The comparison of the angular light-scattering method (ALSM) and the spectral extinction method (SEM) in solving the inverse problem of aerosol size distribution (ASD) are studied. The inverse problem is solved by a SPSO-DE hybrid algorithm, which is based on the stochastic particle swarm optimization (SPSO) algorithm and differential evolution (DE) algorithm. To improve the retrieval accuracy, the sensitivity analysis of measurement signals to characteristic parameters in ASDs is studied; and the corresponding optimal measurement angle selection region for ALSM and optimal measurement wavelength selection region for SEM are proposed, respectively. Results show that more satisfactory convergence properties can be obtained by using the SPSO-DE hybrid algorithm. Moreover, short measurement wavelengths and forward measurement angles are beneficial to obtaining more accurate results. Then, common monomodal and bimodal ASDs are estimated under different random measurement errors by using ALSM and SEM, respectively. Numerical tests show that retrieval results by using ALSM show better convergence accuracy and robustness than those by using SEM, which is attributed to the distribution of the objective function value. As a whole, considering the convergence properties and the independence on prior optical information, the ALSM combined with SPSO-DE hybrid algorithm provides a more effective and reliable technique to obtain the ASDs.

The aerosol size distribution, a vitally important environmental quality evaluation criterion, has a significant influence on radiative transfer and meteorological phenomena. To measure the aerosol size distribution effectively and accurately, the light scattering measurement method combined with a novel artificial bee colony-differential evolution hybrid algorithm which was based on the artificial bee colony algorithm and differential evolution algorithm, was proposed. First, the retrieval accuracy and convergence properties of the artificial bee colonydifferential evolution algorithm were compared with those of the artificial bee colony algorithm. The results revealed that the artificial bee colony-differential evolution algorithm could avoid the phenomenon of local optima and low convergence accuracy which exited in artificial bee colony algorithm. Then, the parametric estimation of two commonly used monomodal aerosol size distribution, i. e. the Gamma distribution and the logarithmic normal distribution were studied under different random measurement errors. The investigation indicated that the retrieval results using the artificial bee colony-differential evolution showed better accuracy and robustness than those using the artificial bee colony. Moreover, the retrieval parameters with better monodromy characteristic would have better inverse accuracy. Finally, the actual measured aerosol size distribution over city of Harbin, China were also retrieved. All the results confirm that the artificial bee colony-differential evolution algorithm was an effective and reliable technique for estimating the aerosol size distribution.