Accelerated, Memory-Efficient Far-Field Scattering Computation with Monte Carlo SBR

TL;DR

This work addresses the computational and memory bottlenecks of high-frequency EM scattering by extending the Shooting and Bouncing Ray method with Monte Carlo integration in a path-space formulation. The authors introduce stratified, Fresnel-based importance, and Russian roulette sampling to focus computation on energetically important paths and to enable efficient GPU execution without maintaining large path trees. They demonstrate that Monte Carlo SBR achieves 10–15x memory savings and up to 4x speedups on multi-layer dielectrics while maintaining 1–2 dB accuracy relative to deterministic SBR, validated on canonical 3D geometries and ISAR imagery. The approach broadens the applicability of SBR to complex dielectric stacks and paves the way for future variance-reduction techniques and incorporation of additional wave phenomena.

Abstract

We introduce a Monte Carlo integration-based Shooting and Bouncing Ray (SBR) algorithm for electromagnetic scattering, specifically targeting complex dielectric materials. Unlike traditional deterministic SBR methods, our approach is the first to reformulate the SBR integral equations using Monte Carlo techniques and advanced variance reduction strategies adapted from photorealistic rendering. This enables efficient, massively parallel computation on modern GPUs, resulting in up to a 10-15x reduction in memory usage and a 4x speed up in runtime, particularly for multilayer dielectric structures. Our method emphasizes high-energy propagation paths, efficiently capturing long multipath and interreflection effects. Verification on canonical 3D geometries and ISAR imaging of both conducting and dielectric representative aircraft models demonstrates that our Monte Carlo SBR achieves high accuracy while maintaining low noise, making it suitable for downstream imaging and analysis tasks.

Figures (13)

• Figure 1: Core steps of the Shooting and Bouncing Ray method on a perfect electrical conductor dihedral. GO rays are traced orthographically to model a plane wave (1). At each hit, currents are computed and scattered to the far field using the electric field integral equation (1a). Rays reflect to the next surface (2), where currents and scattered fields are again calculated, including phase updates (2a). Rays exit the dihedral and no longer contribute to scattering (3).
• Figure 2: Depiction of the path space used in our derivation. All rays start at the incident plane wave. Each object intersection adds a new dimension to the path space with corresponding normal $\hat{n}$ and point $\vec{r}$.
• Figure 3: Visual comparison between deterministic and Monte Carlo integration of dielectric regions. The deterministic algorithm must build a large tree to search the whole space, while the Monte Carlo algorithm must only walk a subset of the possible paths to calculate the scattering.
• Figure 4: Comparison between uniform (left) and stratified (right) sampling. Uniform sampling can produce unexpected cluster of samples. Stratified sampling mitigates the issue by uniformly sampling in subdivisions called strata. In SBR this allows the algorithm to more easily sample the oscillations of induced currents.
• Figure 5: Range profile correctness for dielectric cubes with and without PEC backing. The peaks match between deterministic and Monte Carlo SBR on multiple interreflections and scattering of the field.