Accurate measurements of the size distribution of atmospheric aerosol nanoparticles are essential to build an understanding of new particle formation and growth. This is particularly crucial at the sub-3nm range due to the growth of newly formed nanoparticles. The challenge in recovering the size distribution is due its complexity and the fact that not many instruments currently measure at this size range. In this study, we used the particle size magnifier (PSM) to measure atmospheric aerosols. Each day was classified into one of the following three event types: a new particle formation (NPF) event, a non-event or a haze event. We then compared four inversion methods (stepwise, kernel, Hagen–Alofs and expectation–maximization) to determine their feasibility to recover the particle size distribution. In addition, we proposed a method to pretreat the measured data, and we introduced a simple test to estimate the efficacy of the inversion itself. Results showed that all four methods inverted NPF events well; however, the stepwise and kernel methods fared poorly when inverting non-events or haze events. This was due to their algorithm and the fact that, when encountering noisy data (e.g. air mass fluctuations or low sub-3nm particle concentrations) and under the influence of larger particles, these methods overestimated the size distribution and reported artificial particles during inversion. Therefore, using a statistical hypothesis test to discard noisy scans prior to inversion is an important first step toward achieving a good size distribution. After inversion, it is ideal to compare the integrated concentration to the raw estimate (i.e. the concentration difference at the lowest supersaturation and the highest supersaturation) to ascertain whether the inversion itself is sound. Finally, based on the analysis of the inversion methods, we provide procedures and codes related to the PSM data inversion.
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