Improving Twomey's Algorithm for Inversion of Aerosol Measurement Data

Inversion of aerosol size distribution data is often needed because many aerosol measurement instruments have sufficiently broad responses that assuming sharp channel boundaries when reducing their raw data may result in substantial errors. Several routines are available to do reasonable inversions on cascade impactor and optical particle counter data. However, these routines often give mediocre results when used with Electrical Aerosol Analyzer data. Twomey's algorithm has been widely used, but it depends to some extent on the initial guess and often produces oscillatory results. Adding smoothing to the Twomey algorithm and an intelligent initial guess and stopping point greatly reduce these problems. Negative results do not occur as with unconstrained inversions. If fitting tolerances cannot be met, an approximate solution is always obtained, whereas other inversion techniques may sometimes stop due to lack of convergence in a subroutine. The performance of the improved inversion algorithm is comparable to the better routines for impactor data and offers important advantages over other routines for inversion of Electrical Aerosol Analyzer data.