利用贝叶斯方法提高光谱仪的测量准确度

Improving Spectrograph Accuracy by Bayesian Method

基于贝叶斯条件概率公式并结合卷积定理,推导出一种能够利用系统输出和系统响应函数来反卷积求取系统输入函数的理论公式.根据光谱仪的性能参量,结合点扩散函数的主要来源(狭缝衍射、光栅衍射和光学系统像差)的理论公式,推导出光谱仪的点扩散函数,并对光谱仪的测量结果进行基于贝叶斯反卷积原理的光谱校正;利用反卷积前后的光谱数据差值,引入"光谱曲线标准差"概念,用于判断反卷积结果的数据准确度.实验结果表明,该方法能够有效地通过对系统输出进行迭代,消除点扩散函数的影响,将"模糊"后的光谱数据较好地恢复成原始光谱曲线,从而提高光谱仪的准确度.

Based on Bayesian condition probability formula anc combined with convolution theorem, a theoretical formula is derived that utilizes output and response functions to acquire input function with deconvolution. According to the performance parameter in spectrograph and point-spread functions of main sources （theoretical formula of slit diffraction, grating diffraction and optical system aberration） the point-spread function of the spectrography is derived, and then this function is used to rectify the measuring result based on Bayesian deconvolution; using the difference of spectrum data before and after deconvolution, the concept ＂standard deviation of spectrum curve＂ is introduced to judge the data accuracy of the deconvolution output. The experimental result indicates that this method can effectively eliminate the influence of point spread function through iteration of system output, recover the original spectrum data from a ＂blurred＂ curve, and ultimately improve the accuracy of spectrograph.