Mie散乱理論を用いた粒子サイズ分布決定における最適解の評価

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

関口 健太郎; 神野 智史*   ; 田中 宏尭*; 一ノ瀬 紘佑*; 金崎 真聡*; 榊 泰直; 近藤 公伯; 松井 隆太郎; 岸本 泰明; 福田 祐仁

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

光散乱強度の角度分布データから散乱粒子の粒径分布を得る問題は代表的な逆問題であり、分布関数の形状に特別な仮定を置くことなく安定な解を得るためには、不安定性を引き起こす要因とその影響を精度よく評価することが必要である。本研究では、Mie散乱理論を使って我々が開発したアルゴリズムを用いて、複数の異なる粒径分布を与え得る系を扱う場合の解の不安定要因について検討する。数値解析上の技法の精査と並行して、引き続き実験条件の制御によって評価を行うアプローチを採る。

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.