基于矩阵的Sagnac干涉仪光谱复原理论研究

传统的干涉光谱仪光谱复原算法是利用傅里叶变换复原光谱,该方法为了消除有限光程差造成的旁瓣对光谱复原精度的影响,进行了干涉图切趾处理,但这会降低复原光谱的光谱分辨率.为了保证光谱分辨率和提高光谱复原精度,文章提出一种光谱复原方法——基于仪器特征矩阵的Sagnac干涉光谱仪光谱复原方法.该方法旨在通过实验室定标及理论推导为每个Sagnac干涉光谱仪系统构建一个仪器特征矩阵,对仪器特征矩阵利用最小二乘法复原光谱.利用多种物质的光谱进行仿真实验,测试两种光谱复原方法的光谱复原精度,结果显示仪器矩阵方法的复原误差稳定在1％～3％,而傅里叶变换法的复原误差在3％～7％的范围内.因此,和傅里叶变换光谱复原方法相比,基于仪器特征矩阵的光谱复原方法的光谱复原精度更高.

Theoretic Study of Spectral Recovery on Sagnac Interferometer Based on Matrix

Traditional spectral recovery on interferometric spectrometer uses the Fourier transform to recover spectrum. In order to eliminate the influence of side lobes caused by finite optical path difference on the spectral recovery accuracy, it performs interferogram apodization, but that decreases the spectral resolution of the recovery spectrum. In order to ensure the spectral resolution and improve the spectral recovery accuracy, in this paper, a spectral recovery method on Sagnac interferometric spectrometer based on instrumental eigen matrix is presented. The method is designed to construct an instrumental eigen matrix for every interferometric spectrometer system by laboratory calibration and theoretical derivation, and uses it to recover spectrum by least squares method. The spectra of various substances were used to perform the simulation experiments to test the spectral recovery accuracy of the two spectral recovery methods. The results indicate the recovery error of the instrument matrix method is stabilized at 1%~3%, and that of the Fourier transform method is 3%~7%. The experiments testify that the spectral recovery accuracy using the spectral recovery method based on instrumental eigen matrix is better than that using the Fourier transform spectral recovery method.