An Improved Data Inversion Program for Obtaining Aerosol Size Distributions from Scanning Differential Mobility Analyzer Data

An improved program has been developed that inverts data obtained from an electrical differential mobility analyzer (DMA) to obtain the particle size distribution. The central problem for data inversion is to find a smooth particle size distribution function, N ( x ), from the instrument response, R ( t ). Linear data inversion techniques for this problem, as developed by Hagen and Alofs (1983) work by using a small number of size channels carefully selected so that data channels for multiply-charged particles overlap channels for smaller singly-charged particles. However, these techniques fail when a large number of data channels are used. The program developed here typically uses 300 data channels, making it particularly appropriate for inverting data obtained in scanning mode, where the number of channels can be made arbitrarily large. It is based on regularization procedures like those described by Wolfenbarger and Seinfeld (1990) and Lesnic et al. (1996). To estimate the optimal value of the regularization parameter, an automated L-curve based method has been selected, as described by Hansen and O'Leary (1993). The large number of data channels used ensures that the resolution of the measurements is limited by the capabilities of the instrument and not by the selection of the size channels to be used. Efficient implementation of the inversion program is made possible by supplying analytical expressions for the gradient and hessian of the objective function that is minimized to solve the regularized problem.