Measurement of aerosol size distribution function using Mie scattering—Mathematical considerations

This paper analyzes the applications of Mie scattering to measure the size distribution function (SDF) of aerosols. Measurement of SDF by Mie scattering usually involves solving the Fredholm integral equations of the first kind based on discrete inputs with uncertainties (e.g., extinction measurements at multiple wavelengths or at multiple angles). A set of inputs which are not mutually independent within the measurement error implies that redundancy exists in the measurements and not all the measurements provide useful information for solving the integral equations. To avoid such redundancy, this paper develops a method to analyze the dependency among the kernel functions associated with Mie scattering. Applications of this method are demonstrated and the results provide valuable insights into the optimization of SDF measurement based on Mie scattering, in terms of minimizing the number of measurements needed and revealing the optimal wavelengths and angles to perform the measurements.