Wave Tracing: Generalizing The Path Integral To Wave Optics

2025-08-24

AI Summary

Traditional ray-based models fail to accurately capture wave interference and diffraction, while full-wave simulations suffer from prohibitive computational complexity. To address this, we propose a wave-optical physical modeling method based on bilinear path integrals. This work is the first to extend classical path integral theory to wave optics, establishing a weakly local region-to-region propagation framework. By introducing an elliptical conic geometric structure, we enable efficient path sampling and regional transport, unifying the treatment of interference and diffraction across optical paths. The method significantly improves both accuracy and efficiency in wave-effect simulation. It supports high-fidelity light transport rendering and long-wavelength electromagnetic radiation propagation in complex scenes. As a result, it provides a scalable, physically grounded paradigm for photorealistic rendering and electromagnetic simulation.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Low Level & Physics-based Vision
• Intelligent Robots: Motion and Path Planning

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Modeling the wave nature of light and the propagation and diffraction of electromagnetic fields is crucial for the accurate simulation of many phenomena, yet wave simulations are significantly more computationally complex than classical ray-based models. In this work, we start by analyzing the classical path integral formulation of light transport and rigorously study which wave-optical phenomena can be reproduced by it. We then introduce a bilinear path integral generalization for wave-optical light transport that models the wave interference between paths. This formulation subsumes many existing methods that rely on shooting-bouncing rays or UTD-based diffractions, and serves to give insight into the challenges of such approaches and the difficulty of sampling good paths in a bilinear setting. With this foundation, we develop a weakly-local path integral based on region-to-region transport using elliptical cones that allows sampling individual paths that still model wave effects accurately. As with the classic path integral form of the light transport equation, our path integral makes it possible to derive a variety of practical transport algorithms. We present a complete system for wave tracing with elliptical cones, with applications in light transport for rendering and efficient simulation of long-wavelength radiation propagation and diffraction in complex environments.

Problem

• Generalizing path integral to wave optics for accurate simulation
• Modeling wave interference between light transport paths
• Developing efficient wave tracing with elliptical cones

Innovation

• Generalized bilinear path integral for wave optics
• Weakly-local path integral using elliptical cones
• Efficient wave tracing system for diffraction simulation