基于空域非均匀傅里叶变换的傅里叶望远镜
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摘要
为了在稀疏发射阵列下清晰重构目标图像,提出了一种基于空域非均匀傅里叶变换(NDFT)的傅里叶望远镜信号处理方法。依据傅里叶望远镜的发射器位置与抽取的目标空间频率关系,结合MATLAB程序特点,完成了空域非均匀傅里叶逆变换,重构了目标图像。稀疏发射阵列配置方式为:T型阵列单臂放置11个发射望远镜,连续抽取目标的8个低频信息,再抽取3个高频分量。选择不同形状和灰度分布的4个卫星作为成像目标。与补零均匀快速傅里叶变换(FFT)方法重构的图像对比发现:信噪比为100dB时,相比补零均匀FFT方法,NDFT方法重构图像的Strehl比都有所提升,最高提升了0.159 8。
In order to reconstruct the image using sparse emitter array,a process based on spatial non-uniform Fourier transform(NDFT) method was proposed.According to the relationship between the extracted spatial frequency of target and the position of Fourier telescope emitters and considering the MATLAB program characteristics,we completed the inverse Fourier transform of non-uniform airspace and reconstructed the image of target.Sparse emitter array configuration is as follows: 11 launch telescopes are placed on the T-array single arm,eight low-frequency components are continuously extracted and then followed by three high-frequency components.We selected four satellites with different shape and gray distribution as the imaging target.Comparing our reconstructed images with those by fast Fourier transform with zero-padding,we found that in the presence of noise(100 dB signal-to-noise ratio),the Strehl ratios of the images reconstructed with NDFT method are improved and the highest one is enhanced by 0.159 8.
In order to reconstruct the image using sparse emitter array,a process based on spatial non-uniform Fourier transform(NDFT) method was proposed.According to the relationship between the extracted spatial frequency of target and the position of Fourier telescope emitters and considering the MATLAB program characteristics,we completed the inverse Fourier transform of non-uniform airspace and reconstructed the image of target.Sparse emitter array configuration is as follows: 11 launch telescopes are placed on the T-array single arm,eight low-frequency components are continuously extracted and then followed by three high-frequency components.We selected four satellites with different shape and gray distribution as the imaging target.Comparing our reconstructed images with those by fast Fourier transform with zero-padding,we found that in the presence of noise(100 dB signal-to-noise ratio),the Strehl ratios of the images reconstructed with NDFT method are improved and the highest one is enhanced by 0.159 8.
引文
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[13]董磊,刘欣悦,林旭东,等.傅立叶望远镜外场实验性能改进和结果分析[J].光学学报,2012,32:0201004.(Dong Lei,Liu Xinyue,Lin Xu-dong,et al.Improvement of performance and analysis of results of field experiments of Fourier telescopy.Acta Optica Sinica,2012,32:0201004)
[14]贺宁.基于非均匀傅里叶变换的超声层析成像研究[D].合肥:中国科技大学,2011:27-28.(He Ning.Ultrasonic computed tomography onnon-uniform Fourier transform.Hefei:University of Science and Technology of China,2011:27-28)
[15]张炎,杨春平,郭晶,等.实验室中傅里叶望远术频谱抽取方式[J].强激光与粒子束,2011,23(3):571-576.(Zhang Yan,Yang Chunping,Guo Jing,et al.Spectrum extraction mode for Fourier telescopy in laboratory.High Power Laser and Particle Beams,2011,23(3):571-576)
[16]王海涛,朱永凯,蔡佳慧,等.光学综合孔径望远镜的UV覆盖和孔径排列的研究[J].光学学报,2009,29(4):1112-1116.(Wang Haitao,Zhu Yongkai,Cai Jiahui,et al.Research on the UV coverage and the optimization arrangement of the optical synthetic aperture telescopearray.Acta Optica Sinica,2009,29(4):1112-1116)
[2]MacDonalda K R,Boger J K,Fetrowb M,et al.An experimental demonstration of Fourier telescopy[C]//Proc of SPIE.1999,3815:23-29.
[3]Mathis J,Stapp J,Cuellar E L.Field experiment performance of the receiver elements for a Fourier telescopy imaging system[C]//Proc ofSPIE.2005:58960F.
[4]Cuellar E L,Stapp J,Cooper J.Laboratory and field experimental demonstration of a Fourier telescopy imaging system[C]//Proc of SPIE.2005:58960D.
[5]刘欣悦,董磊,王建立.稀疏采样傅里叶望远镜成像[J].光学精密工程,2010,18(3):521-527.(Liu Xinyue,Dong Lei,Wang Jianli.Fouriertelescopy imaging via sparse sampling.Optics and Precision Engineering,2010,18(3):521-527)
[6]陈涛,李正炜,王建立,等.应用压缩传感理论的单像素相机成像系统[J].光学精密工程,2012,20(11):2523-2530.(Chen Tao,Li Zheng-wei,Wang Jianli,et al.Imaging system of single pixel camera based on compressed sensing.Optics and Precision Engineering,2012,20(11):2523-2530)
[7]于树海,王建立,董磊,等.基于全相位谱分析的傅里叶望远镜外场实验数据处理[J].光学精密工程,2012,20(10):2275-2282.(Yu Shu-hai,Wang Jianli,Dong Lei,et al.Field experiment data processing of Fourier telescopy based on all phase spectrum analysis.Optics andPrecision Engineering,2012,20(10):2275-2282)
[8]Fessler J A,Sutton B P.Nonuniform fast Fourier transforms using min-max interpolation[J].IEEE Trans on Signal Processing,2003,51(2):560-574.
[9]孟小红,郭良辉,张致付,等.基于非均匀快速傅里叶变换的最小二乘反演地震数据重建[J].地球物理学报,2008,51(1):235-241.(MengXiaohong,Guo Lianghui,Zhang Zhifu,et al.Reconstruction of seismic data with least squares inversion based on nonuniform fast Fouriertransform.Chinese Journal of Geophysics,2008,51(1):235-241)
[10]张东坡,刘兴钊.基于NDFT的步进频率雷达信号处理[J].雷达科学与技术,2004,2(5):289-314.(Zhang Dongpo,Liu Xingzhao.Steppedfrequency radar signal processing based on NDFT.Radar Science and Technology,2004,2(5):289-314)
[11]Wu Yong,Song Hongjun,Shang Xiuqin,et al.Improved RMA based on nonuniform fast Fourier transforms(NUFFTs)[C]//9th Interna-tional Conference on Signal Processing.2008:2489-2492.
[12]汪安民.基于非均匀采样的信号频率检测方法及其实现[D].武汉:华中科技大学,2004:23-38.(Wang Anmin.Methods of signal frequencymeasurement and implementation based on nonuniform sampling.Wuhan:Huazhong University of Science and Technology,2004:23-38)
[13]董磊,刘欣悦,林旭东,等.傅立叶望远镜外场实验性能改进和结果分析[J].光学学报,2012,32:0201004.(Dong Lei,Liu Xinyue,Lin Xu-dong,et al.Improvement of performance and analysis of results of field experiments of Fourier telescopy.Acta Optica Sinica,2012,32:0201004)
[14]贺宁.基于非均匀傅里叶变换的超声层析成像研究[D].合肥:中国科技大学,2011:27-28.(He Ning.Ultrasonic computed tomography onnon-uniform Fourier transform.Hefei:University of Science and Technology of China,2011:27-28)
[15]张炎,杨春平,郭晶,等.实验室中傅里叶望远术频谱抽取方式[J].强激光与粒子束,2011,23(3):571-576.(Zhang Yan,Yang Chunping,Guo Jing,et al.Spectrum extraction mode for Fourier telescopy in laboratory.High Power Laser and Particle Beams,2011,23(3):571-576)
[16]王海涛,朱永凯,蔡佳慧,等.光学综合孔径望远镜的UV覆盖和孔径排列的研究[J].光学学报,2009,29(4):1112-1116.(Wang Haitao,Zhu Yongkai,Cai Jiahui,et al.Research on the UV coverage and the optimization arrangement of the optical synthetic aperture telescopearray.Acta Optica Sinica,2009,29(4):1112-1116)
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