基于矩阵的Sagnac干涉仪光谱复原理论研究
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摘要
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。
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 at1%~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.
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 at1%~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.
引文
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[2]David A N,Margaret K T.Apodizing functions for Fourier transform spectroscopy[J].J.Opt.Soc.Am.A,2007,24(11):3644-3648.
[3]李胜,高闽光,徐亮,等.两种红外干涉图采集与光谱复原方法的对比研究[J].光学学报,2015,35(9):0930005.Li Sheng,Gao Minguang,Xu Liang,et al.Comparative study on two infrared interferogram acquisition and spectrum recovery methods[J].Acta Optica Sinica,2015,35(9):0930005.
[4]张鹏,张志辉.一种新的过零单边干涉图切趾加权函数[J].光子学报,2012,41(7):878-882.Zhang Peng,Zhang Zhihui.A novel apodization function of single sided interferogram[J].Acta Photonica Sinica,2012,41(7):878-882.
[5]吕群波,姚涛,相里斌,等.干涉数据光谱反演方法研究[J].光谱学与光谱分析,2010,30(1):114-117.Lv Qunbo,Yao Tao,Xiang Libin,et al.Spectrum recovery method for interferometric data[J].Spectroscopy and Spectral Analysis,2010,30(1):114-117.
[6]柏财勋,李建欣,孟鑫,等.对称楔形干涉高光谱成像的光谱复原方法[J].光学学报,2016,36(2):0230004.Bai Caixun,Li Jianxin,Meng Xin,et al.Spectrum recovery method for hyperspectral imaging based on symmetric wedgy interferometric cavity[J].Acta Optica Sinica,2016,36(2):0230004.
[7]赵葆常,杨建峰,薛彬,等.实体Sagnac干涉仪的设计[J].光子学报,2009,38(3):474-478.Zhao Baochang,Yang Jianfeng,Xue Bin,et al.Design of solid Sagnac interferometer[J].Acta Photonica Sinica,2009,38(3):474-478.
[8]周志良,付强,相里斌.Sagnac干涉仪的几何参量计算[J].光子学报,2009,38(3):689-693.Zhou Zhiliang,Fu Qiang,Xiang Libin.Calculation of geometric parameters of Sagnac interferometers[J].Acta Photonica Sinica,2009,38(3):689-693.
[9]刘秉琦,孙东平,华文深,等.基于双向剪切干涉的CCD像素间距标定[J].半导体光电,2008,29(5):788-791.Liu Bingqi,Sun Dongping,Hua Wenshen,et al.Measurement of pixel spacing in CCD image acquisition system based on double-shearing interference[J].Semiconductor Optoelectronics,2008,29(5):788-791.
[10]罗霞,洪添胜,罗阔,等.高光谱技术在无损检测火龙果可溶性固形物中的应用[J].激光与光电子学进展,2015,52(8):083002.Luo Xia,Hong Tiansheng,Luo Kuo,et al.Application of hyperspectrum technology in non-destructive measurement of soluble solid content in pitaya[J].Laser&Optoelectronics Progress,2015,52(8):083002.
[11]于施淼,卢伟,梁琨,等.基于高光谱成像技术结合PCA-GRNN的糙米发芽率检测方法研究[J].激光与光电子学进展,2015,52(11):113001.Yu Shimiao,Lu Wei,Liang Kun,et al.Study on prediction of germination rate of rice seeds using hyperspectral imaging combined with PCA and GRNN[J].Laser&Optoelectronics Progress,2015,52(11):113001.
[12]郭士华.基于摄像机的CCD电路噪声模型的仿真与测试的研究[D].广州:华南理工大学,2011:7-8.Guo Shihua.Simulation and test study on CCD circuit noise model based on camera[D].Guangzhou:South China University of Technology,2011:7-8.
[13]江宝坦,邱跃洪,文延,等.CCD噪声建模与仿真分析[J].光电技术应用,2010,25(2):64-67.Jiang Baotan,Qiu Yuehong,Wen Yan,et al.Modeling and analyzing the noise of CCD[J].Electro-Optic Technol.Application,2010,25(2):64-67.
[14]常亚运,易维宁,杜丽丽,等.空间调制干涉成像光谱仪在轨相对定标新方法[J].激光与光电子学进展,2015,52(8):083004.Chang Yayun,Yi Weining,Du Lili,et al.A new method of onorbit relative calibration for spatially modulated imaging Fourier transform spectrometer[J].Laser&Optoelectronics Progress,2015,52(8):083004.