中文摘要：

本文研究的傅里叶变换红外光谱仪利用两面多级反射镜阵列替代时间调制型傅里叶变换光谱仪中的平面反射镜，以多级反射镜阵列对干涉图数据进行二维采样，从而减小系统的体积并增加系统的稳定性．由于多级反射镜阵列在其制作过程中加工精度的限制，各子反射镜之间会存在厚度偏差ε与角度偏差θ，这将影响到采样干涉图的光强分布与复原光谱的质量．本文将各子反射镜的￡与臼作为随机变量，利用MonteCarlo方法对傅里叶变换光谱仪中所有子反射镜的误差项进行合成，并通过对误差合成后光谱误差因子Q的统计分析来评价子反射镜的各误差项对复原光谱的影响．统计结果表明，Q的统计均值随着σε与σθ的增加表现为一单调递增的曲面，且与两个偏差之间具有准线性关系．依据对Q的统计分析，可以确定多级反射镜阵列各子反射镜ε与θ的容限．

英文摘要：

To achieve the miniaturization and the static state of the Fourier transform spectrometer, two stepped mirror arrays are introduced into the time-modulation Fourier transform spectrometer to replace of the plane mirrors. The two stepped mirrors can sample the interferogram data in two-dimensional space, which can reduce the size of the instrument and increase the stability of the system. Due to the precision restriction on the stepped mirrors in the fabrication process, the various sub-mirrors of the stepped mirrors may contain various thickness errors and angle errors, which can affect the distribution of the interferogram and the quality of the spectrum. We regard the thickness error and the angle error of all the sub-mirrors as random variables, and synthesize all the error terms into a Fourier transform integration function using Monte Carlo method. By means of statistic analysis on the spectrum error factor, we can appraise the recovered spectrum affected by the thickness error and the angle error of the sub-mirror. The statistical result indicates that the statistical mean of the spectrum error factor increases with thickness standard deviation and angle standard deviation increasing. According to the statistical analysis on spectrum error factor, the tolerances of the thickness standard deviation and the angle standard deviation of the sub-mirror can be determined in the fabrication process of the stepped mirrors.