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, virtually all the light (i.e. electromagnetic radiation) that we observe daily and use for the applications listed above is partially-coherent — that is, highly disorganized radiation, which is composed of many different, independent waves and admits a significant degree of random fluctuations.

The range and accuracy of the physics that we may reproduce and simulate depends on the ways and means we use to describe and model electromagnetic radiation. Of the most accurate approaches are full-wave computational electromagnetic methods: The driving optical principle in computational electrodynamics is Maxwell’s famous theory of electromagnetism, and it is well-known that electromagnetism is able to explain and describe 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, inherently unstable and require working with the EM fields directly, making them difficult to apply and require explicit, high-resolution modelling of matter.

In sharp contrast, classical light transport and geometric optics 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 description of light ignores the light’s wave-nature and treats light energy as packets that travel along straight lines, i.e. a simplified optical formalism commonly known as “geometric-optics” (GO). By ignoring the wave nature of light, all related optical phenomena — diffraction and wave-interference — can not be accounted for or simulated. 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. The implication being that multiple scattering is ignored (i.e., the Born first-order approximation). These integrals are easier to numerically solve, compared with full-wave computational EM methods, but are still very expensive for large geometries. Furthermore, with complicated geometries multiple scattering cannot be ignored. To alleviate these problems, 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 a critical flaw. To see why, note that partially-coherent light admits strong statistical properties — known as its optical coherence — that dictate the physical processes of light propagation, its interaction with matter and media, and its observable properties that are measured by our different sensors. 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 coherence properties, 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. This means that the light’s waveforms are able to maintain their shape over longer distances in spacetime, and therefore are able to superpose and interfere. Indeed, visible thin-film interference effects are reproduced. Despite the fact that the light is of similar colour and intensity, the appearance is remarkably different due to the difference in coherence!

It is important to note that just as the interaction of light with matter is dictated by these statistical properties of light, the converse is also true: the properties of the scattered light are influenced by the properties of the matter. However, 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 — either in full, like classical light transport, or partially, as SBR methods — is a formalism that is intrinsically unable to propagate the coherence properties of partially-coherent light, and hence cannot accurately describe its interaction with matter and its observable quantities. This isn’t limited to iridescence: The way light diffracts and its energy distribution throughout a scene, its spectral and polarization properties all depend on its coherence.

This motivates us to pursue a unified theory of physical light transport, that is devoid of any GO formalisms and is able to efficiently propagate the statistical coherence properties of EM radiation throughout a complex scene, as well as quantify the interaction of that radiation with matter. My goal is then 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: 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 techniques, some of which can be adapted to a degree to our formulation of physical light transport (see our paper A Generic Framework for Physical Light Transport). On the other hand, light-matter interaction formulations and tools from computer graphics are severely lacking in terms of their accuracy, while current PO methods are slow, difficult to apply or incompatible with the statistical description of light that my work employs. 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.