Abstract. Measuring particle size distribution accurately down to approximately 1 nm
is needed for studying atmospheric new particle formation. The scanning
particle size magnifier (PSM) using diethylene glycol as a working fluid has
been used for measuring sub-3 nm atmospheric aerosol. A proper inversion
method is required to recover the particle size distribution from PSM raw
data. Similarly to other aerosol spectrometers and classifiers, PSM inversion
can be deduced from a problem described by the Fredholm integral equation of
the first kind. We tested the performance of the stepwise method, the kernel
function method (Lehtipalo et al., 2014), the H&A linear inversion method
(Hagen and Alofs, 1983), and the expectation–maximization (EM) algorithm.
The stepwise method and the kernel function method were used in previous
studies on PSM. The H&A method and the expectation–maximization algorithm
were used in data inversion for the electrical mobility spectrometers and the
diffusion batteries, respectively (Maher and Laird, 1985). In addition, Monte
Carlo simulation and laboratory experiments were used to test the accuracy
and precision of the particle size distributions recovered using four
inversion methods. When all of the detected particles are larger than 3 nm,
the stepwise method may report false sub-3 nm particle concentrations
because an infinite resolution is assumed while the kernel function method
and the H&A method occasionally report false sub-3 nm particles because
of the unstable least squares method. The accuracy and precision of the
recovered particle size distribution using the EM algorithm are the best
among the tested four inversion methods. Compared to the kernel function
method, the H&A method reduces the uncertainty while keeping a similar
computational expense. The measuring uncertainties in the present scanning
mode may contribute to the uncertainties of the recovered particle size
distributions. We suggest using the EM algorithm to retrieve the particle
size distributions using the particle number concentrations recorded by the
PSM. Considering the relatively high computation expenses of the EM
algorithm, the H&A method is recommended for preliminary data analysis. We
also gave practical suggestions on PSM operation based on the inversion
analysis.
Simultaneous upscaling of two properties of reservoirs in one dimension using adaptive bandwidth in kernel function method