A study on hybrid light extinction model and inversion based on Lambert-Beer Law

A hybrid light extinction model (LEM) applicable only to spherical particles has been proposed, in which the extinction cross-section weighted by mixing ratio and particle size distribution was introduced to study the light extinction characteristics of polydisperse mixed particles. Moreover, an extinction spectra measurement system has been established, and a series of experiments were performed for mixed particles of silica and polystyrene particles, with mixing ratios of 0.25, 0.5, and 0.75. The results show that the hybrid light extinction method calculations agree well with the experimental spectra, with root mean square errors within 0.07. Subsequently, a differential evolutionary algorithm has been investigated to achieve simultaneous multi-parameter inversion of the polydisperse mixed particles under different mixing ratios. The inversion results show that the error for any single parameter is <7.89%. It is worth noting that the LEM is extended to six-parameter measurements, including particle size distribution , mixing ratio, and number concentration. The maximum inversion errors for particle size, mixing ratio, and number concentration are observed at 9.28%, 2.63%, and 16.90%. Furthermore, the resultant distribution parameters also precisely reflected the narrow particle size distribution of the experimental samples, as confirmed by SEM results.