Overview of Active Research

My research is about simulating on a computer the physics of light behaviour as it happens in real-world scenarios and environments. Light consists of electromagnetic energy that propagates through space, interacts with media and matter (for example, light scatters off a surface or passes through a transparent object, like a glass of water), and, at some point, may be sensed by a detector, like the human eye or a camera. This entire process, beginning with the sourcing of this light energy from a light source, till the detection by an observer, is known as light transport. Simulating such light transport efficiently, but in a physically-accurate fashion, is the centre of my study.

"In our time of ever-increasing specialization, there is a tendency to concern ourselves with relatively narrow scientific problems. The broad foundations of our present-day scientific knowledge and its historical development tend to be forgotten too often. This is an unfortunate trend, not only because our horizon becomes rather limited and our perspective somewhat distorted, but also because there are many valuable lessons to be learned in looking back over the years during which the basic concepts and the fundamental laws of a particular scientific discipline were first formulate."
Emil Wolf

A large, diverse collection of real-world applications involve imaging, sensing and communication with electromagnetic radiation. As examples, consider driving-assistive technologies that employ radar and lidar, connectivity problems with WiFi or cellular radios, optical coherence tomography, geolocation and environment mapping using WiFi or other radios, imaging with optical or non-optical frequencies, simulation of ground-penetrating radar, diagnosis and validation of structures and materials with radar or radiation of other frequencies, computation of the RCS (radar cross-section) of ships and aircraft, non-line-of-sight imaging and sensing, scientific visualization and photorealistic rendering, and more. These applications call for computational tools that are able to simulate the propagation of electromagnetic (EM) radiation, as well as the interaction of that radiation with objects and matter in the environment. That environment is often large and involved, it may contain objects of complex geometries and distinct optical properties as well as multiple different radiation sources. Furthermore, the light (i.e. electromagnetic radiation) that we observe daily and use for the applications listed above is often partially-coherent — that is, highly disorganized radiation, which is composed of many different, independent waves and admits a significant degree of random fluctuations.

The accuracy of the numeric simulations that we may reproduce depends on how we describe and model electromagnetic radiation. Of the more accurate approaches are full-wave computational electromagnetic methods: The driving optical principle is Maxwell’s famous theory of electromagnetism, which is well able to explain essentially all observable optical phenomena, where the atomic structure of matter plays no major role. Different methods in this field aim to find accurate solutions to Maxwell’s equations. These methods commonly are variants of the finite-difference time domain (FDTD), finite element method (FEM) and method of moments (MoM) integration techniques, which are accurate, but notoriously slow, and require working with the EM fields directly, making them difficult to apply and require explicit, high-resolution modelling of matter.

In sharp contrast, geometric optics (GO) techniques — common in low-accuracy applications such as computer rendering — employ a radiometric description of light. Radiometry is the scientific field that deals with measuring electromagnetic radiation. The basic quantities have units of power, and indeed our sensors that observe light measure the radiation’s power per unit area. However, such a formulation of light ignores the light’s wave-nature and treats light energy as packets that travel along straight lines. By ignoring the wave nature of light, all related optical phenomena — diffraction and wave-interference — are ignored. To simulate the propagation of light — under that radiometric formalism — a family of numerical algorithms known as path tracing have emerged over the last few decades. Path tracing are Monte-Carlo integration techniques designed to solve the light transport problem in complicated scenes that model real-world environments, and these techniques have been proven tremendously successful: virtually all the computer-generated content you see in modern movies these days have been rendered using these techniques.

In-between these two extremes, other techniques have been developed that aim to be faster than full-wave computational EM methods, but more accurate than geometric-optics approaches. Asymptotic, physical optics (PO) methods seek approximative solutions to Maxwell’s equations away from the source or surface. These analytic methods ignore the static fields and surface waves that arise, and can be formulated as a linearised scattering or diffraction integral over a spatial region. These integrals are easier to numerically solve, compared with full-wave computational EM methods, but are still very expensive for large geometries. To alleviate some of the problems and inaccuracies that arise with such approaches, hybrid geometric-optics/physical-optics (GO/PO) methods have become dominant over the past decade, with the most common being variants of the “shooting-bouncing-ray” (SBR) method: the propagation of EM waves between geometries is done via GO-formulated ray-tracing (as in computer rendering), while the computation of the scattered fields at a surface or medium is done via more accurate PO methods.

Hybrid GO/PO approaches are fast enough for complex, large-scale settings, but a GO propagation of light admits an inherent flaw. GO ignores the wave properties of light, and fails to propagate them. An experiment that showcases the importance of these properties can be carried out at home: the following video demonstrates a pair of soap bubbles of similar chemical composition, illuminated by light sources of similar spectrum and intensity.

The light source on the left admits very poor optical coherence, meaning that the light’s random fluctuations dominate the process of scattering off the bubble’s thin layer, and virtually no visible wave-interference effects arise. On the right, despite similar radiant spectrum and intensity, the light source produces more coherent radiation. There, the waveforms generated by that light are able to maintain their shape over longer distances in spacetime, and have greater capacity to produce observable interference phenomena. Indeed, visible thin-film interference visual effects are reproduced. Both light sources are of similar colour and intensity, but the appearance is dictated by the optical coherence of light. It can be shown that a radiometric, geometric-optics formulation of light is inconsistent with electromagnetism, and is unable to describe, quantify and propagate these coherence properties of electromagnetic radiation. Therefore, a formalism that relies on geometric-optics for propagation is often unable to accurately describe its interaction with a complicate environment, its energy distribution throughout a scene and its observable quantities.

This motivates us to pursue an unified theory of physical light transport, that is devoid of any GO. My goal is to bridge the gap between the classical light transport theories and physical optics, and develop a general framework of light transport that remains consistent with electromagnetism and is applicable to scenarios where traditional full-wave EM are intractable and impractical: real-life, large, complicated environments. Such research gives rise to a variety of multifaceted challenges, of computational and theoretical natures: The field of computer graphics has invested decades of active research into designing fast path tracing and sampling techniques, some of which can be adapted to a degree to our formulation of physical light transport (see publications). On the other hand, these computer graphics tools oft depend on unacceptable physical approximations; while current PO methods are very slow, and hard to work with. Those challenges make for a unique and highly interdisciplinary field of study, which involves the development of the relevant underlying mathematical primitives and optical tools, as well as the integration of these into a computational framework of physical light transport. Furthermore, engineering challenges also arise in developing fast, efficient, GPU-accelerated physical light transport renderers.