Sampling time-resolved phenomena

Abstract

Broadly speaking, time-resolved phenomena refers to three dimensional capture of a scene based on the time-of-flight principle. Since speed and and time are proportional quantities, knowing time-of-flight allows one to estimate distances. This time-of-flight may be attributed to a pulse of light or a wave packet of sound. Depending on the sub-band of the electromagnetic spectrum, the interaction of waves or pulses with the scene of interest results in measurements and based on this proxy of the physical world, one is interested in inferring physical properties of the scene. This may be something simple as depth, or something more involved such as fluorescence lifetime of a biological sample or the diffusion coefficient of turbid/scattering medium. The goal of this work is to develop a unifying approach to study time-resolved phenomena across various sub-bands of the electromagnetic spectrum, devise algorithms to solve for the corresponding inverse problems and provide fundamental limits. Sampling theory, which deals with the interplay between the discrete and the continuous realms, plays a critical role in this work due to the continuous nature of physical world and the discrete nature of its proxy, that is, the time-resolved measurements.