Two-dimensional inversion routines for tandem mass-aerodynamic diameter measurements

Many aerosol measurement techniques rely on aerosol classifiers to select quasi-monodisperse fractions of a selected particle property from polydisperse distributions. Although such classifiers are well established for single property characterization, resolving the inherently multidimensional nature of atmospheric particles necessitates tandem measurement configurations. In these systems, the measured response represents a convolution of the true particle property distribution with the instrumental transfer functions, with additional contributions arising from multiple charging.
While inversion frameworks have been extensively developed for mass–mobility and refractory black carbon–total mass distributions, comparatively little attention has been given to the two-dimensional mass–aerodynamic diameter (m–da) distribution. As recently shown by Hassim et al. (2025), for non-spherical particles, simplified peak-fitting approaches may introduce significant bias in retrieved parameters, particularly when aerodynamic diameter is one of the classified variables.
In the present work, several inversion schemes are implemented to reconstruct the two-dimensional m–da distribution from tandem measurements combining a centrifugal particle mass analyzer (CPMA) and an aerodynamic aerosol classifier (AAC). Synthetic datasets are first employed to systematically assess the performance of each inversion approach for both narrow and broad distributions. In addition to simulated cases, DOS and soot particles are experimentally investigated as representative examples of narrow and broad distributions, respectively. To further constrain the inversion, one-dimensional aerodynamic diameter distributions obtained with the AAC while the CPMA is bypassed are used to match the marginal distributions derived from the CPMA–AAC inversion.

The performance of each inversion scheme is then evaluated based on its reconstruction accuracy, assessed through comparison of the recovered marginal distributions with independently measured aerodynamic and mobility diameter distributions. Overall, this framework provides a systematic basis for assessing the reliability of m–da reconstructions and for comparing reconstruction accuracy across different regularization approaches for both narrow and broad distributions.

References:
Hassim, J. S., Hochgreb, S., & Boies, A. M. (2025). Assessing the influence of morphological variability and classifier arrangement on tandem particle classification analysis. Journal of Aerosol Science, 106707.