A rapid approximate inversion of extinction data for partially absorbing particles

Retrieval of particle size distribution from extinction data is solved analytically using a product kernel concept and its extension to partially absorbing materials. While a conventional analytical method overestimates the portion of large particles, the correction to the integral formula makes the solution acceptable also for larger absorbing particles. A set of numerical experiments on synthetically generated aerosol optical depths has proven improved accuracy of new formula that is simple and keeps requirements on computational time or memory consumption low enough. The numerical tests shown that original and reproduced size distributions are quite consistent, including the peak position and full width at half maximum. The main advantage of the analytical approach presented here is its easy applicability in fast sampling of rapidly evolving particulate systems, where quick estimation of modal radius or PM1.0, PM2.5 and other fractions of the aerosol population is required.