Asymptotics and da Vinci: understanding diffuse optics and radiation transport

Abstract

The apparent softening of harsh collimated light sources into diffuse patterns with fading gradients that is foundational in fields such as diffuse optics and astrophysics was first studied and exploited by Renaissance artists, most famously Leondardo da Vinci. It is now understood that harsh, ballistic light is well described by radiation transport whereas diffusion theory becomes more appropriate as features in the radiation field soften. Because diffusion theory is far more tractable analytically and numerically, examples of reckoning with or exploitation of the transition between the two regimes may be found in many disciplines concerned with radiation systems; complete descriptions, however, are rarely attempted. Thorough asymptotic analyses of radiation transport dynamics are given and applied to long open problems in two radiation transport topics: diffuse optical tomography measurements and radiation transport code verification. The asymptotic analyses give mathematical expressions that do not require transport solutions yet are able to capture important phenomena of the more detailed, angularly-dependent physics.