多级反射镜阵列Monte Carlo法误差合成与统计分析  

Error synthesis and statistical analysis on stepped mirror array by Monte Carlo method

作　　者：吕金光[1,2] 梁静秋[1] 梁中翥[1] 

机构地区：[1]中国科学院长春光学精密机械与物理研究所应用光学国家重点实验室,长春130033 [2]中国科学院研究生院,北京100049

出　　处：《物理学报》2012年第22期161-166,共6页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:61027010;60977062);国家高技术研究发展计划(批准号:2009AA04Z315);吉林省科技发展计划(批准号:201205025);应用光学国家重点实验室自主基金资助的课题~~

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ε与θ作为随机变量,利用Monte Carlo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.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.

关 键 词：傅里叶变换光谱仪 多级反射镜 误差合成 MONTE Carlo法 

分 类 号：TH744.1[机械工程—光学工程]