复原红外光谱的希尔伯特-史密特方法

Reconstruction of spectrum in infrared spectrometers using the Hilbert-Schmidt method

对几种典型红外光谱仪,利用希尔伯特-史密特方法解积分方程能得到高分辨复原光谱,并能有效地抑制噪声影响。把较大波数范:围分成几个小区域,适当选取参数,可大大减少计算点数(～41)。对非对称核的积分方程,用修正的希尔伯-史密特方法能进一步减少计算时间和容量。该方法还可以用于增大傅里叶光谱仪的光源立体角。

Based on the theory of Hilbert and Schmidt, the original spectrum is recovered with a high resolution from an integral equation representing the relation between the spectrum and its interferogram or intensity distribution given by several kinds of infrared spectrometers. The computer simulations of solving integral equations with corresponding kernels are performed. In this paper, we greatly reduce the number of calculating points ( -41) by dividing the large wave number into smaller ones and choosing appropi'iate parameters. The results also show bhat after modification of the theory of Hilbert and Schmidt, both the calculating time and the capacity of a computer are further reduced for the integral equation with an asymmetric kernel. Furthermore, the recovered spectrum well corresponds to the original one even when the noise of the order of 10-4 or 10-2 is in existence.