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.

Abstract In this work, we discuss elliptical cone traversal in scenes that employ typical triangular meshes. We derive accurate and numerically‐stable intersection tests for an elliptical conic frustum with an AABB, plane, edge and a triangle, and analyze the performance of elliptical cone tracing when using different acceleration data structures: SAH‐based K‐d trees, BVHs as well as a modern 8‐wide BVH variant adapted for cone tracing, and compare with ray tracing. In addition, several cone traversal algorithms are analyzed, and we develop novel heuristics and optimizations that give better performance than previous traversal approaches. The results highlight the difference in performance characteristics between rays and cones, and serve to guide the design of acceleration data structures for applications that employ cone tracing.

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.

Ray optics is the foundation of modern path tracing and sampling algorithms for computer graphics; crucially, it allows high-performance implementations based on ray tracing. However, many applications of interest in computer graphics and computational optics demand a more precise understanding of light: as waves. For example, accurately modelling scattering effects like diffraction or interference requires a model that provides the coherence of light waves arriving at surfaces. While recent work in Physical Light Transport [Steinberg et al. 2022; Steinberg and Yan 2021] has introduced such a model, it requires tracing light paths starting from the light sources, which is often less efficient than tracing them from the sensor, and does not allow the use of many effective importance sampling techniques. We introduce a new model for wave optical light transport that is based on the fact that sensors aggregate the measurement of many light waves when capturing an image. This allows us to compactly represent the statistics of light waves in a generalized ray. Generalized rays allow sampling light paths starting from the sensor and applying sophisticated path tracing sampling techniques while still accurately modelling the wave nature of light. Our model is computationally efficient and straightforward to add to an existing path tracer; this offers the prospect of wave optics becoming the foundation of most renderers in the future. Using our model, we show that it is possible to render complex scenes under wave optics with high performance, which has not been possible with any existing method.

Physical light transport (PLT) algorithms can represent the wave nature of light globally in a scene, and are consistent with Maxwell's theory of electromagnetism. As such, they are able to reproduce the wave-interference and diffraction effects of real physical optics. However, the recent works that have proposed PLT are too expensive to apply to real-world scenes with complex geometry and materials. To address this problem, we propose a novel framework for physical light transport based on several key ideas that actually makes PLT practical for complex scenes. First, we restrict the spatial coherence shape of light to an anisotropic Gaussian and justify this restriction with general arguments based on entropy. This restriction serves to simplify the rest of the derivations, without practical loss of generality. To describe partially-coherent light, we present new rendering primitives that generalize the radiometric radiance and irradiance, and are based on the well-known Stokes parameters. We are able to represent light of arbitrary spectral content and states of polarization, and with any coherence volume and anisotropy. We also present the wave BSDF to accurately render diffractions and wave-interference effects. Furthermore, we present an approach to importance sample this wave BSDF to facilitate bi-directional path tracing, which has been previously impossible. We show good agreement with state-of-the-art methods, but unlike them we are able to render complex scenes where all the materials are new, coherence-aware physical optics materials, and with performance approaching that of "classical" rendering methods.

Tremendous effort has been extended by the computer graphics community to advance the level of realism of material appearance reproduction by incorporating increasingly more advanced techniques. We are now able to re-enact the complicated interplay between light and microscopic surface features—scratches, bumps and other imperfections—in a visually convincing fashion. However, diffractive patterns arise even when no explicitly defined features are present: Any random surface will act as a diffracting aperture and its statistics heavily influence the statistics of the diffracted wave fields. Nonetheless, the problem of rendering diffraction effects induced by surfaces that are defined purely statistically remains wholly unexplored. We present a thorough derivation, from core optical principles, of the intensity of the scattered fields that arise when a natural, partially coherent light source illuminates a random surface. We follow with a probability theory analysis of the statistics of those fields and present our rendering algorithm. All of our derivations are formally proven and verified numerically as well. Our method is the first to render diffraction effects produced by a surface described statistically only, and bridges the theoretical gap between contemporary surface modelling and rendering.

Physically accurate rendering often calls for taking the wave nature of light into consideration. In computer graphics, this is done almost exclusively locally, i.e. on a micrometre scale where the diffractive phenomena arise. However, the statistical properties of light, that dictate its coherence characteristics and its capacity to give rise to wave interference effects, evolve globally: these properties change on, e.g., interaction with a surface, diffusion by participating media and simply by propagation. In this paper, we derive the first global light transport framework that is able to account for these properties of light and, therefore, is fully consistent with Maxwell's electromagnetic theory. We show that our framework is a generalization of the classical, radiometry-based light transport---prominent in computer graphics---and retains some of its attractive properties. Finally, as a proof of concept, we apply the presented framework to a few practical problems in rendering and validate against well-studied methods in optics.

Our purpose in this paper is two-fold: introduce a computationally-tractable decomposition of the coherence properties of light; and, present a general-purpose light-matter interaction framework for partially-coherent light. In a recent publication, Steinberg and Yan [2021] introduced a framework that generalises the classical radiometry-based light transport to physical optics. This facilitates a qualitative increase in the scope of optical phenomena that can be rendered, however with the additional expressibility comes greater analytic difficulty: This coherence of light, which is the core quantity of physical light transport, depends initially on the characteristics of the light source, and mutates on interaction with matter and propagation. Furthermore, current tools that aim to quantify the interaction of partially-coherent light with matter remain limited to specific materials and are computationally intensive. To practically represent a wide class of coherence functions, we decompose their modal content in Hermite-Gauss space and derive a set of light-matter interaction formulae, which quantify how matter scatters light and affects its coherence properties. Then, we model matter as a locally-stationary random process, generalizing the prevalent deterministic and stationary stochastic descriptions. This gives rise to a framework that is able to formulate the interaction of arbitrary partially-coherent light with a wide class of matter. Indeed, we will show that our presented formalism unifies a few of the state-of-the-art scatter and diffraction formulae into one cohesive theory. This formulae include the sourcing of partially-coherent light, scatter by rough surfaces and microgeometry, diffraction grating and interference by a layered structure.

We present a novel method for devising a closed-form analytic expression to the light transport through the bulk of inhomogeneous optically anisotropic media. Those optically anisotropic materials, e.g., liquid-crystals and elastic fluids, arise in a plethora of established applications and exciting new research; however, current state-of-the-art methods of visually deducing their optical properties or rendering their appearance are either lacking or non-existent. We formulate our light transport problemunder the context of electromagnetism and derive, from first principles, a differential equation of the transmitted complex wave fields that fully account for the complicated interference phenomena that arise. At the core of our proposed rendering framework is a powerful mathematical representation, carefully crafted to enable us to produce highly accurate analytic approximative solutions for the light transport. This approach is previously unused in computer rendering, and our framework is capable of accurately rendering optically anisotropic materials with spatially varying optical properties at orders-of-magnitude better performance compared to existing methods. We demonstrate a few practical applications of our method, and we validate it against polarized photos of liquid-crystals as well as numerically against numerical solvers and qualitatively against brute-force renderings.

Abstract Optical phenomena that are only observable in optically anisotropic materials are generally ignored in the computer graphics. However, such optical effects are not restricted to exotic materials and can also be observed with common translucent objects when optical anisotropy is induced, e.g. via mechanical stress. Furthermore accurate prediction and reproduction of those optical effects has important practical applications. We provide a short but complete analysis of the relevant electromagnetic theory of light propagation in optically anisotropic media and derive the full set of formulations required to render birefringent materials. We then present a novel method for spectral integration of refraction and reflection in an anisotropic slab. Our approach allows fast and robust rendering of birefringence‐induced iridescence in a physically faithful manner and is applicable to both real‐time and offline rendering.