Determination of the aerosol size distribution by analytic inversion of the extinction spectrum in the complex anomalous diffraction approximation

A new derivation is presented for the analytical inversion of aerosol spect ral extinction data to size distributions. It is based on the complex analy tic extension of the anomalous diffraction approximation (ADA). We derive i nverse formulas that are applicable to homogeneous nonabsorbing and absorbi ng spherical particles. Our method simplifies, generalizes, and unifies a n umber of results obtained previously in the literature. In particular, we c larify the connection between the ADA transform and the Fourier and Laplace transforms. Also, the effect of the particle refractive-index dispersion o n the inversion is examined. It is shown that, when Lorentz's model is used for this dispersion, the continuous ADA inverse transform is mathematicall y well posed, whereas with a constant refractive index it is ill posed. Fur ther. a condition is given, in terms of Lorentz parameters, for which the c ontinuous inverse operator does not amplify the error. (C) 2000 Optical Soc iety of America OCIS codes: 010.1110, 010.1310, 290.3200, 290.2200.