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## A comparative study of three methods to detect the upper atmospheric wind speed by DASH

Li Wen-Wen, Hui Ning-Ju, Li Cun-Xia, Liu Yang-He, Fang Yan, Li Ling-Qing, Wang Yan-Long, Tang Yuan-He
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• #### 摘要

采用多普勒非对称空间外差仪(Doppler asymmetric spatial heterodyne, DASH)被动遥感探测高层大气风速, 目前有傅里叶级数法和流行的傅里叶变换两种测风方法. 本文提出“四强度法”测风. 比较研究了傅里叶级数法、傅里叶变换法和“四强度法”测风的原理、正演、噪声和反演等内容, 3种测风方法均从DASH斐索干涉条纹的相位差变换而来. 假设风速为0—100 m/s, 利用傅里叶级数法、傅里叶变换法和“四强度法”得到正演的斐索干涉图后, 再对应得到正演风速的误差分别为2.93%, 4.67%和3.00%. 人为添加均值为0、标准差为0.1的高斯噪声后, 假设风速是0—100 m/s, 用傅里叶级数、傅里叶变换和“四强度法”分别对平场后的数据正演, 得到相对误差对应分别为2.30%, 11.66%, 2.27%. 人为添加高斯噪声后, 假设风速为31—39 m/s和30.1—30.9 m/s, 用傅里叶级数法和“四强度法”得到正演风速值, 两种情况的傅里叶级数法的测风误差是3.55%和4.15%, 均高于“四强度法”的测风误差2.20%和2.69%. 利用GBAII-DASH野外拍摄西安上空98 km的O(1S) 557.7 nm气辉, 得到天顶角为0°和45°的成像干涉图, 再用傅里叶级数、傅里叶变换和“四强度法”得到反演风速分别为32.21 m/s, 43.55 m/s和32.17 m/s. 从DASH的正演、反演结果看, 本文提出的“四强度法”探测高层大气风速的结果较好, 计算简便, 测风精度相对较高.

#### Abstract

The DASH (Doppler asymmetric spatial heterodyne) is used to detect the upper atmospheric wind speed by its imaging Fizeau interference fringes. There are two wind measurement methods: Fourier series method (FSM) and popular Fourier transform method (FTM). However, the wind speed measurement accuracy of FTM is greatly influenced by window function, and the calculation is relatively complicated. The Four-point algorithm (FPA) for DASH’s wind speed measurement is proposed in this paper. The contents of wind speed measurement principle, forward modeling, noise and inversion by the FSM, FTM and FPA are wholly compared and studied. The three wind speed measurement methods are all derived from the phase difference transformation of DASH Fizeau interference fringes. The Fizeau interference fringes with wind speed of 0–100 m/s at the interval of 10 m/s are simulated, and the forward wind speeds are obtained by FSM, FTM and FPA, and the corresponding wind measurement errors are 2.93%, 4.67% and 3.00%, respectively. After artificially adding Gaussian noise with a mean value of 0 and a standard deviation of 0.1, FSM, FTM and FPA are used to forward the Fizeau interference fringes after flat field, and the corresponding relative errors are 2.30%, 11.66% and 2.27%, respectively. After artificially adding Gaussian noise, the Fizeau interference fringes of wind speeds of 31–39 m/s with 1 m/s interval and 30.1–30.9 m/s with 0.1 m/s interval are simulated, and the forward wind speeds are obtained by FSM and FPA. In both cases, the wind speed measurement errors of FSM are 3.55% and 4.15% higher than those of FPA. The O(1S) 557.7 nm airglow at peak altitude of 98 km in Xi’an was photographed by using our GBAII (ground based airglow imaging interferometer)-DASH, and the imaging interferograms with zenith angles of 0° and 45° were obtained. Then by the methods of Fourier series, Fourier transform and FPA are used to obtain the inversion wind speed of 32.21 m/s, 43.55 m/s and 32.17 m/s, respectively. From the forward and inversion results of DASH, we can see that the FPA has a better result for detecting the upper atmospheric wind due to its simple calculation and smaller wind measurement error.

#### 作者及机构信息

###### 通信作者: 唐远河, ltp1801@163.com
• 基金项目: 国家自然科学基金(批准号: 41975040)和陕西省自然科学基金(批准号: 2020JZ-46, 2021JQ-469)资助的课题.

#### Authors and contacts

###### Corresponding author: Tang Yuan-He, ltp1801@163.com
• Funds: Project supported by the National Natural Science Foundation of China (Grant No. 41975040) and the Natural Science Foundation of Shaanxi Province, China (Grant Nos. 2020JZ-46, 2021JQ-469).

#### 施引文献

• 图 1  DASH的光路图[7]

Fig. 1.  Optical path diagram of DASH.

图 2  闪耀光栅结构图

Fig. 2.  Blazing grating structure diagram.

图 3  GBAII-DASH的光路图

Fig. 3.  Optical path diagram of GBAII-DASH.

图 4  两出射波面夹角示意图

Fig. 4.  Angle of emergent wave surface.

图 5  干涉图的傅里叶级数正演结果

Fig. 5.  Fourier series forward results of interferograms.

图 6  图5中正演结果的局部放大

Fig. 6.  Local amplification of forward results in Fig. 5.

图 7  傅里叶变换的相位分布图

Fig. 7.  Phase distribution diagram of Fourier transformation

图 8  函数拉伸后的“四强度法”

Fig. 8.  Four steps of phase determination.

图 9  两种方法的测风误差

Fig. 9.  Wind measurement error of two methods.

图 10  GBAII-DASH 的实验系统

Fig. 10.  GBAII-DASH system in the laboratory.

图 11  GBAII-DASH拍摄O(1S) 557.7 nm气辉的成像干涉图　(a) 0°天顶角时拍摄的干涉图; (b) 45°天顶角时拍摄的干涉图

Fig. 11.  Imaging interferogram of O(1S) 557.7 nm gas glow obtained by GBAII-DASH: (a) Interferogram taken at 0° zenith angle; (b) interferogram taken at 45° zenith angle.