Atmospheric imaging with differential absorption Lidar off-beam returns

Abstract

Environmental monitoring has become increasingly important in recent years. The quantification and analysis of particle concentrations in the atmosphere are not only fundamen tal to our understanding of global climate but also have applications in hazard assessment after chemical accidents where they can be critical in mitigating the risk for first responders and those in the vicinity of the event. The underpinning three-dimensional imaging problem in which one seeks to determine the concentration of gas at every point within a given spatial domain is especially challenging because the typically large scales of these gas plumes make individual concentration measurements at each location virtually impossible. Although remote sensing modalities can overcome this challenge by being able to yield information about a particular region without having to make physical contact with it, the recorded data is typically corrupted by noise, caused either by the instrument itself or the inability to control the dynamic nature of the atmosphere, and are thus accompanied by their own set of difficulties. The primary subject of this work is the inverse problem of fitting parameters related to atmospheric dispersion along with the associated image, based on time-resolved back-scattered differential absorption Lidar (DIAL), an optical remote sensing modality suited for measurements of small molecules with narrow absorption features. In contrast to other state-of-the-art DIAL methods and motivated by the fact that atmospheric dispersion behaves in a way such that long-term averages inevitably have diminishing sensitivity to certain gas features, the problem is approached without making a single scattering assumption but rather a new modality that includes the collection of multiply scattered photons from wider/multiple fields-of-view (FOV) is proposed. It is argued that this data when paired with a time-dependent radiative transfer equation (RTE) model, can be beneficial for the reconstruction of certain key aspects of the image. The resulting inverse problem is formulated as a semi-parametric statistical model in which the quantity of interest is reduced to a small number of dispersion-related parameters accompanied by a high-dimensional but computationally convenient nuisance component. This not only effectively avoids a high-dimensional inverse problem but simultaneously provides a natural regularisation mechanism along with parameters that are directly related to the dispersion model. These can be associated with meaningful physical units while spatial concentration profiles can be obtained employing forward evaluation of the dispersion process. The typically high cost associated with RTE-based inverse problems is overcome with the development of a randomised solver which makes use of concentration properties for smooth low-dimensional functions. This facilitates fast estimation of the gas concentration and at the same time paves the way for quantifying the uncertainties within those estimates.