## 1 Introduction  
Atmospheric aerosols are important drivers of air quality, atmospheric heat radiative balance, human health and climate, etc. Generally, there are three vitally important properties of aerosols, i.e., aerosol size distributions (ASDs), aerosol optical depths (AODs) and Angstrom exponents [1; 2]. The knowledge of ASDs is essential to a better understanding of their potential contributions to climate change, source identification and environmental quality, necessary to control pollution and preserve citizen health. Therefore, in situ measuring the ASDs presented in the atmosphere is of great necessity [3; 4]. Nowadays, although there are several global ground-based aerosol observation networks and satellite instrument networks that have been established to study the properties of the atmospheric aerosols, e.g., AERONET, MODIS [5; 6; 7; 8], determining the ASDs accurately is still regarded as an unsolved problem and needs further research.  
During the past several years, various types of methods have been proposed to study the ASDs, e.g., the aerodynamic method, the optical measurement method, electrical mobility and condensation method, electrical sensing zone method and the electron microscopy method [9]. Owing to offering a useful and effective approach, reliable measurement results and broad size ranges, the optical measurement method coupled with inverse methods has drawn much attention in the field of determining the ASDs [10]. Usually the optical measurement method could be divided into several categories, such as spectral extinction method (SEM), angular light-scattering method (ALSM) and optical depth measurement method, etc. During our previous work, the ASDs were reconstructed effectively by using SEM, and the retrieval accuracy was improved by increasing the number of measurement wavelengths [11]. However, all the satisfactory results obtained by using SEM were based on having sufficient spectral measurement information about the aerosol dispersion system beforehand, e.g., the multi-spectral transmittance signals. To obtain these information measurements, the multi-spectral light source and detector should be needed, and the multi-spectral optical constants of aerosol should be known, which may increase the difficulty and the cost of experiment. Unlike the SEM, only single spectral information of aerosol is required by using ALSM, and the ASDs can be recovered by measuring multi-angle light-scattering signals [12; 13].  
In the present study, the comparison of ALSM and SEM in retrieval of ASDs are studied. The inverse problem is solved by using a SPSO-DE hybrid algorithm, which is based on the stochastic particle swarm optimization (SPSO) algorithm and differential evolution (DE) algorithm. The research is organized as follows. First, the principles of ALSM and SPSO-DE hybrid algorithm are introduced, and that of SEM, available in Reference [14], is not repeated here. Then, the sensitivity analysis of optical 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. Finally, common monomodal and bimodal ASDs are retrieved by SEM and ALSM, respectively, and the main conclusions and perspectives are provided.