Technical note: A corrected two dimensional data inversion routine for tandem mobility-mass measurements

Abstract Tandem mobility and mass measurements of aerosol particles, performed with a differential mobility analyzer-aerosol particle mass analyzer-condensation particle counter (DMA-APM-CPC) or DMA-centrifugal particle mass analyzer-CPC, find increasing application in the analysis of combustion derived aerosols and complex aerosol mixtures. In addition to determining the average mass of mobility classified particles, DMA-APM-CPC measurements can, in principle, be inverted to yield a two-dimensional number based size-mass distribution function (the number concentration per unit mobility diameter change and per unit mass change), and this distribution function can in turn be integrated to yield a variety of one-dimensional distribution functions quantifying an aerosol. In this technical note, we present a revised and more robust algorithm to invert two dimensional distribution functions from DMA-APM-CPC measurements than we have presented previously. The inversion algorithm accounts for the DMA transfer function, the APM transfer function, and the particle charge distribution. We additionally provide source code files as Supplemental information to implement this algorithm.