The POCS-Algorithm—An effective tool for calculating 2D particle property distributions via data inversion of exemplary CDMA measurement data

Abstract

In many cases particle characterization is not trivial, so that data inversion routines are needed in order to determine particle size distributions from measurement data. In particular, determination of two-dimensional particle property distributions, which are very valuable for analyzing complex shaped particles, results in large ill-posed systems of equations which are challenging to be solved. In this paper the Projections onto Convex Sets (POCS) method is implemented for solving such problems in particle characterization for the first time. The POCS method is an iterative algorithm which allows the use of all available information about the distribution to significantly reduce the number of potential solutions. Here, the application of this method is shown for the example of a Centrifugal Differential Mobility Analyzer (CDMA), which measures the number concentration of a nanoscaled aerosol after classification in a gap between two concentric cylinders with a combination of different voltages and angular speeds, i.e. controlled electrical and centrifugal forces. The application of the POCS algorithm to this problem comprising the formulation of appropriate boundary conditions and projection operators to include all available information, is described in detail. Further on, the implementation of the algorithm is explained. The algorithm is then used to invert constructed ideal data and constructed data with superimposed noise. It is demonstrated that the POCS algorithm in either case is well suited to obtain a stable and efficient inversion of the measurement data and to obtain highly accurate 2-dimensional particle property distributions with respect to mobility equivalent diameter and Stokes diameter, respectively. Finally, the algorithm is applied to real measurement data obtained from a prototype of the new device to derive real 2D density distributions.