Evaluating stability of the solution of the problem to determine the size distributions of particles using Mie scattering theory

Sekiguchi, Kentaro; Jinno, Satoshi*   ; Tanaka, Hirotaka*; Ichinose, Kosuke*; Kanasaki, Masato*; Sakaki, Hironao; Kondo, Kiminori; Matsui, Ryutaro; Kishimoto, Yasuaki; Fukuda, Yuji

The size of clusters, produced in an expansion of supercooled, high pressure molecular hydrogen gas into vacuum, has been evaluated by measuring the angular distribution of scattered light. The data are analyzed based on the Mie scattering theory. Here obtaining the size distribution of clusters reduces to solving the inverse problem. Since the scattering coefficient is a matrix, it is necessary to determine the inverse matrix. However, if you solve this equation straightforward, the size distribution often oscillates to the negative values and becomes the discrete distribution by external factors such as noise included in the measurement results. Therefore, we have built an algorithm to determine the size distribution in combination with a non-negative least square method and a Phillips-Twomey method to obtain a smooth solution.