Direct inversion for bidimensional distributions of aerosol characteristics

Aerosol classifiers allow particle populations to be described in terms of mass, mobility diameter, or aerodynamic diameter distributions. When this classification is combined with a second layer of classification, a bidimensional distribution can be retrieved that provides additional insights into the distribution of aerosol properties. Bidimensional distributions are often transformed from extensive quantities related to the measurement (e.g., particle mass) to intensive ones that provide more intuitive insights of particle morphology (e.g., effective density or black-carbon mass fraction). Further, most extensive properties are highly correlated with one another (e.g., particle mass and mobility diameter). This complicates inversion, resulting in retrieved distributions that are considerably broader than the true distribution. In this work, we show that these problems can be solved using a single analysis step to compute distributions-of-interest, phrased in terms of intensive properties. This yields a direct inversion scheme that (1) avoids the need for post-processing to retrieve common distributions-of-interest; (2) reduces the correlation between the aerosol properties for which the bidimensional distribution is defined; (3) makes regularization easier and more objective; and (4) improves the minimum resolvable distribution width by up to 96 %. The approach is demonstrated using both simulated distributions (phantoms) and experimental data.