Abstract: Objective　The existing approaches for retrieving aerosol particle size characteristics from lidar observations commonly utilize backscattering and extinction coefficients at multiple wavelengths. However, most of these methods rely on multiwavelength lidar, which entails high hardware requirements, large equipment volume, and high costs, thereby limiting their suitability for compact and portable applications. To address these limitations, this study proposes an inversion algorithm for effective radius and number concentration of aerosol particles based on dual-wavelength lidar. And the extinction coefficients at specified dual wavelengths are simulated to analyze the factors that affect the simulation results and their potential impact on the inversion of effective radius of particles, thereby providing a theoretical basis for dual-wavelength lidar detection and inversion. Methods　 Based on the Mie scattering theory and the assumed Gamma particle size distribution, the backscattering and extinction efficiency factor, and particle sizes of aerosols at 355 nm, 532 nm, and 1064 nm were simulated using wavelengthdependent complex refractive indices obtained from the Optical Properties of Aerosols and Clouds (OPAC) database. The calculated efficiency factors were integrated over the assumed particle-size distribution to obtain wavelength-dependent backscattering and extinction coefficients, from which the corresponding dual-wavelength coefficient ratios were derived. A lookup table was then established to relate the dual-wavelength backscattering coefficient ratio to effective radius over 0.01– 0.1 μm and the extinction coefficient ratio to effective radius over 0.1–1 μm. And then the effective radius of aerosol particles within the range of 0.01–1 μm was inverted by inputting the lidar-detected backscattering and extinction coefficient ratios into this lookup table , after which particle number concentration was estimated using the retrieved effective radius and associated optical parameters. According to the control-variable method, the Gamma distribution parameter u and the complex refractive index were varied independently during simulation. The resulting errors of the inverted effective radius and number concentration relative to their respective reference values were quantified to evaluate the sensitivity of the dualwavelength retrieval to assumptions concerning particle-size distribution and refractive index. Results and Discussion　It was found that the Gamma distribution parameter u affects simulation results by altering the shape of the aerosol particle size distribution. Depending on the effective-radius interval, a larger assumed value of u can lead to either larger or smaller inverted effective radius values, although the overall relative error remains small. If u = 2 is taken as the actual value, when u values are 3, 4, 5, 6, and 7, the maximum errors of backscattering ratio within the 0.01–0.1 μm range of particle radius can be controlled within 8%, 15%, 20%, 25%, and 30%, respectively, and the extinction coefficient ratio errors within the 0.1 – 1 μm range can be controlled within 5%, 8%, 10%, 13%, and 15%, respectively. Variations in the complex refractive index also affect simulation results by influencing the backscattering and extinction efficiency factors, and generally, increases in either the real or imaginary component of the refractive index will lead to smaller inverted effective radius values. Conclusions　The simulations based on the proposed inversion algorithm for dual-wavelength lidar demonstrate that dualwavelength backscattering and extinction coefficient ratios can provide size-dependent information for retrieving the aerosol effective radius under an assumed Gamma particle-size distribution and wavelength-dependent complex refractive indices derived from OPAC. Both the backscattering coefficient ratio and the extinction coefficient ratio of aerosol particles exhibit linear intervals, and the effective radius of aerosol particles in the 0.01–1 μm range can be inverted by leveraging the singlevalued relationship within these linear intervals. The errors introduced into the backscattering coefficient ratio, extinction coefficient ratio, and lidar ratio by the Gamma-distribution parameter and the complex refractive index were analyzed, along with their potential influence on the inversion results. The results indicate that the spectral distribution parameter u affects the spectral shape and causes some variations in the inverted effective radius, although the overall relative error remains small. Similarly, the complex refractive index also influences efficiency factors, with a larger imaginary or real part tending to yield a smaller inverted effective radius. This study on dual-wavelength backscattering coefficient ratio, extinction coefficient ratios and lidar ratios provides a new approach for inverting the effective radius and number concentration of atmospheric aerosol particles, offering a potential support for the development of more compact and cost-effective lidar systems.

Key words: lidar, dual-wavelength, spectral distribution, effective radius, complex refractive index