# Bounding Volume Hierarchy-Assisted Fast SAR Image Simulation Based on Spatial Segmentation
## 2 BVH-Assisted Computation of the Target Multiple Backscatter Field
### BVH-Assisted Simulation of Electromagnetic Wave Transmission  
EM wave transmission simulation is the first task of target backscatter field calculation. The workflow of BVH-assisted EM wave transmission is shown in Figure 1. The method uses the geometric relationship between the real-time slant range and incidence angle in the zero Doppler plane of the radar beam, adopts the SAR space traversal mode, discretizes the target model surface facets in the real-time radiation area of the radar beam along the azimuthal direction of each sampling moment into lattices, and takes the value of the lattice spacing in line with the requirements of Nyquist's sampling law so as to effectively store the total radiation area of the radar beam in the form of lattices, while its shadow area has no corresponding lattices. Then, combined with the BVH algorithm to simulate the backscatter field, the beam radiation area of the radar beam can be effectively stored in the form of lattices, while its shadow area has no corresponding lattices. Combined with the real-time position of the radar sensor, only discrete EM waves are launched to all the real-time point-matrix targets that are kept in the line of sight so as to complete the task of simulating the EM wave launching and reproduce the time-varying radiation area of the radar beam and the corresponding shadow area. The BVH algorithm is used to accelerate the intersection of each EM wave with the target model in the process of latticing the target model in the real-time radiation area of the radar beam. This method can reproduce the time-varying characteristics of the radar beam radiation and shadow area and also provides the basic conditions for the target multiple backscatter field calculation. (1) Geometric scene construction. Using the RD geometric imaging model, the SAR spatial traversal mode is adopted to determine the zero Doppler plane by the pulse repetition time (PRT). Then, the real-time slant range is obtained through the range gate within the pulse, and the real-time incidence angle is calculated by combining it with the platform flight height to complete the simulation of EM wave transmission in the Doppler plane and determine the base scanning plane. The specific process is as follows. (a) The SAR spatial traversal model is adopted to determine the position of the zero Doppler plane by PRT and then obtain the instantaneous slant range by each preset range gate within the pulse. Combined with the platform flight height, the instantaneous incidence angle can be calculated. Then, the EM wave transmission simulation within the zero Doppler plane can be carried out to determine the beam scanning reference. The radar transmits pulses continuously by PRT, and the transmitted discrete pulse train can be regarded as the discrete zero Doppler plane set. Then, according to the range of the simulation scene, pulse duration, and range sampling frequency, the range gate position in the pulse is divided. In order to ensure the quality of the echo simulation signal, the distance gate size is smaller than the sampling interval and the sampling interval is smaller than the theoretical resolution, according to the Nyquist sampling theorem. Instantaneous slant range can be calculated from the slant range gate within the pulse. Finally, the instantaneous incidence angle is calculated by combining the instantaneous slant range and the platform height. \[\left\{ \begin{array}{l}M=\left[\frac{x_{\max}-x_{\min}}{\rho_{A}}\right]\\ N=\left[\frac{R_{\max}-R_{\min}}{\dot{\rho}r}\right]\\ R_{\min}=\sqrt{\left(H\cdot\tan\theta+y_{\min}\right)^{2}+H^{2}}\\ R_{\max}=\sqrt{\left(H\cdot\tan\theta+y_{\max}\right)^{2}+H^{2}}\\ R_{I}=R_{\min}+j*\rho_{r}\\ \theta_{j}=\arccos(H/R_{I})\ \ \ \ j\leq N\\ \frac{\partial}{\dot{\
u}_{0}}=\left[0,\ \ \sin\theta_{j},\ \ -\cos\theta_{j}\right]\end{array} \right.