基于最小二乘法拟合估计傅里叶望远镜的缺失分量  

Estimation of missing components of Fourier Telescopy based on least square fitting

作　　者：于树海[1,2] 王建立[1] 董磊[1] 刘欣悦[1] 王亮[1,2] 

机构地区：[1]中国科学院长春光学精密机械与物理研究所,吉林长春130033 [2]中国科学院大学,北京100049

出　　处：《光学精密工程》2015年第1期282-287,共6页Optics and Precision Engineering

基　　金：国家863高技术研究发展计划资助项目(No.2012AAXXXX003)

摘　　要：为了采用非均匀发射阵列的傅里叶望远镜清晰重构深空目标图像,提出了一种基于最小二乘法拟合缺失傅里叶分量的新方法。首先采用T型非均匀发射阵列作为傅里叶望远镜的激光发射系统,并对返回的时域信号进行直流滤波;然后,基于傅里叶望远镜的基本原理对信号进行解调并通过相位闭合得到三重积。采用最小二乘法对没有抽取的傅里叶分量进行拟合估计,作为连乘恢复单一傅里叶分量信息的基础;最后,进行非均匀傅里叶逆变换重构目标图像。在不同信噪比条件下对4个目标进行了数值模拟,并与简单估算方法进行了对比。结果显示:信噪比(SNR)为200db,采用7阶最小二乘法拟合估计时,重构图像细节分辨更为清晰,其斯特里尔比(Strehl)比衍射极限图像的斯特里尔比(Strehl)最高可提高0.074 2,最低可提高0.009 8。采用新方法对外场实验数据进行重构的结果表明:提出的方法克服了频谱偏差造成的重构图像失真,可为实际工程系统提供理论参考。To reconstruct the image of a deep space target by using non-uniform sparse launch array of a Fourier Telescopy（FT）,a new method based on the least square fitting was proposed to estimate the lack of Fourier component of the target.Firstly,the T-sparse emitter array of laser transmitter system was used as transmitter configuration of FT,and the returned time-domain signal was processed by a DC filter.According to the basic principle of FT,the signal was demodulated to obtain a triple product by the phase closure.The least square fitting method was used to estimate and fit the absent Fourier components and to take it for the information recovery basis.Finally,the image was reconstructed with inverse non-uniform Fourier transform.Four targets were simulated with different SNRs.As compared with the original method,the new method resolutes the details of targets and the Strehl Ratios are improved by a maximum value of 0.074 2 and the minimum value of 0.009 8 at a SNR of 200 db and seven rank fitting.Obtain data in a field experiment show that the new method overcomes the distortion of reconstructed image come from frequency spectral deviation and provides a reference for practical engineering.

关 键 词：傅里叶望远镜 成像系统 非均匀发射阵列 非均匀傅里叶变换 最小二乘法 图像重构 

分 类 号：TH743[机械工程—光学工程]