Matt Pharr’s research while affiliated with NVIDIA and other places

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.

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.

2D texture maps and 3D voxel arrays are widely used to add rich detail to the surfaces and volumes of rendered scenes, and filtered texture lookups are integral to producing high-quality imagery. We show that applying the texture filter after evaluating shading generally gives more accurate imagery than filtering textures before BSDF evaluation, as is current practice. These benefits are not merely theoretical, but are apparent in common cases. We demonstrate that practical and efficient filtering after shading is possible through the use of stochastic sampling of texture filters. Stochastic texture filtering offers additional benefits, including efficient implementation of high-quality texture filters and efficient filtering of textures stored in compressed and sparse data structures, including neural representations. We demonstrate applications in both real-time and offline rendering and show that the additional error from stochastic filtering is minimal. We find that this error is handled well by either spatiotemporal denoising or moderate pixel sampling rates.

2D texture maps and 3D voxel arrays are widely used to add rich detail to the surfaces and volumes of rendered scenes, and filtered texture lookups are integral to producing high-quality imagery. We show that applying the texture filter after evaluating shading generally gives more accurate imagery than filtering textures before BSDF evaluation, as is current practice. These benefits are not merely theoretical, but are apparent in common cases. We demonstrate that practical and efficient filtering after shading is possible through the use of stochastic sampling of texture filters. Stochastic texture filtering offers additional benefits, including efficient implementation of high-quality texture filters and efficient filtering of textures stored in compressed and sparse data structures, including neural representations. We demonstrate applications in both real-time and offline rendering and show that the additional error from stochastic filtering is minimal. We find that this error is handled well by either spatiotemporal denoising or moderate pixel sampling rates.

We present a novel algorithm for implementing Owen-scrambling, combining the generation and distribution of the scrambling bits in a single self-contained compact process. We employ a context-free grammar to build a binary tree of symbols, and equip each symbol with a scrambling code that affects all descendant nodes. We nominate the grammar of adaptive regular tiles (ART) derived from the repetition-avoiding Thue-Morse word, and we discuss its potential advantages and shortcomings. Our algorithm has many advantages, including random access to samples, fixed time complexity, GPU friendliness, and scalability to any memory budget. Further, it provides two unique features over known methods: it admits optimization, and it is in-vertible, enabling screen-space scrambling of the high-dimensional Sobol sampler.

Monte Carlo rendering algorithms often utilize correlations between pixels to improve efficiency and enhance image quality. For real-time applications in particular, repeated reservoir resampling offers a powerful framework to reuse samples both spatially in an image and temporally across multiple frames. While such techniques achieve equal-error up to 100 × faster for real-time direct lighting [5] and global illumination [39, 49], they are still far from optimal. For instance, spatiotemporal resampling often introduces noticeable correlation artifacts, while reservoirs holding more than one sample suffer from impoverishment in the form of duplicate samples. We demonstrate how interleaving Markov Chain Monte Carlo (MCMC) mutations with reservoir resampling helps alleviate these issues, especially in scenes with glossy materials and difficult-to-sample lighting. Moreover, our approach does not introduce any bias, and in practice we find considerable improvement in image quality with just a single mutation per reservoir sample in each frame.

Procedural noise functions are widely used in computer graphics as a way to add texture detail to surfaces and volumes. Many noise functions are based on weighted sums that can be expressed in terms of random variables, which makes it possible to compute Monte Carlo estimates of their values at lower cost. Such stochastic noise functions fit naturally into many Monte Carlo estimators already used in rendering. Leveraging the dense image-plane sampling in modern path tracing renderers, we show that stochastic evaluation allows the use of procedural noise at a fraction of its full cost with little additional error.

2D texture maps and 3D voxel arrays are widely used to add rich detail to the surfaces and volumes of rendered scenes, and filtered texture lookups are integral to producing high-quality imagery. We show that filtering textures after evaluating lighting, rather than before BSDF evaluation as is current practice, gives a more accurate solution to the rendering equation. These benefits are not merely theoretical, but are apparent in common cases. We further show that stochastically sampling texture filters is crucial for enabling this approach, which has not been possible previously except in limited cases. Stochastic texture filtering offers additional benefits, including efficient implementation of high-quality texture filters and efficient filtering of textures stored in compressed and sparse data structures, including neural representations. We demonstrate applications in both real-time and offline rendering and show that the additional stochastic error is minimal. Furthermore, this error is handled well by either spatiotemporal denoising or moderate pixel sampling rates.

Under ray-optical light transport, the classical ray serves as a local and linear "point query" of light's behaviour. Such point queries are useful, and sophisticated path tracing and sampling techniques enable efficiently computing 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. We rigorously formulate the generalized ray, which enables local and linear point queries of the wave-optical phase space. Furthermore, we present sample-solve: a simple method that serves as a novel link between path tracing and computational optics. We will show that this link enables the application of modern path tracing techniques for wave-optical rendering, improving upon the state-of-the-art in terms of the generality and accuracy of the formalism, ease of application, as well as performance. Sampling using generalized rays enables interactive rendering under rigorous wave optics, with orders-of-magnitude faster performance compared to existing techniques.

Monte Carlo rendering algorithms often utilize correlations between pixels to improve efficiency and enhance image quality. For real-time applications in particular, repeated reservoir resampling offers a powerful framework to reuse samples both spatially in an image and temporally across multiple frames. While such techniques achieve equal-error up to 100 times faster for real-time direct lighting and global illumination, they are still far from optimal. For instance, unchecked spatiotemporal resampling often introduces noticeable correlation artifacts, while reservoirs holding more than one sample suffer from impoverishment in the form of duplicate samples. We demonstrate how interleaving Markov Chain Monte Carlo (MCMC) mutations with reservoir resampling helps alleviate these issues, especially in scenes with glossy materials and difficult-to-sample lighting. Moreover, our approach does not introduce any bias, and in practice we find considerable improvement in image quality with just a single mutation per reservoir sample in each frame.