# Bounding Volume Hierarchy-Assisted Fast SAR Image Simulation Based on Spatial Segmentation
## 2 BVH-Assisted Computation of the Target Multiple Backscatter Field
### Calculation of the Multiple Backscatter Field  
The basic scattering model of EM wave is the GO model, and according to the high-frequency ray theory, [PERSON]'s theorem can be used to simulate the incidence and reflection of EM waves, in which the main contributions to the scatter field of an electrically large-size-distributed target are geometrically optically direct and reflected waves. We combine the bidirectional reflectance distribution function (BRDF) and the high-frequency ray theory with the ideal specular reflection of microfacts as the starting point for the scattering mechanism analysis, and according to the statistics of the orientation distribution of the normal vectors of the microfacets, the macroscopic scattering mechanism can be subdivided into diffuse, directional specular reflection, sub-surface scattering, diffraction, and absorption. There is a certain overlap degree in the field areas of the various scattering mechanisms mentioned above, which can be reasonably merged. Time-varying magnetic and electric field excitation produces EM waves transmitting to the target surface. A part of the EM waves enters the dielectric layer in front of the target surface and is then transmitted from the sub-surface scattering emitted from the shallow surface of the dielectric. The sub-surface scattering still belongs to the components of diffuse scattering. While the carrier space of the line and point-like structure surface are too small, the number of microfacets is limited, and the statistics of its normal vector distribution is random. The scattering energy of the incident EM wave tends to be a disk shaped or have conical distribution at the edge of a typical prismatic cleavage structure or sharp structure. The non-directional scatter field listed above has a certain range of overlapping areas with the diffuse reflection field based on the microfacets theory, which is collectively categorized as diffuse scattering in this paper. The wavefront width of the  
Figure 4: EM wave transmission simulation. specular reflection depends on the smoothness of the surface of the medium; for a given smooth surface of the medium, the greater the gloss, the narrower the wavefront width, and the more concentrated the forward scattered energy. The value of its projection in the receiving direction of the reflection direction is affected by the angle between the receiving direction and the direction of the specular reflection. On the basis of the EM wave transmission simulation, we combine the actual properties of the target material with a non-transparent surface in the test and regard the backscatter energy received by the transceiver co-located SAR sensor as the sum of the diffuse and specular energy. The property parameters of the target material include relative permittivity, the specular coefficient, the diffuse coefficient, the specular index, and the energy decay coefficient, which are explained in detail in the following material property assignment session to ensure the fidelity of the target backscatter energy. Finally, the propagation distance attenuation factor is set in conjunction with the classical radar equations to correct the target backscatter field, and the multiple backscatter amplitude of each EM wave can be calculated by Equation (7). \[\left\{\begin{array}{l}I_{S(k)}=\frac{K_{k}^{d}}{\pi}*I_{T(k)}*\max(0, \overrightarrow{v_{k}}\cdot\overrightarrow{N_{k}})+K_{k}^{f}*I_{T(k)}\max(0, \overrightarrow{v_{k}^{\prime\prime}}\cdot\overrightarrow{r_{k}})^{K_{k}^{f}} \\ \delta_{k}=4\pi R_{k}^{2}*\left[\frac{1}{R_{k}^{d}}\right]*I_{T(1)}*\rho( \varepsilon_{k})\\ \overrightarrow{r}_{k}=\overrightarrow{v}_{k}-2*\max(0,\overrightarrow{v}_{ k}\cdot\overrightarrow{N_{k}})*\overrightarrow{N_{k}}\\ I_{T(k)}=I_{T(1)}*(1-K_{los1})*(1-K_{los2})\ \ \ldots\ \ \ (1-K_{losk})\ \ \ (I_{T(k)}<I_{end}\ \right) \tag{7}\]  
The parameter subscript \(k\) indicates the instantaneous state of the \(k\)-th backward sub-scattering.