INVERSION TECHNIQUES FOR PERSONAL CASCADE IMPACTOR DATA

We examined two inversion procedures for solving the Fredholm integral equation of the first kind to obtain aerosol particle size distributi ons from a set of measured masses collected on the various stages of a personal cascade impactor. The problem is essentially ill-conditioned , in that many solutions satisfy exactly an integral equation slightly perturbed from the original due to measurement error. The two methods , although derived from different families of inversion techniques, fi t into the general framework of Tikhonov regularization. Both try to o ptimize the a posteriori degree of matching of the solution to the mea sured data and the a priori judgments about the likelihood of a soluti on in terms of its smoothness. The first method uses a, weighted least squares optimization and zeroth-order regularization to fit a priori bi-modal log-normal distribution functions, using an intermediate step to define an appropriate starting point for the optimization routine. The second involved ''blind'' inversion of the impactor data to expre ss the second derivative of the particle size distribution function as a linear combination of orthogonal basis functions, chosen so that th e resulting solution is smooth and positive. The orthogonal functions are constructed from the eigenvectors and eigenvalues of a kernel cova riance matrix. The personal inhalable dust spectrometer (PIDS), used t o illustrate the application of these methods, is an eight-stage casca de impactor which selects the inhalable fraction of the aerosol by mea ns of a specially designed inlet. Both inversion methods explicitly in clude consideration of the aerosol that is collected in the sampler en try between the inlet and the first impactor stage, something that app lies to all cascade impactors but which has not usually been taken int o account in the past. An important parameter in inversions, the expec ted value of measurement error for each stage, was estimated from a se ries of wind-tunnel experiments. Both methods work well for simulated PIDS data as well as for experimental wind-tunnel data for a wide rang e of sets of aerosol size distribution parameters. Copyright (C) 1996 Elsevier Science Ltd.