Path tracing simulation of signal coverage. (a) We simulate the propagation of cellular radiation (λ = 10 cm) in an urban scene, consisting of various buildings. The light source is placed on top of the highlighted antenna. (b) Also shown is a top-down view upon the region shadowed by the large buildings. Visualized is the colour-coded irradiance impinging upon the visible surfaces. The scene consists of 181 000 triangles, and the meshes were not optimized for long-wavelength rendering: they admit many small details and wavelength-scale edges, making the computations of free-space diffractions expensive. For comparison, displayed are the ray optics-only renderings. Observe the difference (compared with ray optics) insets: the long-wavelength radiation diffracts around the building edge’s into the shadow regions, yielding a signal distribution that deviates sharply from the ray optics-only simulation. Also notice the multiple interactions (reflections and diffractions) of radiation with the scene—effects which are very difficult to simulate with existing methods.
Abstract
Free-space diffractions are an optical phenomenon where light appears to “bend” around the geometric edges and corners of scene objects. In this paper we present an efficient method to simulate such effects. We derive an edge-based formulation of Fraunhofer diffraction, which is well suited to the common (triangular) geometric meshes used in computer graphics. Our method dynamically constructs a free-space diffraction BSDF by considering the geometry around the intersection point of a ray of light with an object, and we present an importance sampling strategy for these BSDFs. Our method is unique in requiring only ray tracing to produce free-space diffractions, works with general meshes, requires no geometry preprocessing, and is designed to work with path tracers with a linear rendering equation. We show that we are able to reproduce accurate diffraction lobes, and, in contrast to any existing method, are able to handle complex, real-world geometry. This work serves to connect free-space diffractions to the efficient path tracing tools from computer graphics.
@article{Steinberg_fsd_2024,
author = {Steinberg, Shlomi and Ramamoorthi, Ravi and Bitterli, Benedikt and Mollazainali, Arshiya and D'Eon, Eugene and Pharr, Matt},
title = {A Free-Space Diffraction BSDF},
year = {2024},
issue_date = {July 2024},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {43},
number = {4},
issn = {0730-0301},
doi = {10.1145/3658166},
journal = {ACM Trans. Graph.},
month = {jul},
articleno = {113},
numpages = {15},
keywords = {wave optics, optical coherence, light transport, PLT, diffraction}
}
Overview
This paper provides an analytic closed-form solution to Fraunhofer diffraction of an arbitrary light beam with a spatially smoothly-varying profile by an arbitrary triangular geometric mesh.
This allows us to formulate a BSDF that quantifies the effect of light diffracting, i.e. “bending” around geometry, edges, and apertures, described by the scene’s geometric meshes.
No special handling of the geometry is needed.
Our BSDF fits within a standard linear path tracing framework, is easy to evaluate and can be importance sampled.
To construct that BSDF, we search for triangles around interaction points.
Time complexity of BSDF construction and evaluation is linear in triangle count.
Accessing the acceleration structure and looking for triangles is the dominant cost, optimizations are left for future work.
One application is the wave simulation of long-wavelength radiation (RADAR, cellular, WiFi, etc.) in scenes orders-of-magnitude more complex than possible with any existing method, as seen in the figure above.
This work is designed to operate with a wave-optical light transport framework.
Physical light transport (which we introduced in Towards Practical Physical-Optics Rendering and A Generalized Ray Formulation For Wave-Optics Rendering) decomposes light into Gaussian beams (i.e. the generalized rays of PLT), which accurately define the spatial extend over which interference effects may arise.
The spatial size of these beams dictates the region where we search for the diffracting geometry that is used in this work to construct the free-space diffraction BSDF.
Note that a classical ray-optical light transport framework is not able to provide that information: a ray is not Wigner-representable and admits no well-defined wavefunction.
Nevertheless, a classical rendering framework may set the search region ad hoc, potentially to an upper bound on the expected spatial coherence of radiation.
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Additional renders
Polychromatic collimated beam in a participating medium diffracted by a complex aperture
Long-wavelength beam diffracted by a star-of-david aperture
