Deconvolution of particle size distributions by means of extreme value estimation method

Abstract

Aerosol particle size analyzers such as diffusion battery, cascade impactors and optical particle analyzers need powerful deconvolution algorithms to determine size distributions from measurements. Deconvolution problems usually do not have one single solution. Instead there is in principle an infinite set of possible solutions. Deconvolution algorithms often select one solution and call this the correct one. In the present Extreme Value Estimation (EVE) method, all possible solutions are considered simultaneously. They form the set of possible solutions. The quantities of interest are estimated within this set. The user may choose a higher or lower confidence level, thereby including more or fewer solutions in the set. These confidence levels have been analyzed, they have been demonstrated to be typically 90 or 95 %. This is a unique property of EVE method: the results are in the form of confidence intervals with known confidence levels. The user can choose to represent the unknown distribution either by monodisperse models, which would be typical in a laboratory experiment, or by a set of log-normal distributions, which are more propable in nature. The use of log-normal models makes other kinds of regularization unnecessary. As an application of the EVE method, data analysis of diffusion battery and cascade impactor measurement is presented.