of time-domain iterations and improving the computational efficiency of electromagnetic scattering. By constructing a total field-scattered field connection boundary adapted to the RCM24 algorithm and combining it with precise numerical wavenumber derivation to achieve high-precision loading of the incident wave, the incident wave error caused by numerical dispersion mismatch is eliminated from the source, ensuring the phase accuracy of electromagnetic field propagation. A dedicated convolution fully matched layer absorbing boundary is constructed for the differential structure characteristics of the RCM24 algorithm, which can efficiently and fully absorb electromagnetic waves at the boundary of the computational region, reduce the interference of boundary reflection on the calculation results, avoid numerical errors and computational instability caused by reflected waves, and ensure that the true scattering characteristics of rough surfaces and targets above them can be captured in open space electromagnetic propagation simulations. From updating the electromagnetic field equations and loading the incident wave to constructing the absorbing boundary, a complete electromagnetic scattering calculation system fully adapted to the RCM24 algorithm has been formed. The technical solutions of each link cooperate and optimize each other, thus avoiding the drawback of sacrificing one aspect for stability, accuracy and efficiency. The explicit high-precision calculation method replaces the complex matrix solving and iteration process of some implicit methods, reducing computational complexity, memory consumption and computational overhead while maintaining high-precision calculation results. Attached Figure Description

[0014] Figure 1 This is a flowchart illustrating a high-order RCM24 electromagnetic scattering calculation method for rapid generation of SAR image data, provided by an embodiment of the present invention.

[0015] Figure 2 The magnetic field component of the RCM24 method provided in the embodiments of the present invention. Update the difference template.

[0016] Figure 3 This is the numerical dispersion error provided by the embodiments of the present invention.

[0017] Figure 4 The electric field component near the connection boundary provided by the embodiments of the present invention The diagram of the magnetic field components involved in the update is being prepared. Detailed Implementation

[0018] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0019] like Figure 1 As shown, an embodiment of the present invention proposes a high-order RCM24 electromagnetic scattering calculation method for rapid generation of SAR image data. The method includes the following steps:

[0020] Step 1: Establish an electromagnetic scattering calculation model for the rough surface and the target above the rough surface, and set the calculation area, spatial grid size, electromagnetic parameters, electromagnetic wave incident direction and polarization mode.

[0021] Step 2: Based on the electromagnetic scattering calculation model, construct the high-order RCM24 electromagnetic field update equation;

[0022] Step 3: Based on the higher-order RCM24 electromagnetic field update equation and the incident direction of the electromagnetic wave, construct the RCM24 total field-scattered field connection boundary, calculate the corresponding numerical wavenumber according to the incident direction of the electromagnetic wave, substitute the numerical wavenumber into the analytical plane wave expression, and realize the loading of the incident wave in the calculation region.

[0023] Step 4: Based on the high-order RCM24 electromagnetic field update equation, construct a convolution fully matched layer absorbing boundary suitable for the RCM24 algorithm at the boundary of the computational region.

[0024] Step 5: Based on the high-order RCM24 electromagnetic field update equation, incident wave, and convolution fully matched layer absorption boundary, perform time-domain iterative calculation to obtain electromagnetic scattering echo data of the rough surface and the target above the rough surface; output electromagnetic scattering echo data for SAR image data generation.

[0025] In this embodiment of the invention, the proposed high-order RCM24 electromagnetic field update equation relaxes the time step limitation while maintaining high phase accuracy, thereby reducing the number of time-domain iterations and improving the computational efficiency of electromagnetic scattering. By constructing a total field-scattered field connection boundary adapted to the RCM24 algorithm and combining it with precise numerical wavenumber derivation to achieve high-precision loading of the incident wave, the incident wave error caused by numerical dispersion mismatch is eliminated from the source, ensuring the phase accuracy of electromagnetic field propagation. A dedicated convolution fully matched layer absorption boundary is constructed for the differential structure characteristics of the RCM24 algorithm, which can efficiently and fully absorb electromagnetic waves at the boundary of the computational region, reduce the interference of boundary reflection on the calculation results, avoid numerical errors and computational instability caused by reflected waves, and ensure that the true scattering characteristics of rough surfaces and targets above them can be captured in open space electromagnetic propagation simulation. From updating the electromagnetic field equations and loading the incident wave to constructing the absorbing boundary, a complete electromagnetic scattering calculation system fully adapted to the RCM24 algorithm has been formed. The technical solutions of each link cooperate and optimize each other, thus avoiding the drawback of sacrificing one aspect for stability, accuracy and efficiency. The explicit high-precision calculation method replaces the complex matrix solving and iteration process of some implicit methods, reducing computational complexity, memory consumption and computational overhead while maintaining high-precision calculation results.

[0026] In a preferred embodiment of the present invention, step 1 involves establishing an electromagnetic scattering calculation model of the rough surface and the target above the rough surface, and setting the calculation region, spatial grid size, electromagnetic parameters, and electromagnetic wave incident direction and polarization mode, including:

[0027] In this embodiment of the invention, considering the phase accuracy, scene adaptability, and large-scale computational requirements of SAR imaging simulation for electromagnetic scattering data, an integrated electromagnetic scattering numerical calculation model of a rough surface and targets above it is first constructed. During the model construction process, the actual geometric features of the rough surface and the spatial structure features of the targets above it are restored, fully reproducing the distribution of ground features in the actual SAR detection scenario, ensuring that the model is highly matched with the real SAR application scenarios for Earth observation and target detection. After completing the integrated model of the rough surface and targets, based on the core requirements of SAR imaging simulation, such as the preset 3GHz electromagnetic wave frequency band and the corresponding actual detection range of a cubic region of 200Δ×200Δ×200Δ (Δ is the spatial step size), the overall calculation area for electromagnetic scattering is delineated. The delineation principle is to maximize the compression of invalid calculation areas and reduce regional redundancy while ensuring complete coverage of all areas of the rough surface and targets above it without omission, thus balancing the integrity and computational efficiency of electromagnetic scattering calculation and avoiding unnecessary computational consumption. After determining the computational region, based on the actual wavelength of the 3GHz radio wave used in the simulation and the accuracy requirements of SAR imaging for electromagnetic scattering data, a uniform spatial grid size of Δ=0.005m (corresponding to a grid resolution of R=20) was set. This grid size enabled precise discretization of electromagnetic field nodes within the computational region, ensuring that each electromagnetic field node accurately corresponds to its physical location within the computational region. Simultaneously, for the two different media within the computational region—the rough surface and the target above—corresponding electromagnetic parameters were configured, and key parameters characterizing the electromagnetic properties of the media, such as dielectric constant and permeability, were set. This ensured that the electromagnetic properties of different media were realistically reflected in the computational model, guaranteeing the physical accuracy of the electromagnetic scattering calculation. Finally, based on the incident wave angles set in the actual SAR imaging detection—namely, a zenith angle of 39°, an azimuth angle of 59°, and a polarization angle of 45°—the incident direction of the electromagnetic wave in the computational region was precisely determined. Then, combined with the specific requirements of the SAR imaging simulation, the linear polarization mode of the electromagnetic wave was selected, clarifying the vibration directions of the electric and magnetic fields.

[0028] In a preferred embodiment of the present invention, step 2 includes:

[0029] In the CM24 time-stepping formula, a third-order spatial difference term with second-order accuracy, consisting of electric field components, is introduced to obtain the magnetic field components. The RCM24 time-step expression; the magnetic field components The RCM24 time step expression is:

[0030] ;

[0031] in, They are respectively Spatial grid index of orientation, For time step index; In the CM24 method The time step formula for the component; These are the coefficients of the third-order difference term; Indicates the time step; and They are respectively direction and The second-order precision third-order difference operator for direction is defined as follows:

[0032] ;

[0033] ;

[0034] in, and They are respectively direction and Spatial grid step size in the direction; This represents the speed of light in a vacuum.

[0035] The magnetic field components were obtained in the same way. , and electric field components , , The RCM24 time-step expression is derived to construct the complete high-order RCM24 electromagnetic field update equation.

[0036] In this embodiment of the invention, after establishing the electromagnetic scattering calculation model for the rough surface and the target above it, a high-order RCM24 electromagnetic field update equation is constructed based on the traditional finite-difference time-domain (FDTD) calculation framework and the high-order CM24 algorithm. The core is to introduce a high-order difference structure into the CM24 time-step formula to relax the time-step constraint while maintaining the accuracy of the electromagnetic wave propagation phase, and simultaneously ensuring the stability of the numerical calculation. The specific process is as follows: First, the criteria for introducing the difference structure and the basic formula are determined, using the magnetic field components... As the core derivation benchmark, first clarify the CM24 method. The original time step formula for the component is as follows: =CM24, this is the core foundation introduced by the RCM24 difference structure; in this CM24 time step formula, a third-order spatial difference term with second-order accuracy is introduced, consisting of electric field components. This difference term is composed of 8 field points in the (i+1 / 2)th column and (j+1 / 2)th row of the electromagnetic field nodes, which can effectively suppress numerical instability problems when increasing the Coulomb number. The introduced magnetic field components The RCM24 time step expression is:

[0037] ;

[0038] in This part refers to the second-order precision third-order spatial difference term introduced. In the CM24 method The original time step formula term for the component.

[0039] For difference coefficients Targeted optimization was conducted, with the optimization method guided by the core requirements of SAR imaging simulation. Numerical simulation experiments were performed under multiple sets of different Coulomb numbers to test different... The algorithm's numerical dispersion error and stability performance corresponding to the selected values ​​are analyzed, specifically, as the Courant number gradually increases from 0.4 to 1.0, different values ​​are selected... Numerical dispersion error of the RCM24 algorithm was calculated, and the numerical dispersion error curves of the standard FDTD (S22), higher-order FDTD (2,4) (S24), CM24 algorithm, and Sekido methods 1 and 2 were compared to select those that allow the RCM24 algorithm to maintain numerical stability even when the Courant number increases to 1.0. The range of values ​​is then used to select candidate methods with numerical dispersion errors significantly lower than those of existing Sekido methods. The optimal difference coefficients for the RCM24 algorithm were determined by considering both the computational efficiency requirements of actual SAR imaging simulations and the actual values. This achieves a balance between accuracy and efficiency.

[0040] With magnetic field components Based on the derivation logic of the RCM24 time-step expression, and using the same high-order difference structure introduction method, third-order difference operator definition rules, and coefficient constraint criteria, the magnetic field components are sequentially processed. , and electric field components , , The RCM24 time-step formulas for each electromagnetic field component are derived, ensuring that all electromagnetic field component updates use a unified high-order difference framework to guarantee the consistency of electromagnetic field calculations; the derived magnetic field components are then... , , and electric field components , , All RCM24 time-step expressions are integrated to construct a complete high-order RCM24 electromagnetic field update equation. Based on the optimized difference coefficients, this equation can break through the strict limitation of the Courant stability condition of the traditional FDTD method while maintaining high phase accuracy, and effectively relax the time step size, so that the algorithm remains stable when the Courant number increases to 1.

[0041] In this embodiment, the high-order RCM24 electromagnetic field update equation introduces a second-order accurate third-order spatial difference structure on the basis of the CM24 framework. With the coefficient constraint conditions and difference coefficient optimization, the algorithm can still maintain numerical stability when the Courant number increases to 1. Compared with the standard FDTD (S22), high-order FDTD (2,4) (S24) and CM24 algorithms, it effectively relaxes the time step limit, reduces the number of time-domain iterations, and significantly improves the time-domain computation efficiency of electromagnetic fields. Compared with the existing Sekido method 1 and Sekido method 2, under the same condition of increasing the Courant number to 1, the RCM24 algorithm has smaller numerical dispersion error and can guarantee high phase accuracy of electromagnetic wave propagation, solving the problem that traditional improved FDTD methods are difficult to balance stability and phase accuracy. The complete high-order RCM24 electromagnetic field update equation covers all electric and magnetic field components and is suitable for complex electromagnetic scattering calculation scenarios with rough surfaces and targets above them.

[0042] In a preferred embodiment of the present invention, step 3, based on the higher-order RCM24 electromagnetic field update equation and the incident direction of the electromagnetic wave, constructs the RCM24 total field-scattered field connection boundary. The construction of the RCM24 total field-scattered field connection boundary includes:

[0043] Step 300a, for the grid index located in the total field region = or = electric field component at point 1 When updating using the higher-order RCM24 electromagnetic field update equation, the incident wave superposition of the magnetic field components located in the scattering field region is performed in the following manner; for the interface = place The components, including the incident wave components superimposed on the magnetic field components 5, 6, 7, 8, 13, 14, 17, 18, 21, and 22, specifically include:

[0044] When constructing the RCM24 total field-scattered field (TF / SF) connection boundary based on the higher-order RCM24 electromagnetic field update equation and the electromagnetic wave incident direction, the RCM24 algorithm introduces a second-order accurate third-order spatial difference structure on the basis of the CM24 framework. The electromagnetic field update process involves more coupling relationships between adjacent nodes, and the construction logic and operation details of its connection boundary are more complex than the traditional FDTD method. It is not possible to directly use the traditional FDTD total field-scattered field boundary processing method. Therefore, it is necessary to perform targeted incident wave superposition or subtraction correction processing on the electromagnetic field components at the connection boundary and adjacent grids to compensate for the numerical deviation caused by cross-regional field quantity calls, and ensure the continuity and numerical consistency of the field quantities at the boundary between the total field and the scattered field regions. The specific process is as follows: In the defined 200Δ×200Δ×200Δ (Δ=0.005m) electromagnetic scattering cube computational region, the core grid index surface of the total field-scattered field connection boundary is first determined. = This interface is the physical boundary between the total field and the scattered field. The total field region is a 160Δ×160Δ×160Δ cube region at the center of the computational region, and the surrounding region with a thickness of 20Δ is the scattered field region. = This is the key boundary between the total field region and the scattering field region.

[0045] For the main field area = Electric field components at the interface The interface was updated and corrected using the higher-order RCM24 electromagnetic field update equation. During time-step updates, due to the multi-node coupling characteristics of the RCM24 high-order difference structure, updating this electric field component requires calling the magnetic field components of multiple adjacent nodes, including some magnetic field components belonging to the scattering field region. To avoid calculation errors caused by directly calling cross-regional field quantities and to ensure the continuity of field quantities, the magnetic field components 5, 6, 7, 8, 13, 14, 17, 18, 21, and 22 (numbered corresponding to those in the RCM24 electromagnetic field update equation) within the scattering field region involved in the update process are... (Update directly related spatial location nodes) and perform incident wave superposition processing. The superimposed incident wave component is a wave field component consistent with the parameters of the 3GHz time-harmonic plane wave used in the simulation. This component is the incident wave superposition term, whose amplitude, phase and incident wave vector are related. The spatial grid node positions are matched to accurately correspond to the incident wave field characteristics required for the total field region. After the incident wave superposition is completed, the... = Interface The components are updated in time steps according to the RCM24 method, and the update process uses a correction formula. In the formula, This represents the electric field components before the incident wave is corrected. The time-step update results have been completed according to the RCM24 method. For the incident wave superposition term matched with the 3GHz time-harmonic plane wave, this formula organically combines the incident wave superposition correction with the RCM24 time-step update, compensating for numerical differences in cross-regional field quantity calls and ensuring... = Interface The accuracy of component updates.

[0046] Step 301a, for the interface = 1 The components, including the incident wave components superimposed on the magnetic field components 13, 17, and 21, specifically include those located within the total field region and connected to the core boundary. = Directly adjacent = Electric field components at the grid index surface The higher-order RCM24 electromagnetic field update equation is continued for time-step updates. Although this interface is within the total field region, it is still related to the core boundary. = Adjacent, its The component update still requires calling some magnetic field components within the scattering field region. Based on the consistency principle of field quantity correction, to avoid the field quantity discontinuity problem caused by uncorrected adjacent grids, the magnetic field components 13, 17, and 21 in the scattering field region involved in the update are subjected to incident wave superposition processing. The superimposed incident wave components are... = Incident wave superposition terms with completely identical interfaces This ensures the consistency between the correction logic and the field parameters; after superposition, the correction is performed according to the correction formula. = 1 interface The component completion time is updated in steps, that is... In the formula This is the RCM24 time-step update result before incident wave correction. The superposition term of incident waves with the same parameters is achieved through this formula. = 1. Field quantity correction at the interface to maintain the continuity and numerical consistency of the field quantities in the total field region and the scattering field region. Step 302a: For the grid index located in the scattering field region... = electric field component at point 1 When updating the electromagnetic field using the higher-order RCM24 electromagnetic field update equation, the incident wave components are subtracted from the magnetic field components 9, 10, 11, 12, 16, 20, and 24 located in the total field region. The numbering of the magnetic field components corresponds to the values ​​in the higher-order RCM24 electromagnetic field update equation. The spatial positions related to component updates specifically include: those located within the scattering field region and connected to the core boundary. = Directly adjacent = Electric field components at the +1 grid index surface When updating the electric field using the higher-order RCM24 electromagnetic field update equation, the update of this electric field component requires calling some magnetic field components belonging to the total field region. The core calculation requirement for the scattered field region is to retain only the scattered field components of the rough surface and the target above it, necessitating the removal of the original field quantity information of the incident wave. Therefore, the magnetic field components 9, 10, 11, 12, 16, 20, and 24 (numbered corresponding to those in the RCM24 electromagnetic field update equation) within the total field region involved in its update process are... (Update relevant spatial location nodes) and perform incident wave subtraction processing. The subtracted incident wave component is the incident wave subtraction term that is completely consistent with the superposition term of the total field region. To ensure the consistency of field quantity correction values ​​and the accuracy of reverse cancellation; after completing the incident wave subtraction, adjust according to the correction formula. = +1 interface The component completion time is updated in steps, that is... In the formula This is the RCM24 time-step update result before incident wave correction. For incident wave subtraction terms with the same parameters, this formula removes the original incident wave information carried in the magnetic field component of the total field region, ensuring that the field quantity of the scattered field region only includes the scattered wave components of the rough surface and the target above.

[0047] Step 303a involves performing the corresponding incident wave superposition or subtraction processing on the residual electric and magnetic field components located at the connection boundary and adjacent grids using the same method to maintain the continuity and numerical consistency of the field quantities in the total field region and the scattered field region. Specifically, this includes completing the core connection boundary... = and adjacent grids = 1. = Electric field component at +1 After the incident wave superposition / subtraction correction (and the time step update of formulas 4, 5, and 6 is completed), with The correction logic for the components is based on a unified benchmark, employing the same cross-regional field quantity judgment principle, component number correspondence rule, and incident wave correction method. This applies to all remaining electric field components located at the RCM24 total field-scattered field connection boundary and adjacent grids. , ) and magnetic field components ( , , ) Targeted incident wave correction processing is performed sequentially, where the incident wave superposition and subtraction terms are matched with the corresponding electromagnetic field components. , , , , Its parameters correspond to the incident wave vector, polarization mode, and spatial node position of the 3GHz time-harmonic plane wave.

[0048] For all nodes within the total field area that require the use of the electromagnetic field components of the scattered field region, the incident wave superposition term matching the component type is precisely superimposed in the corresponding electromagnetic field components of the scattered field region. , , , , To compensate for numerical deviations in cross-regional field quantity calls, the update is completed according to the RCM24 time step formula for the corresponding electromagnetic field component after correction, and the update format is uniformly set as follows: ( For all nodes within the scattered field region that require the use of the total field region electromagnetic field components, the incident wave subtraction term matching the component type is precisely deducted from the corresponding total field region electromagnetic field component. , , , , After removing the original incident wave field quantity information, ensuring that the scattered field region contains only the scattered wave component, the correction is also completed according to the RCM24 time step formula for the corresponding electromagnetic field component. The update format is uniformly as follows: ( (For the corresponding electromagnetic field components).

[0049] In the magnetic field component ( , , During the update process, for all magnetic field components at the boundary between the total field and the scattered field regions, the electric field components involved in the update are subjected to corresponding incident wave superposition or subtraction processing according to the above rules. Then, the corrected electric field components are substituted into the RCM24 magnetic field component time step expression (e.g., ...). The field quantity is updated using the RCM24 time-step formula, thus maintaining the consistency and stability of the electromagnetic field update at the connection boundary. By comprehensively and uniformly correcting all electromagnetic field components, the incident wave superposition term, subtraction term and the corresponding RCM24 time-step formula of each component are deeply combined to complete the update, realizing the seamless connection of all field quantities in the total field region and the scattered field region at the connection boundary, maintaining the continuity and numerical consistency of the field quantities in the two regions, ensuring the solution accuracy of the high-order RCM24 electromagnetic field update equation at the connection boundary, and effectively avoiding the interference caused by the discontinuity of the boundary field quantity on the subsequent 3GHz time-harmonic plane wave incident wave propagation calculation. Numerical experiments have verified that this correction method can ensure that, under the condition of Courant number C=1.00, the incident wave propagates in the total field region without any leakage to the scattered field region.

[0050] This embodiment addresses the multi-node coupling characteristics of the higher-order differential structure in the RCM24 algorithm by specifically designing a correction rule for the electromagnetic field components at the connection boundary between the total field and the scattered field. This solves the problem of poor adaptability of the traditional FDTD connection boundary method in the RCM24 algorithm, achieving accurate separation of the total field and the scattered field under higher-order algorithms. Following the principle of superimposing the incident wave in the total field region and subtracting the incident wave in the scattered field region, scene-specific corrections are applied to the electromagnetic field components of the core surface of the connection boundary and adjacent grids. This effectively avoids numerical deviations caused by cross-regional field quantity calls, ensuring the continuity and numerical consistency of the field quantities at the connection boundary. Using components as a benchmark, a unified correction is achieved for all electromagnetic field components, ensuring the integrity of the correction logic for the connection boundary between the total RCM24 field and the scattered field, and avoiding interference from discontinuities in boundary field quantities on the calculation of incident wave propagation. The magnetic field component numbers precisely correspond to the spatial positions of the higher-order RCM24 electromagnetic field update equations, making the correction operations for incident wave superposition and subtraction more targeted, reducing numerical calculation errors at the connection boundary, and improving the overall accuracy of electromagnetic scattering calculations.

[0051] In another preferred embodiment of the present invention, the numerical wavenumber corresponding to the incident direction of the electromagnetic wave is calculated, and the numerical wavenumber is substituted into the analytical plane wave expression to realize the loading of the incident wave in the calculation region. The realization of the loading of the incident wave in the calculation region includes:

[0052] Step 300b: Based on the higher-order RCM24 electromagnetic field update equation, solve the RCM24 numerical dispersion relation using the Newton-Raphson iteration method to obtain the numerical wavenumber corresponding to the electromagnetic wave incident direction. Specifically, this includes: based on the already constructed higher-order RCM24 electromagnetic field update equation, combined with the electromagnetic wave incident direction set by SAR imaging simulation (… =39° =59° =45°, where For the zenith angle, For azimuth, (where the polarization angle is used) to solve the numerical dispersion relation of the RCM24 algorithm. Since the RCM24 algorithm uses a second-order accurate third-order central difference scheme, its corresponding numerical dispersion relation is a nonlinear transcendental equation, which cannot be solved directly analytically. Therefore, the Newton iteration method is used for high-precision numerical solution. The specific process is as follows: First, define the RCM24 three-dimensional numerical dispersion equation and the Newton iteration objective function. The expression for the RCM24 three-dimensional numerical dispersion relation is:

[0053] ;

[0054] ;

[0055]

[0056] ;

[0057] ;

[0058] ;

[0059] ;

[0060] in, ,and , , , These are the higher-order difference coefficients of the original CM24; this dispersion relation must satisfy the RCM24 difference coefficient constraint condition: In the formula, =2 Electromagnetic wave angular frequency ( =3GHz). Let be the Courant number. For time step, =0.005m is the spatial grid step size. , , For numerical wavenumber components, These are the coefficients of the third-order difference term; combined with the correspondence between the incident direction of the electromagnetic wave and the wave number component. , , Substituting the wavenumber components into the dispersion equation, we further construct and explicitly give the coupling function between the Newton iteration objective function and the spatial difference function. , .

[0061] Among them, the spatial difference coupling function The formula is:

[0062] ;

[0063]

[0064] ;

[0065]

[0066] ;

[0067] ;

[0068] ;

[0069] Set initial values ​​for iteration and a convergence accuracy threshold, and select the free-space physical wavenumber. As the initial value for Newton's iteration, and at the same time, the iteration accuracy threshold is set to... This accuracy fully meets the ultra-high phase accuracy calculation requirements for SAR imaging simulation; based on this, Newton's iterative solution is performed according to the standard iterative format. Perform iterative calculations. Indicates the first Wavenumber in the next iteration The corresponding function value, Describe the objective function exist The first derivative at that point, Indicates the first The numerical wavenumber approximation obtained in the second iteration Indicates the first The numerical wavenumber approximation is updated in each iteration, and the wavenumber value is continuously updated until the wavenumber results obtained in two consecutive iterations satisfy the condition. When the iteration converges, the calculation stops; the final output is the RCM24 numerical wavenumber that matches the incident direction. The iteration convergence result is defined as the RCM24 numerical wavenumber that completely corresponds to the set electromagnetic wave incident direction. This numerical wavenumber can be adapted to higher-order RCM24 structures, eliminating computational errors caused by numerical dispersion mismatch at the source.

[0070] Step 301b involves substituting the numerical wavenumber into the analytical plane wave expression and, in conjunction with the RCM24 total field-scattered field boundary, loading the incident wave into the computational domain. Specifically, after obtaining the RCM24 numerical wavenumber obtained in step 300b, this numerical wavenumber is used as the core parameter, combined with the constructed RCM24 total field-scattered field boundary, to accurately load the 3 GHz time-harmonic plane wave into the computational domain. The specific process is as follows: First, the analytical expression for the three-dimensional time-harmonic plane wave is defined, and the electric field incident wave expression is... The expression for the incident wave of a magnetic field is: ,Mode For RCM24 numerical wave vectors, For free space wave impedance, Spatial grid coordinates, For time variables, Let be the incident electric field intensity vector, and be the spatial position. and time The function, The polarization amplitude of the incident wave, The incident magnetic field strength vector is the spatial position. and time The function; the numerical wavenumber obtained by solving Substituting the above expression, we can obtain the incident wave field expression that is fully adapted to the RCM24 algorithm, ensuring the consistency of numerical dispersion between the incident wave and the computational region.

[0071] To ensure the stability of the incident wave loading, virtual source point timing calibration was performed based on the electromagnetic wave incident direction. , Determine the spatial location of the virtual source point, and use this to calculate the incident wave delay time at each grid node on the boundary between the total field and the scattered field, ensuring... At time 0, the incident wave field quantity at all nodes is 0, enabling the incident wave to be smoothly and continuously injected into the total field region along the set direction. Finally, the incident wave loading is completed by combining the total field-scattered field (TF / SF) connection boundary. Using the 200Δ×200Δ×200Δ (Δ=0.005m) electromagnetic scattering calculation region and the central 160Δ×160Δ×160Δ total field region as the carrier, the adapted plane wave field quantity expression is substituted into the connection boundary field quantity correction rule. That is, the field quantity of the total field boundary node is the sum of the RCM24 update value and the incident wave superposition term, and the field quantity of the scattered field boundary node is the difference between the RCM24 update value and the incident wave subtraction term. Finally, the incident wave is accurately loaded in the calculation region without reflection or leakage.

[0072] In this embodiment, the Newton-Raphson iteration method is used to solve the numerical dispersion relation of RCM24. The high-order difference characteristics of the numerical wavenumber matching algorithm obtained by replacing the traditional physical wavenumber effectively ensure the consistency of numerical dispersion between the incident wave and the RCM24 computational region, reducing the incident wave error caused by numerical dispersion mismatch. The timing loading of the incident wave is realized by combining virtual source points, ensuring the consistency of the incident wave propagation timing at the connection boundary and avoiding the calculation deviation caused by abrupt changes in field quantities. At the same time, based on the loading foundation of the RCM24 total field-scattered field connection boundary, leakage-free loading of the incident wave is realized. Experiments have verified that leakage in the unidirectional scattering field region of the incident wave in the total field region is eliminated under the condition of Courant number C=1.00. The adapted analytical plane wave expression is highly matched with the simulation requirements of 3GHz time-harmonic plane waves. Combined with accurate numerical wavenumbers and loading methods, high-precision loading of the incident wave in the computational region is achieved, improving the phase accuracy of the overall electromagnetic scattering calculation.

[0073] In a preferred embodiment of the present invention, constructing the convolutionally perfectly matched layer absorbing boundary suitable for the RCM24 algorithm includes:

[0074] Step 400: Based on the frequency domain coordinate stretching, a complex frequency shift stretching operator containing complex frequency shift parameters is defined, and it is transformed into a time domain discrete form using the recursive convolution method. A discrete scheme matching the higher-order RCM24 electromagnetic field update equation is then derived. For the electric field components... The RCM24 update equation in the CPML region is obtained as follows:

[0075] ;

[0076] in, Indicates the first electric field strength at each time step Quantity, Indicates the first electric field strength at each time step Quantity, Indicates the first Magnetic field strength at each time step Quantity, Indicates the first Magnetic field strength at each time step Quantity, For time step, Where is the dielectric constant. and They are respectively direction and The coordinate scaling factor of the direction. and They are respectively direction and Spatial difference operator of direction, It corresponds to the electric field component exist Auxiliary variables for recursive convolution in the direction, It corresponds to the electric field component exist The update expression for the recursive convolution auxiliary variable in the direction is:

[0077] ;

[0078] ;

[0079] Among them, coefficient Determined by CPML parameters, which include the conductivity distribution function Coordinate scaling factor Complex frequency shift parameters polynomial order Absorbing layer thickness And the depth of CPML The specific relationship is as follows:

[0080] , , ;

[0081] in, It is the vacuum permittivity; This is the coordinate direction index, with a value of or ; In a rectangular coordinate system direction; In a rectangular coordinate system direction; for The conductivity distribution function in the direction, , for Maximum conductivity in the direction for The coordinate scaling factor of the direction. , for Maximum coordinate scaling factor in the direction; For complex frequency shift factor, , for directional maximum complex frequency shift factor; is the base of the natural logarithm;

[0082] Step 401: Obtain the magnetic field components using the same method. , , and electric field components , The update equations in the CPML region are used to construct the complete convolutional fully matched layer absorbing boundary suitable for the RCM24 algorithm.

[0083] In this embodiment of the invention, to accurately simulate the reflection-free electromagnetic propagation environment in open space, based on the complex frequency domain coordinate stretching theory and recursive convolution method, the CPML absorbing boundary update equation, which perfectly matches the higher-order RCM24 electromagnetic field update equation, is derived. The entire derivation process is based on the frequency domain Maxwell's curl equation, the expression of which is: ;in It is the electric field intensity vector. It is the magnetic field strength vector. It is a coordinate stretching operator. Imaginary unit, It is the angular frequency of electromagnetic waves. It is the magnetic permeability of the medium. It is the dielectric constant of the medium. First, a frequency domain coordinate stretching transformation is performed, and the CPML coordinate scaling function is defined. In the formula Represents a rectangular coordinate system In any direction, This is the coordinate scaling factor. For electrical conductivity, The complex frequency shift factor; the conventional spatial partial derivative operator in Cartesian coordinates in the original Maxwell curl equations. It can be directly replaced by the partial derivative operator in the frequency domain stretched coordinates. This paper completes the transformation of Maxwell's curl equation from the conventional coordinate system to the CPML stretched coordinate system, enabling electromagnetic waves to gradually attenuate along the stretched coordinate direction as they propagate to the boundary of the computational region, achieving reflection-free asymptotic absorption. Based on this, the frequency-domain coordinate stretching function is transformed to the time domain using an inverse Fourier transform. The convolution terms generated in the time domain are discretized using recursive convolution, ultimately transforming the frequency-domain coordinate stretching in the absorbing boundary region into an iterable recursive convolution form in the time domain. The coordinate stretching function is then expanded into a frequency-domain fractional form. direction( Taking the example of a absorbing boundary, the reciprocal of the scaling function can be expressed as: ,in, This fractional form clearly demonstrates the combined effect of the coordinate scaling factor, conductivity, and complex frequency shift factor on the absorption characteristics. Performing an inverse Fourier transform on the above frequency-domain fractional operator transforms it from the frequency domain to the time domain, yielding a time-domain convolution integral form. Taking the correlation of electric field components in the absorption boundary region as an example, the result after the inverse transform is:

[0084] ;

[0085] In the formula, For frequency domain field quantities, For the corresponding time-domain field quantity, This represents the inverse Fourier transform operator, where the integral term is the core of the time-domain convolution, reflecting the time-domain cumulative effect of the absorption characteristics. This is the integration variable in the time-domain convolution integral.

[0086] To avoid the temporal convolution integral depending on all historical data, the integral term is approximated as a recursive iterative format; this is achieved by discretizing the time step. Let the first The convolution result at time step is Then the first The convolution result at time step 1 can be represented as follows: Only the convolution result from the previous time step needs to be retained. and the current field volume This allows for the update of the convolution term at the current time step without storing all historical field data, thus reducing computational complexity. Through the above-described formulaic transformation process, it absorbs the convolution integral terms generated in the boundary region from the frequency domain to the time domain, which are difficult to process directly, and successfully transforms them into recursive convolution discrete iteration terms that can be embedded in the RCM24 time-domain update process. This allows the CPML absorption characteristics to be seamlessly integrated into the time-domain iterative update process of the higher-order RCM24 electromagnetic field, ensuring the compatibility of the absorption boundary with the higher-order difference algorithm. Based on this, the following derivation is made... The RCM24 update equation for the components in the CPML region, combined with the characteristics of the RCM24 higher-order difference scheme, is used to... Directional electric field components Taking this as the research object, we finally obtained its complete update formula within the CPML region. =16.67ps (Courant number C=1.00), while determining the update formula for the recursive convolution term, and finally clarifying the quantitative relationship between CPML coefficients and core parameters.

[0087] The CPML update equations for the remaining electric field components are derived, using the same method as... The electric field components are obtained using a completely consistent frequency domain coordinate stretching and recursive convolution transformation method. In the CPML region, the RCM24 update equations are used to ensure that each equation precisely matches the spatial difference operator, coordinate scaling factor, and recursive convolution term in the corresponding direction. Then, the CPML update equations for all magnetic field components are derived, following the duality of Maxwell's curl equations, to complete the magnetic field component update. , The derivation of the RCM24 update equations in the CPML region ensures that the update equations for all electromagnetic field components satisfy the electromagnetic conservation relations. After completing the derivation of all components, the complete set of CPML-RCM24 update equations is integrated. , The CPML region update formula is unified and integrated, and combined with the spatial grid step size Δ=0.005m, the core parameters of CPML are set, including the absorption layer thickness, polynomial order, maximum conductivity, and complex frequency shift factor. Finally, a high-performance CPML absorbing boundary is constructed that covers the entire outer boundary of the 200Δ×200Δ×200Δ computational region, is fully compatible with the high-order RCM24 algorithm, and is reflection-free, thus realizing the absorption of electromagnetic waves emitted from the boundary of the computational region.

[0088] This embodiment, targeting the high-order differential characteristics of the RCM24 algorithm, constructs the CPML absorbing boundary through frequency domain coordinate stretching and recursive convolution. The derived update equation perfectly matches the high-order RCM24 electromagnetic field update equation, solving the problem of poor compatibility between traditional PML and high-order FDTD algorithms, and realizing the simulation of electromagnetic propagation in open space under the RCM24 algorithm; Based on this, the CPML update equations for all electromagnetic field components are derived, and a complete absorbing boundary system is constructed. Combined with reasonably set CPML parameters, it can effectively absorb electromagnetic waves at the boundary of the computational region, including low-frequency waves and evanescent waves, reducing the impact of boundary reflection on the electromagnetic scattering calculation results. The absorption characteristics of CPML are integrated into the time-domain iteration process of RCM24, and the update of the recursive convolution term is synchronized with the time-step update of the electromagnetic field components without adding additional computational complexity, balancing absorption effect and computational efficiency, while ensuring the numerical stability of electromagnetic scattering simulation. The complete CPML absorbing boundary covers all outer boundaries of the computational region, effectively eliminating boundary reflection errors, making the calculation results more consistent with the electromagnetic scattering characteristics of actual open space, and improving the calculation accuracy of electromagnetic scattering echo data of rough surfaces and targets above them.

[0089] In a preferred embodiment of the present invention, step 5 involves performing a time-domain iterative calculation based on the high-order RCM24 electromagnetic field update equation, the incident wave, and the absorption boundary of the convolutionally perfectly matched layer to obtain electromagnetic scattering echo data of the rough surface and the target above the rough surface; outputting the electromagnetic scattering echo data for SAR image data generation. The time-domain iterative calculation includes:

[0090] The high-order RCM24 electromagnetic field update equation is adopted, the incident wave is used as the excitation source, and a convolutional fully matched layer is used to absorb the boundary at the boundary of the computational region. The electromagnetic scattering calculation model containing the rough surface and the target above the rough surface is iterated in time step, and the electromagnetic field value at each time step is recorded until the preset simulation time is reached. Finally, the electromagnetic scattering echo data of the rough surface and the target above the rough surface are extracted.

[0091] In this embodiment of the invention, an integrated electromagnetic scattering calculation model of a rough surface and an above-ground target, which completes the reconstruction of geometric morphology, spatial structure, and electromagnetic parameters, serves as the core carrier. This model defines a 200Δ×200Δ×200Δ (Δ=0.005m) cubic electromagnetic scattering calculation region, with a central 160Δ×160Δ×160Δ region as the total field area, surrounded by a 20Δ-thickness scattering field region. Furthermore, key electromagnetic parameters such as dielectric constant and permeability are precisely configured according to the medium characteristics of the rough surface and the target. A 3GHz time-harmonic plane wave, obtained through numerical wavenumber replacement and virtual source timing calibration using the Newton iteration method, is used as the iterative excitation source. This incident wave has been... =39° (zenith angle) =59° (azimuth angle) An incident direction of 45° (polarization angle) achieves accurate loading in the total field region without leakage into the scattering field region. Simultaneously, CPML absorbing boundaries are activated on all outer boundaries of the computational domain. The update equations for these boundaries perfectly match the RCM24 high-order difference structure, and the conductivity distribution function has been appropriately set based on a mesh step size Δ=0.005m. Key parameters such as absorption layer thickness, polynomial order, and complex frequency shift factor are considered, demonstrating efficient electromagnetic wave absorption capabilities. After initializing all physical models and excitation sources, the electric field components of all grid nodes within the computational region are calculated. , , ) and magnetic field components ( , , The initial value of each step is set to zero, and the time step index for time-domain iteration is set. It starts from 0 and increases sequentially.

[0092] Based on the requirements of SAR imaging simulation for the temporal span and phase integrity of electromagnetic scattering echo data, the overall simulation duration is preset based on the standard that the incident wave starts from the loading start position, completely covers the 200Δ×200Δ×200Δ calculation area, and completes sufficient electromagnetic interaction with the rough surface and the target above, producing a stable scattering response. The time step is determined after optimization using the RCM24 algorithm. =16.67 ps (Courant number C=1.00, (Total simulation duration ÷ Single time step) The conversion method is used to obtain the total number of steps in this time-domain iteration. The iteration termination condition is defined as the time step index increasing to the preset total number of steps. This ensures that the iteration process can fully capture the propagation, reflection, refraction, and scattering of the incident wave with the rough surface and target within the calculation area, avoiding problems such as missing scattered echo data and incomplete phase information caused by insufficient simulation time or insufficient iteration steps.

[0093] Following the RCM24 algorithm's time-domain update logic of first electric field, then magnetic field, and global update followed by boundary correction, the electromagnetic field components are updated cyclically step by step, with time step index n as the reference. The specific operation process within each time step follows the core requirements of the high-order RCM24 electromagnetic field update equation, ensuring the accuracy and coupling consistency of the field quantity updates. The global update of the electric field components is based on the complete high-order RCM24 electromagnetic field update equation, calculating the magnetic field components of all grid nodes in the region from the previous time step (time n). , , Based on the instantaneous value, the electric field components at the current time step (time n+1) are updated node by node. , , The update process strictly adheres to the definition of the third-order spatial difference operator, the constraint conditions of the difference coefficients, and the difference coefficients optimized by numerical dispersion error in the RCM24 algorithm to ensure the phase accuracy of the electric field component update while also considering numerical stability. The global coupled update of the magnetic field component is performed after the electric field component updates of all grid nodes are completed, using the updated electric field component at the current time step (time n+1). , , Based on this, the RCM24 time step expression corresponding to each magnetic field component is used to update the magnetic field component of the current time step node by node. , , This enables coupled updates of the electric and magnetic field components, adhering to the physical laws of Maxwell's curl equations to ensure consistency in the updates of the electromagnetic field components. Real-time correction of the total field-scattered field boundary is performed during the global update of the electric and magnetic field components, adjusting the total field-scattered field boundary and adjacent grids. The field quantity at the location is synchronously corrected in real time; according to the boundary correction rule, the electromagnetic field components of the scattered field region involved in the update of the boundary nodes of the total field region are superimposed with the corresponding incident wave term; the electromagnetic field components of the total field region involved in the update of the boundary nodes of the scattered field region are deducted from the corresponding incident wave term to ensure the continuity and numerical consistency of the field quantity at the connection boundary and avoid calculation deviations caused by cross-regional field quantity calls; the CPML absorbing boundary region-specific update is for all grid nodes within the CPML absorbing boundary outside the computational region. Its electromagnetic field component update does not use the globally universal RCM24 electromagnetic field update equation, but uses the CPML update equation adapted to the RCM24 high-order difference structure. During the update process, the real-time iteration of the recursive convolution term is used ( • Corresponding field quantity), the absorption characteristics of coordinate stretching are incorporated into the time-domain iteration to achieve progressive, non-reflective absorption of electromagnetic waves emitted at the boundary, reducing the interference of boundary reflection on the calculation of internal field quantity and ensuring the numerical stability of the iteration process.

[0094] After all the electric and magnetic field component updates and boundary correction operations are completed at each time step, the instantaneous values ​​of the electric and magnetic field components of all grid nodes in the computational domain are fully recorded and stored. During the recording process, refined key control is implemented. In addition to the global field quantity data, the field quantity data of the rough surface, target surface and surrounding adjacent grid nodes in the total field region are recorded in detail to capture the interaction details between the incident wave and the scattering body. At the same time, the field quantity data of the preset observation points in the scattering field region are recorded simultaneously, including the near excitation source observation point P1 (25Δ, 25Δ, 50Δ) and the far excitation source observation point P2 (175Δ, 175Δ, 50Δ), to ensure that the propagation process of the incident wave in the computational domain and the scattering interaction process with the rough surface and target are fully preserved in the full time domain field quantity response. When the time step index increases to the preset total number of steps of 8000, the time-domain step iteration calculation is immediately stopped. Based on the recorded and stored full-time-domain, full-grid electromagnetic field raw data, the electromagnetic scattering echo data is accurately extracted and its format is converted. First, the pure scattering field is extracted using the time-domain field quantity subtraction algorithm, and the total field value of each observation point and each time step is calculated. Given the magnitude of the incident wave field, i.e. according to The calculation rules precisely remove the original field quantity information of the incident wave from the original field quantity data, retaining only the scattered field component data generated by the scattering of the incident wave by the rough surface and the target above, ensuring the purity of the extracted data; among which Represents the scattered electric field intensity vector. Represents the total electric field intensity vector. Represents the incident electric field intensity vector. Represents the vector of scattered magnetic field intensity. Represents the total magnetic field strength vector. This represents the incident magnetic field strength vector. Considering the actual detection requirements of SAR imaging, the extracted scattered field time-domain data is standardized and converted, and the echo amplitude is calculated by taking the square root of the time-domain amplitude. The echo phase is calculated using the arctangent of the time-domain signal. The discrete-time series is directly extracted as a time-domain waveform, and the scattering coefficient is calculated by the square of the ratio of the scattered field amplitude to the incident wave amplitude. ;in , , Let x, y, and z represent the components of the scattered electric field in the x, y, and z directions, respectively, and As represent the amplitude of the scattered field. It represents the incident wave amplitude; by integrating all characteristic parameters into electromagnetic scattering echo data that conforms to the standard format for generating SAR image data, complete and accurate electromagnetic scattering echo data of the rough surface and the target above it can be directly used for SAR image data generation or SAR imaging processing.

[0095] This embodiment, based on the complete high-order RCM24 algorithm system and combined with incident wave excitation and high-performance CPML absorbing boundary, realizes the full-process time-domain simulation of electromagnetic scattering from rough surfaces and targets. The iterative process strictly follows the physical laws of electromagnetic propagation, ensuring the authenticity and reliability of the scattered echo data. The time step is widened to 16.67 ps, reducing the number of time-domain iterations compared to the traditional FDTD method, improving the computational efficiency of electromagnetic scattering while maintaining phase accuracy. Boundary correction and absorption mechanisms are applied simultaneously during the iteration process, effectively avoiding numerical errors caused by incident wave leakage and boundary reflection, ensuring that the extracted scattered echo data only contains the scattering response of rough surfaces and targets, improving data purity and computational accuracy. Recording full-time electromagnetic field data and selectively extracting scattered echoes can provide rich and accurate raw data support for SAR image data generation, meeting the core requirements of SAR imaging for phase accuracy and temporal integrity of electromagnetic scattering data.

[0096] like Figure 2 As shown, the magnetic field components of the RCM24 method provided in the embodiment In the updated differential template diagram, the differential template is located in the xy plane, and the electric field components... Distributed along the x-direction; electric field components Distributed along the y-direction; magnetic field components Located at the center of the grid cell. The grid nodes containing the electromagnetic field components are represented using half-integer indices, including but not limited to: , , , In the attached diagram, solid and dashed lines represent different integration loops in the CM24 method; solid arrows represent magnetic field components in the CM24 method. The electric field components involved in updating the difference template; hollow arrows indicate the RCM24 method in the magnetic field components. The electric field components involved in the second-order precision third-order spatial difference terms introduced during the update process.

[0097] like Figure 3 As shown in the figure, the numerical dispersion error diagram provided in the embodiment uses the Courant number as the horizontal axis and the global numerical dispersion error (represented on a logarithmic scale) as the vertical axis. The figure compares the error variations of the S22 method, S24 method, CM24 method, Sekido format 1, Sekido format 2, and the RCM24 method proposed in this invention. Figure 3 It is evident that within a relatively small Courant number range, the errors of both the CM24 and RCM24 methods remain at a low level. Furthermore, the RCM24 method proposed in this invention can still maintain a low level of numerical dispersion error under larger Courant numbers, especially in the region where the Courant number is close to 1, where its error is significantly lower than that of the comparative methods, indicating that this method has superior error control capability under high Courant numbers.

[0098] like Figure 4 As shown, the embodiment provides electric field components near the connection boundary. The updated schematic diagram of the magnetic field components involved in the Chinese side shows the electric field components at the boundary between the total field region and the scattered field region. The update involves the distribution of magnetic field components. For example... Figure 4 As shown, the computational region is spatially divided into a total field region and a scattered field region along the z-direction, wherein the region located in... The region above and above is the scattering field region, located in The area below it constitutes the total field area. The connecting boundary is located at... At the location. Near the connection boundary, in order to realize the electric field component. The update incorporates magnetic field components from multiple neighboring grid nodes into the calculation. Wherein: [the following is a list of components] is marked as [the following]. to The nodes represent the magnetic field components that participate in the update. Marked as to The nodes represent the magnetic field components that participate in the update. Furthermore, the arrows in the attached diagram indicate the direction of the corresponding magnetic field component in updating the electric field component. The direction of the time difference action, the magnetic field components at different locations are combined to form a spatial difference term.

[0099] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A high-order RCM24 electromagnetic scattering calculation method for rapid generation of SAR image data, characterized in that, The method includes: Step 1: Establish an electromagnetic scattering calculation model for the rough surface and the target above the rough surface, and set the calculation area, spatial grid size, electromagnetic parameters, electromagnetic wave incident direction and polarization mode. Step 2: Based on the electromagnetic scattering calculation model, construct the high-order RCM24 electromagnetic field update equation; Step 3: Based on the higher-order RCM24 electromagnetic field update equation and the incident direction of the electromagnetic wave, construct the RCM24 total field-scattered field connection boundary, calculate the corresponding numerical wavenumber according to the incident direction of the electromagnetic wave, substitute the numerical wavenumber into the analytical plane wave expression, and realize the loading of the incident wave in the calculation region. Step 4: Based on the high-order RCM24 electromagnetic field update equation, construct a convolution fully matched layer absorbing boundary suitable for the RCM24 algorithm at the boundary of the computational region. Step 5: Based on the high-order RCM24 electromagnetic field update equation, incident wave, and convolution fully matched layer absorption boundary, perform time-domain iterative calculation to obtain electromagnetic scattering echo data of the rough surface and the target above the rough surface; output electromagnetic scattering echo data for SAR image data generation. Step 2 includes: In the CM24 time-stepping formula, a third-order spatial difference term with second-order accuracy, consisting of electric field components, is introduced to obtain the magnetic field components. The RCM24 time step expression; The magnetic field components were obtained in the same way. , and electric field components , , The RCM24 time-step expression is derived to construct the complete high-order RCM24 electromagnetic field update equation; The magnetic field component The RCM24 time step expression is: ； in, They are respectively Spatial grid index of orientation, For time step index; In the CM24 method The time step formula for the component; These are the coefficients of the third-order difference term; Indicates the time step; and They are respectively direction and The second-order precision third-order difference operator for direction is defined as follows: ； ； in, and They are respectively direction and Spatial grid step size in the direction; This represents the speed of light in a vacuum.

2. The high-order RCM24 electromagnetic scattering calculation method for rapid generation of SAR image data according to claim 1, characterized in that, The construction of the RCM24 total field-scattered field connection boundary includes: For grid index located in the total field area = or = electric field component at point 1 When updating the electromagnetic field using the higher-order RCM24 electromagnetic field update equation, the incident wave superposition of the magnetic field components located in the scattering field region is performed in the following manner: For the interface = place The components are superimposed on the incident wave components, which are the magnetic field components 5, 6, 7, 8, 13, 14, 17, 18, 21, and 22 involved. For the interface = 1 The components are the incident wave components superimposed on the magnetic field components 13, 17, and 21 involved. For grid index located in the scattering field region = electric field component at point 1 When updating the electromagnetic field using the higher-order RCM24 electromagnetic field update equation, the incident wave component is deducted from the magnetic field components 9, 10, 11, 12, 16, 20, and 24 located in the total field region. The numbering of the magnetic field components corresponds to the information in the higher-order RCM24 electromagnetic field update equation. Spatial location related to component updates; The residual electric and magnetic field components located at the connection boundary and adjacent grids are superimposed or subtracted from the incident waves in the same way to maintain the continuity and numerical consistency of the field quantities in the total field region and the scattered field region.

3. The high-order RCM24 electromagnetic scattering calculation method for rapid generation of SAR image data according to claim 2, characterized in that, The loading of the incident wave in the computational region includes: Based on the higher-order RCM24 electromagnetic field update equation, the numerical dispersion relation of RCM24 is solved by Newton's iteration method to obtain the numerical wavenumber corresponding to the incident direction of the electromagnetic wave. Substitute the numerical wavenumber into the analytical plane wave expression, and combine it with the RCM24 total field-scattered field connection boundary to load the incident wave in the computational domain.

4. The high-order RCM24 electromagnetic scattering calculation method for rapid generation of SAR image data according to claim 3, characterized in that, The construction of the convolutionally perfectly matched layer absorbing boundary suitable for the RCM24 algorithm includes: Based on frequency domain coordinate stretching, a complex frequency shift stretching operator incorporating complex frequency shift parameters is defined. This operator is then transformed into a time-domain discrete form using recursive convolution, and a discrete scheme matching the higher-order RCM24 electromagnetic field update equation is derived. For the electric field components... Thus, its RCM24 update equation in the CPML region is obtained; The magnetic field components were obtained in the same way. , , and electric field components , The update equations in the CPML region are used to construct the complete convolutional fully matched layer absorbing boundary suitable for the RCM24 algorithm.

5. The high-order RCM24 electromagnetic scattering calculation method for rapid generation of SAR image data according to claim 4, characterized in that, The RCM24 update equation in the CPML region is: ； in, Indicates the first electric field strength at each time step Quantity, Indicates the first electric field strength at each time step Quantity, Indicates the first Magnetic field strength at each time step Quantity, Indicates the first Magnetic field strength at each time step Quantity, For time step, Where is the dielectric constant. and They are respectively direction and The coordinate scaling factor of the direction. and They are respectively direction and Spatial difference operator of direction, It corresponds to the electric field component exist Auxiliary variables for recursive convolution in the direction, It corresponds to the electric field component exist The update expression for the recursive convolution auxiliary variable in the direction is: ； ； Among them, coefficient Determined by CPML parameters, which include the conductivity distribution function Coordinate scaling factor Complex frequency shift parameters polynomial order Absorbing layer thickness And the depth of CPML The specific relationship is as follows: ， ， ； in, It is the vacuum permittivity; This is the coordinate direction index, with a value of or ; In a rectangular coordinate system direction; In a rectangular coordinate system direction; for The conductivity distribution function in the direction, , for Maximum conductivity in the direction for The coordinate scaling factor of the direction. , for Maximum coordinate scaling factor in the direction; For complex frequency shift factor, , for directional maximum complex frequency shift factor; is the base of the natural logarithm.

6. The high-order RCM24 electromagnetic scattering calculation method for rapid generation of SAR image data according to claim 5, characterized in that, The time-domain iterative calculation includes: The high-order RCM24 electromagnetic field update equation is adopted, the incident wave is used as the excitation source, and a convolutional fully matched layer is used to absorb the boundary at the boundary of the computational region. The electromagnetic scattering calculation model containing the rough surface and the target above the rough surface is iterated in time step, and the electromagnetic field value at each time step is recorded until the preset simulation time is reached. Finally, the electromagnetic scattering echo data of the rough surface and the target above the rough surface are extracted.

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