采用小波变换的空间外差干涉图误差分析方法  

An Error Analysis Method for Spatial Heterodyne Interferograms Using Wavelet Transformation

作　　者：王方原 李晓静 叶松[1,2] 李树 王新强[1,2] WANG Fang-yuan;LI Xiao-jing;YE Song;LI Shu;WANG Xin-qiang(School of Optoelectronic Engineering,Guilin University of Electronic Technology,Guilin 541004,China;Guangxi Key Laboratory of Optoelectronic Information Processing,Guilin 541004,China)

机构地区：[1]桂林电子科技大学光电工程学院,广西桂林541004 [2]广西光电信息处理重点实验室,广西桂林541004

出　　处：《光谱学与光谱分析》2025年第1期8-14,共7页Spectroscopy and Spectral Analysis

基　　金：国家自然科学基金项目(41961050);广西科技基地和人才项目(AD19245184);广西光电信息处理重点实验室主任基金项目(GD21102);国家重点研发计划项目(2022YFB3901800,2022YFB3901803)资助。

摘　　要：空间外差光谱技术(SHS)是一种应用于微弱物质探测、行星勘探以及大气遥感等领域的超光谱分析技术。受实验环境复杂及被测目标信号微弱等因素的影响,空间外差光谱仪的测量结果易出现干涉条纹倾斜、干涉图有斑点噪声等情况,从而最终影响测量光谱的精度。为了尝试解决这些问题,提出了基于小波变换的干涉图误差分析方法,对干涉图的斑点噪声水平和条纹倾斜误差进行有效的评价,从而为后续误差校正提供理论基础。首先对无误差的钾灯仿真干涉图加入不同标准差的高斯噪声,利用小波分解提取复小波系数,采用三种噪声估计法对干涉图数据进行计算,结果表明空域相关小波变换法噪声估计结果与真实值偏差最小,而Donoho估计法在修正截距后与真实值具有更好的吻合度。随后采用Db2小波对噪声水平不同的仿真钾灯干涉图进行一层小波分解并提取水平、对角及垂直三个方向的细节系数,采用Donoho估计法对干涉图进行二维噪声分析,有效表征了三幅干涉图各方向上的噪声水平特征。最后对仿真连续光干涉图进行小波分解并提取系数分析,研究了干涉条纹倾斜角度与小波分解系数的关系。研究结果表明,三个方向的小波细节系数估值变化分别在分解到不同层数时具有相似的变化规律:小波细节系数估值与条纹倾斜方向和小波细节系数的所属方向的夹角成反比,条纹倾斜方向与该小波细节系数的方向夹角越小,估值越大,反之则越小,且水平方向分解到第一层、对角方向分解到第二层、垂直方向分解到第三层符合变化规律。该研究是利用小波分解进行空间外差光谱误差分析的有益尝试,也为后续干涉图条纹倾斜误差的校正提供了一种新途径。Spatial Heterodyne Spectroscopy(SHS)is a hyperspectral analysis technique applied in weak matter detection,planetary exploration,and atmospheric remote sensing.Influenced by the complex experimental environment and the weak signal of the measured target,the measurement results of the Spatial Heterodyne Spectrograph are prone to tilted interference fringes and speckle noise in the interferograms,which ultimately affect the accuracy of the measured spectra.To solve these problems,this paper proposes a wavelet transform-based interferogram error analysis method,which effectively evaluates the interferogram's speckle noise level and stripe tilt error,thus providing a theoretical basis for the subsequent error correction.In this paper,Gaussian noise with different standard deviations is added to the error-free simulated interferograms of potassium lamps.The complex wavelet coefficients are extracted by using wavelet decomposition.Three noise estimation methods are used to compute the interferogram data.The results show that the noise estimation results of the spatial correlation wavelet transform method have the smallest deviation from the real value.The Donoho estimation method matches the real value better after the intercept correction.Subsequently,the Db2 wavelet decomposes the potassium lamp interferograms with different noise levels in one wavelet layer and extracts the detail coefficients in the horizontal,diagonal,and vertical directions.Donoho estimation is used to analyze the interferograms for two-dimensional noise analysis,which effectively characterizes the noise levels of the three interferograms in each direction.The research results show that the three directions of the wavelet detail coefficient valuation change respectively in the decomposition to different layers have a similar rule of change:the wavelet detail coefficient valuation and the stripe tilt direction,and the wavelet detail coefficient belongs to the direction of the angle is inversely proportional to the direction of the stripe tilt dire

关 键 词：空间外差光谱技术 噪声标准差估计 干涉图 小波变换 

分 类 号：O433.1[机械工程—光学工程]