关于干涉反演光谱技术能否扩大F-P干涉仪光谱范围的探讨

本文从物理学的角度提出了Fredholm第一类积分方程数值解的可靠性概念,证明了在被称为Fabry-Perot干涉反演光谱技术中,当△σ=2/x,△σ=2/σ时,若取样点数为一个适当的奇数,那么积分方程的数值解是稳定的.但是进一步的计算机模拟实验表明,该数值解不是原积分方程的可靠解,因此,干涉反演光谱技术不能扩大Fabry-Perot干涉仪的光谱范围.理论分析表明,在前述条件下,积分方程数值解不可靠的根本原因在于该积分方程本身没有唯一解.

STUDY ON THE POSSIBILITY OF ENLARGING THE SPECTRAL RANGE OF THE F-P INTERFEROMETER BY THE INVERSE INTERFERENCE SPECTROSCOPY

The authors advance,from the view point of physics, the reliability of the nfimerical solution of the Fredholm integral equation of the first kind. It is proved that in what is called Fabry-Perot inverse interference spectroscopy,when △б= 2/x and △x= 2σ, the numerical solution of the integral equation is stable if the number of sampling points is equal to a suitable odd number. But computer simulation experiments show that this numerical solution is not the reliable solution of theintegral equation. That is to say, the inverse interference spectroscopy can not enlarge the spectral range of the Fabry-Perot interferometer. Theoretical analysis indicates that the reason is that the integral equation itself under the stated condition has no unique solution.