Fabry-Perot干涉仪研究光谱线超精细结构的理论分析 Ⅱ——一种Fredholm第一类积分方程稳定数值解之分析

THEORETICAL ANALYSIS OF THE RESEARCH FOR SUPERFINE SPECTRAL LINE STRUCTURE BY FABRY-PEROT INTRFEROMETER-An analysis of the stable numerical solution of a Fredholm Integral Equation of the first kind

在以前的论文中,我们从计算机模拟实验及相关的光学现象出发提出了Fabry—Perot(以下简称F—P)干涉光谱技术中的积分方程 数值求解的稳定条件。本文将进一步从数学上利用积分方程的本征值理论阐明这些稳定条件产生的原因,从而为F—P干涉光谱技术奠定坚实的基础。

In previous paper1-3, from the results of the electronic computer simulation experiments and the analysis of the corresponding optical properties, we presented a stabilization condition for numerically solving a Fredholm Integral equation of the first kindσ2σ1k(x, σ)B(σ)dσ =I (x) in Fabry-Perot interferencespectroscopy. In this paper, the author will demostrate why the condition makes the linear simultaneous equations stable using the eigenvalue theory of the integral equations. This work may lay the foundation of Fabry-Perot interference spectroscopy.