arXiv subjects

Shlomi Steinberg

Publications and source records attributed to Shlomi Steinberg.

3 recordsLinked to original sources

arXiv2025

Wave Tracing: Generalizing The Path Integral To Wave Optics

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.

physics.optics↗

arXiv2024

A Generalized Ray Formulation For Wave-Optics Rendering

Under ray-optical light transport, the classical ray serves as a linear and local "point query" of light's behaviour. Linearity and locality are crucial to the formulation of sophisticated path tracing and sampling techniques, that enable efficient solutions to light transport problems in complex, real-world settings and environments. However, such formulations are firmly confined to the realm of ray optics, while many applications of interest -- in computer graphics and computational optics -- demand a more precise understanding of light: as waves. We rigorously formulate the generalized ray, which enables linear and weakly-local queries of arbitrary wave-optical distributions of light. Generalized rays arise from photodetection states, and therefore allow performing backward (sensor-to-source) wave-optical light transport. Our formulations are accurate and highly general: they facilitate the application of modern path tracing techniques for wave-optical rendering, with light of any state of coherence and any spectral properties. We improve upon the state-of-the-art in terms of the generality and accuracy of the formalism, ease of application, as well as performance. As a consequence, we are able to render large, complex scenes, as in Fig. 1, and even do interactive wave-optical light transport, none of which is possible with any existing method. We numerically validate our formalism, and make connection to partially-coherent light transport.

cs.GR↗

arXiv2021

On the Properties of the Anisotropic Multivariate Hermite-Gauss Functions

The Hermite-Gauss basis functions have been extensively employed in classical and quantum optics due to their convenient analytic properties. A class of multivariate Hermite-Gauss functions, the anisotropic Hermite-Gauss functions, arise by endowing the standard univariate Hermite-Gauss functions with a positive definite quadratic form. These multivariate functions admit useful applications in optics, signal analysis and probability theory, however they have received little attention in literature. In this paper, we examine the properties of these functions, with an emphasis on applications in computational optics.

math-ph↗