Related papers: Wave Tracing: Generalizing The Path Integral To Wa…
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…
We consider how vectorial aspects (polarization) of light propagation can be implemented, and its origin, within a Feynman path integral approach. A key part of this scheme is in generalising the standard optical path length integral from a…
A new method of solution is proposed for solution of the wave equation in one space dimension with continuously-varying coefficients. By considering all paths along which information arrives at a given point, the solution is expressed as an…
The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its…
The high computational expense of simulating light through ray-tracing in large, sparsely instrumented particle detectors such as IceCube and Antares is a critical outstanding problem in particle physics. When the detector is sparsely…
We describe a generalized formalism, addressing the fundamental problem of reflection and transmission of complex optical waves at a plane dielectric interface. Our formalism involves the application of generalized operator matrices to the…
In this work we include the elastic scattering of longitudinal electromagnetic waves in transport theory using a medium filled with point-like, electric dipoles. The interference between longitudinal and transverse waves creates two new…
This paper describes the use of Feynman photon path integrals to compute the probability of detecting reflected, diffracted, and scattered photons at different points in space after interacting with conduction electrons. Five examples are…
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…
A formula to investigate wave effect in multi-lens system is presented on the basis of path integral formalism by generalizing the work by Nakamura and Deguchi (1999). Wave effect of a system with two lenses is investigated in an analytic…
Light emitted from a source into a scene can undergo complex interactions with scene surfaces of different material types before being reflected. During this transport, every surface reflection is encoded in the properties of the photons…
When gravitational waves travel from their source to an observer, they interact with matter structures along their path, causing distinct deformations in their waveforms. In this study we introduce a novel theoretical framework for wave…
Accurate real-time simulation of lens optics remains challenging due to the computational expense of full ray tracing and the limitations of existing approximations. The commonly used pinhole model and thin-lens model ignore many optical…
Modern computer vision algorithms have brought significant advancement to 3D geometry reconstruction. However, illumination and material reconstruction remain less studied, with current approaches assuming very simplified models for…
A path integral formulation is developed to study the spectrum of radiation from a perfectly reflecting (conducting) surface. It allows us to study arbitrary deformations in space and time. The spectrum is calculated to second order in the…
Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have influence of a universal sort and manifest themselves in scaling…
We propose a time-domain boundary integral method to model linear wave propagation with refractive, focusing, and Doppler effects arising from medium heterogeneities and moving obstacles. In contrast to existing techniques, our method…
We write a space-time Feynman path integral representation for scattered elastic wave fields from a weakly compact supported anisotropic non-homogeneity.Replacement by a new version where We (I!) propose a new tomographic inversion…
Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…
Rendering volumetric scattering media, including clouds, fog, smoke, and other complex materials, is crucial for realism in computer graphics. Traditional path tracing, while unbiased, requires many long path samples to converge in scenes…