多普勒差分干涉仪干涉图信噪比对相位不确定度研究

A propagation of interferogram signal-to-noise(SNR) and phase uncertainty in Doppler asymmetric spatial heterodyne spectrometer

多普勒差分干涉仪通过测量干涉图相位变化反演大气风速.干涉图信噪比是工程应用中影响测风干涉仪相位反演精度的核心指标之一,基于观测数据分析多普勒差分干涉仪中相位不确定度与干涉图信噪比之间的定量关系建立解析模型,对仪器设计、性能评价及风场数据应用具有重要意义.本文基于傅里叶变换光谱学噪声传递理论和多普勒差分干涉仪相位反演模型,建立干涉图信噪比与相位不确定度传递的理论模型.利用多组不同信噪比仿真及实验实测数据,将相位反演模型计算的统计结果与本文提出的理论模型分析结果进行比较验证,结果表明,多组实验数据平均残差小于0.07 mrad,两者的一致性较好,建立的模型为多普勒差分干涉仪效能评估、干涉仪设计优化提供理论依据.

Passive atmospheric wind detection technique retrieves atmospheric wind profile by measuring the Doppler shift of airglow emissions.Doppler asymmetric spatial heterodyne spectrometer(DASH),which is a Fourier transform spectrometer(FTS),retrieves the Doppler shift information of airglow emissions by detecting the phase shift of interferograms,and the measured phase accuracy directly affects the retrieved wind speed precision.The signal-to-noise(SNR)ratio is one of the significant indexes for evaluating the performance of wind-measuring interferometers in engineering applications.Studying the quantitative relationship between retrieved phase uncertainty and original interferogram SNR that is based on observations is quite essential for the DASH design,performance evaluation and wind profile applications.In this paper,the study is based on the noise propagation theory in FTS and DASH phase retrieval model.According to the Fourier transform relationship between time and frequency domain,we start from original interferogram expression,then we conduct the Fourier transforming,single frequency extracting,inverse Fourier transforming,phase calculating and first-order Taylor expanding,and finally we establish a theoretical relationship model between original interferogram SNR and retrieved phase uncertainty.In order to verify the theoretical relationship model,firstly,we generate 20 groups of interferograms(each group with 1000 frames)randomly with varying the 30–250 times SNR value.After removing the low frequency baseline,we calculate the phase of each interferogram by DASH phase retrieval model,and obtain the phase uncertainty by calculating standard deviation of the 512 th sampling of each group interferogram.Another phase retrieval uncertainty is obtained by using the theoretical relationship model between SNR and retrieved phase uncertainty derived from this paper.Secondly,a total of23 groups of experimental interferograms(each group with 100 frames)with different intensities are collected through the self-developed DASH with a center wavelength of 632.8 nm,basic optical path difference of 50 mm,spectral resolution of 0.78 cm-1.Combining physical characteristics of shot noise and DASH parameters,interferogram SNR of each frame is calculated.We calculate phase uncertainty of experimental data through the two methods mentioned above.The results from the two different calculation methods are compared with each other to determine whether the conclusion is correct.In order to improve the accuracy of phase calculation,three lines are averaged as input to reduce the random error.The average residual between the two methods is only 0.03 mrad,the high consistency of the results indicates that the theoretical relationship model between SNR and retrieved phase uncertainty for DASH is correct.The phase uncertainty can be evaluated by interferogram SNR directly in engineering,which provides a theoretical basis for optimizing the interferometer design.