Abstract

Many remote sensing experiments, including both multispectral extinction and aureole scattering for the determination of aerosol size distributions, require the inversion of a first kind Fredholm integral equation. Due to the combination of inherent instability and measurement error, this is a notoriously difficult task. We have used the singular function theory, which is the natural framework for the solution of such equations, to study the inversion of both multispectral extinction and aureole scattering measurements. By examining the first few singular values, it is readily seen how many pieces of information may be determined for a given noise level. Equally important, however, is a study of the expansion of a set of typical size distributions in terms of the corresponding singular functions. Thus it is advisable to compare different types of remote sensing experiment (e.g., multispectral extinction vs aureole scattering) as well as different wavelength ranges. In particular, we show that extinction measurements in the visible and near IR provide very little information about the Aitken nuclei mode (radii 0.1 μm).

© 1985 Optical Society of America