Physical light-matter interaction in hermite-gauss space

Abstract

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.

On the properties of the anisotropic multivariate Hermite-Gauss functions

“…It is often important to evaluate the AHG functions at 0, e.g., for computation of the peak energy of optical beams or the determination of the total energy carried by a wave ensemble [13]. The next corollary provides an explicit expression for the values at 0 and may admit interesting combinatorics.…”

“…The positive definite matrix can be used for the representation of spatial deformations, geometric properties and energy tensors of structured optical beams, and potential other future applications. In the context of optical coherence theory, it was shown that this anisotropy matrix has a clear physical meaning [13]: the spatial coherence of light. This allows for the representation of a large family of coherence functions using a limited count of AHG modes, making the representation computationally-tractable.…”

A Generalized Ray Formulation For Wave-Optics Rendering

“…Similar to PLT, Cuypers et al [2012]; Oh et al [2010] also aim to simulate the global evolution of light's optical coherence, by using a form of a "generalized radiance" (the Wigner distribution function in its optical context [Testorf et al 2010]), acting as a descriptor of partially-coherent light. Further comparison between this line of work and PLT is given by Steinberg and Yan [2021b]. We stress that the sampling problem inevitably arises in these approaches, as they quantify and propagate partiallycoherent light.…”