改进的分段式多项式拟合的二维谱图还原算法  

Improved Segmental Polynomial Fitting Algorithm for Two-Dimensional Spectral Restoration

作　　者：盖巧娜 娄小平[1] 吕盛钰婕 牟涛涛 GAI Qiao-na;LOU Xiao-ping;LüSheng-yu-jie;MU Tao-tao(School of Instrument Science and Opto-Electronics Engineering,Beijing Information Science and Technology University,Beijing 100192,China)

机构地区：[1]北京信息科技大学仪器科学与光电工程学院,北京100192

出　　处：《光谱学与光谱分析》2024年第9期2594-2599,共6页Spectroscopy and Spectral Analysis

基　　金：国家自然科学基金项目(61735002)资助。

摘　　要：中阶梯光栅光谱仪兼具光谱范围宽和光谱分辨率高的优势,为将因中阶梯光栅衍射级次高而导致混叠的光谱分开,中阶梯光栅光谱仪的色散系统使用了两个分别在相互垂直的方向进行交叉色散的元件,并最终在探测器上形成二维光谱图像。为了获取光谱仪所检测物质的直观光谱信息,需要通过谱图还原算法将二维光谱图像转换成光强与波长对应的一维谱图,谱图还原算法的优劣直接决定了中阶梯光栅光谱仪的精度和效率。结合已有的谱图还原算法,提出了一种改进的分段多项式拟合的二维谱图还原算法。该算法所基于的中阶梯光栅光谱仪采用透射式棱镜,与传统的光线追迹获取拟合数据点的方法不同,通过中阶梯光栅和棱镜的色散规律获取波长所对应的像元坐标数据,之后将探测器像面在横轴上按像元坐标划分成多个区域;由于X坐标与衍射级次m具有一定的相关性,因此算法的原理是通过建立X坐标与m的拟合关系式,即可由光线落在探测器像面的X坐标得到光线所属衍射级次,并结合像面的Y坐标与波长的关系式最终得到坐标与波长的关系式;分别对各个区域进行多项式拟合,得到每个区域的波长与像元坐标的关系式,实现整个区域谱图还原模型的建立。实验表明:所建立的谱图还原模型的计算误差为0.0001nm。综上,该算法运算简单、能够快速实现谱图还原,并且提高了谱图还原的准确率。The middle Echelle grating spectrometer has the advantages of wide spectral range and high Spectral resolution.To separate the spectra that are aliased due to the high diffraction order of the middle Echelle grating,the dispersion system of the middle Echelle grating spectrometer uses two elements that conduct cross dispersion in mutually perpendicular directions,and finally forms a two-dimensional spectral image on the detector.To obtain the intuitive spectral information of the substances detected by the spectrometer,it is necessary to convert the two-dimensional spectral image into the one-dimensional spectral image corresponding to the light intensity and wavelength through the spectral image reduction algorithm.The quality of the spectral image reduction algorithm directly determines the material analysis accuracy and efficiency of the middle Echelle grating spectrometer.An improved piecewise polynomial fitting two-dimensional spectrogram restoration algorithm is proposed based on existing spectrogram restoration algorithms.The middle Echelle grating spectrometer based on the algorithm in this paper uses a transmission prism,which is different from the traditional method of ray tracing to obtain fitting data points.The pixel coordinate data corresponding to the wavelength is obtained through the dispersion law of the middle Echelle grating and prism.Then the detector image surface is divided into multiple areas according to pixel coordinates on the horizontal axis;Due to the certain correlation between the Xcoordinate and the diffraction level m,the principle of the algorithm is to establish a fitting relationship between the X coordinate and m,which can be used to obtain the diffraction level of the light ray from the X coordinate of the detector's image plane.By combining the relationship between the Y coordinate of the image plane and the wavelength,the relationship between the coordinate and the wavelength can be obtained.Perform polynomial fitting on each region to obtain the relationship between each r

关 键 词：中阶梯光栅光谱仪 交叉色散 谱图还原 分段式 多项式拟合 

分 类 号：TH744.1[机械工程—光学工程]