Linear and Nonlinear Inverse Problems in Aerosol Spectroscopy
Kyrion, Tobias; Frank, Martin (Thesis advisor); Herty, Michael Matthias (Thesis advisor)
Dissertation / PhD Thesis
Dissertation, RWTH Aachen University, 2017
In this work we study the evaluation of optical aerosol measurements. Our aim is to reconstruct the size distributions of aerosol particles from optical light extinction measurements in order to obtain a safe measurement technology for potentially harmful aerosols inside a nuclear reactor containment. The first half of this work is devoted to linear inverse problems. In particularwe study the linear integral equation relating aerosol particle size distributions tooptical extinction measurements via Mie theory. We derive reconstruction algorithms which work independently from a human operator and thus do not require any monitoring or further adjustments. Based on statistical observations, we deriveresidual-based methods for finding the appropriate number of discretization points and the regularization parameter for Tikhonov regularization. Since particle size distributions are non negative, we apply non negativity constraints throughout the whole reconstruction process and all results are derived for constrained regression problems. A special emphasis lies on computational efficiency, since we demand that a single inversion must be completed in less than thirty seconds on a regular notebook.We compare our method based on the discrepancy principle with a Monte Carlo inversion method, where we also apply non negativity constraints. Here the regularization parameter is considered as a model variable and retrieved together with the sought-after size distributions. Then the discrepany principle strategy is generalized to the case of two-component aerosols, where the aerosol particle material is a mixture of two pure component materials. In addition to the particle size distribution, we retrieve the unknown mixingratio of the two components. In the second half of this work we study the nonlinear inverse problem of reconstructing the refractive indices of an aerosol material from measurements of monodisperse aerosols. First we investigate this problem for a fixed light wavelength. We take into account all local minima found here and regard them all ascandidate solutions. Then we apply a selection method based on smoothness estimates for refractive index curve sections covering consecutive light wavelengths. The resulting coupled refractive index reconstructions are regularized further using Phillips-Twomey regularization.