高斯光束经含失调透镜的猫眼系统反射特性研究

为了分析猫眼光学系统中透镜失调对高斯光束反射特性的影响,将分划板的光瞳函数展为有限项复高斯函数之和,并利用适用于失调光学系统的广义衍射公式,求解了高斯光束经含失调透镜的猫眼光学系统的反射光场近似解析式,针对给定猫眼光学系统定量分析了透镜失调量对反射光束场分布的影响.结果表明,透镜的角位移比横位移对反射光束传输特性的影响...     

猫眼光学系统的硬边光阑效应研究

采用矩阵分解以及将硬边光阑窗口函数展开为复高斯函数叠加的方法,研究了高斯光束猫眼光学系统后的光阑效应;通过数值计算,分析了激光的反射规律.研究表明,入射光束束腰距离猫眼光学系统越远,光学系统的光阑效应越大;调整合适的正离焦量,可以使猫眼光学系统回波光强更高.理论分析和数值计算对猫眼系统的研究具有一定的参考意义.     

高斯光束经含光阑失调光学系统的传输特性

为分析光学系统中圆孔光阑和透镜失调对高斯光束传输特性的影响,利用硬边椭圆光阑的近似展开式和适用于失调光学系统的广义衍射公式,推导了高斯光束经含失调圆孔光阑的失调光学系统传输的近似解析式,得出了输出光束场分布与光束参量、孔径尺寸、ABCD矩阵元、光阑和光学系统失调量间的关系。针对特定光学系统,定量分析了各失调量对输出光束场分布的影响。     

平顶高斯光束在失调光学系统中的传输特性

为了研究平顶高斯光束经含失调窄缝光阑的失调光学系统的传输特性,采用广义衍射积分法和用有限个复高斯函数之和来逼近窄缝光阑孔径函数的方法,得出了输出光束场分布的近似解析公式,并针对给定的光学系统和平顶高斯光束进行了分析和数值模拟。结果表明,当光阑半宽度与光束束腰半宽度之比较大时(大于1),光学系统的失调量比光阑的失调量对输出光束特性影响更显著。这一结果对分析平顶高斯光束传输特性是有帮助的。     

光学系统设计中的光阑应用分析

基于远心镜头、显微镜头等成像镜头的光学系统在半导体装备上应用非常广泛。光学系统设计中需要规定对一定成像范围内的物点,以要求孔径角成像,这些对成像光束起到约束作用的孔径称为光阑;依据作用不同,一般分为孔径光阑、视场光阑、渐晕光阑和消杂散光阑;结合光学系统设计案例,深入分析了各类光阑对光学系统的影响。     

椭圆对称奇异空心光束通过硬边光阑的传输特性

通过将圆孔光阑函数展开为有限复高斯函数和的方法,利用惠更斯-菲涅耳衍射积分推导出了椭圆对称奇异空心光束通过具有圆孔光阑的近轴ABCD光学系统的传输近似解析公式,并对椭圆对称奇异空心光束在自由空间中通过不同孔径下的硬边光阑的传输特性进行了数值模拟研究。结果表明:自由空间中的近轴光学系统无论在近场还是远场,椭圆对称奇异空心光束的衍射光强分布都与光阑大小有很大的关系。该研究方法对椭圆对称奇异空心光束通过具有圆孔光阑的传输和变换的研究非常有益。     

“猫眼效应”的物理模型及证明

本文阐述了光学系统中存在的"猫眼效应"物理模型,利用傅氏变换性质证明了"猫眼效应".当激光光束以任一角度入射至"猫眼"光学系统时,将沿入射光方向返回。对普通目标和"猫眼"目标的光学反回率作了比较。     

“猫眼”目标探测距离方程

利用矩阵光学方法对探测过程进行了建模,对探测距离方程进行了推广,使方程适用于猫眼光学系统离焦、探测光束斜入射的一般情况,通过室外探测实验对探测距离方程进行了验证。理论分析和数值计算表明:回波方向相对于入射光方向存在微小的回波方向偏差角,但相同条件下回波发散角要远大于回波方向偏差角,使回波足以形成对探测系统的覆盖;在相同的探测参数条件下,回波功率只与猫眼光学系统焦距和离焦量有关,而与探测光束入射角、猫眼光学系统接收孔径无关。     

离焦量对“猫眼效应”反射特性的影响

为了研究目标光学系统在焦平面反射元件离焦情况下的"猫眼效应"反射特性,采用ZEMAX光学设计及分析软件对"猫眼"目标进行建模和仿真,得出了入射激光通过"猫眼"目标后的能量通过率、后向反射激光束的发散角、远场光斑及其能量分布情况等特性,以及正负离焦量对反射特性影响的区别,并且得出在离焦情况下能够产生"猫眼效应"后向反射光所必需的入射激光束的入射角范围.结果表明,离焦量对"猫眼效应"后向反射光特性有决定性的影响,尤其是对远场光强影响较为显著,这为激光主动探测体制的探测能力分析提供了可靠性依据.     

贝塞尔光束通过环形硬边光阑的ABCD光学系统传输

通过把环形光阑函数展开为复高斯函数的方法,推导出贝塞尔光束通过有环形光阑限制的近轴ABCD光学系统的传输近似解析公式。通过数值计算,对贝塞尔光束通过环形光阑的传输特性进行了详细的研究,给出了光阑内、外半径等参数对光强分布的影响规律。     

大摆角摆臂式干涉仪非线性干涉信号光谱反演

为快速实现大摆角摆臂式干涉仪非线性干涉信号的光谱反演,通过分析大摆角摆臂式干涉仪的工作过程和干涉信号的非线性对光谱反演的影响,提出了基于非均匀快速傅里叶变换(NUFFT)的光谱反演方法。该方法先利用核函数和卷积算法让非线性干涉信号线性化,然后对线性化的干涉信号进行快速傅立叶变换实现光谱反演。实验将光程差替换法和NUFFT算法分别应用于非线性干涉信号的光谱反演。结果表明:两者光谱反演精度相近,但NUFFT算法速度更高。     

Iterative tomographic image reconstruction using Fourier-based forward and back-projectors

Iterative image reconstruction algorithms play an increasingly important role in modern tomographic systems, especially in emission tomography. With the fast increase of the sizes of the tomographic data, reduction of the computation demands of the reconstruction algorithms is of great importance. Fourier-based forward and back-projection methods have the potential to considerably reduce the computation time in iterative reconstruction. Additional substantial speed-up of those approaches can be obtained utilizing powerful and cheap off-the-shelf fast Fourier transform (FFT) processing hardware. The Fourier reconstruction approaches are based on the relationship between the Fourier transform of the image and Fourier transformation of the parallel-ray projections. The critical two steps are the estimations of the samples of the projection transform, on the central section through the origin of Fourier space, from the samples of the transform of the image, and vice versa for back-projection. Interpolation errors are a limitation of Fourier-based reconstruction methods. We have applied min-max optimized Kaiser-Bessel interpolation within the nonuniform FFT (NUFFT) framework and devised ways of incorporation of resolution models into the Fourier-based iterative approaches. Numerical and computer simulation results show that the min-max NUFFT approach provides substantially lower approximation errors in tomographic forward and back-projection than conventional interpolation methods. Our studies have further confirmed that Fourier-based projectors using the NUFFT approach provide accurate approximations to their space-based counterparts but with about ten times faster computation, and that they are viable candidates for fast iterative image reconstruction.     

Optimized Least-Square Nonuniform Fast Fourier Transform

The main focus of this paper is to derive a memory efficient approximation to the nonuniform Fourier transform of a support limited sequence. We show that the standard nonuniform fast Fourier transform (NUFFT) scheme is a shift invariant approximation of the exact Fourier transform. Based on the theory of shift-invariant representations, we derive an exact expression for the worst-case mean square approximation error. Using this metric, we evaluate the optimal scale-factors and the interpolator that provides the least approximation error. We also derive the upper-bound for the error component due to the lookup table based evaluation of the interpolator; we use this metric to ensure that this component is not the dominant one. Theoretical and experimental comparisons with standard NUFFT schemes clearly demonstrate the significant improvement in accuracy over conventional schemes, especially when the size of the uniform fast Fourier transform (FFT) is small. Since the memory requirement of the algorithm is dependent on the size of the uniform FFT, the proposed developments can lead to iterative signal reconstruction algorithms with significantly lower memory demands.      

Iterative algorithm for nonuniform inverse fast Fourier transform(NU-IFFT)

A nonuniform inverse fast Fourier transform (NU-IFFT) for nonuniformly sampled data is realised by combining the conjugate-gradient fast Fourier transform (CG-FFT) method with the newly developed nonuniform fast Fourier transform (NUFFT) algorithms. An example application of the algorithm in computational electromagnetics is presented     

基于非均匀FFT的压缩感知雷达信号快速重构方法

雷达处理是压缩感知理论重要的应用方向之一,基于压缩感知的雷达处理可以降低对回波信号的采样速率要求,并且在部分应用中也可改善处理性能。然而,压缩感知重构算法的计算复杂性限制了压缩感知理论在实际雷达信号处理中的应用,尤其是大尺度雷达数据的处理。本文提出了一种基于压缩感知的雷达信号快速重构方法,利用均匀和非均匀快速傅里叶变换运算实现了常规压缩感知重构算法中的矩阵-向量乘法运算,有效降低了重构算法的计算复杂度,加快了压缩感知雷达信号的重构速度。同时,由于引入了快速傅里叶变换运算,该方法消除了大多数常规重构算法对感知矩阵的存储需求。仿真实验验证了该方法的可行性和高效性。      

基于NUFFT的三次相位信号参数估计

在雷达多脉冲相参积累过程中,高速机动目标的速度模型可建模为三次相位信号, 其中,调频率和二次调频率是引起多普勒频移的因素。如何快速估计调频率和二次调频率对雷达多脉冲相参积累至关重要。针对传统算法在三次相位信号参数估计中存在低计算复杂度与高抗噪声性能矛盾的问题,本文提出一种基于非均匀傅立叶变换的三次相位信号参数估计方法。首先, 基于非均匀傅立叶变换对 HAF-ICPF 方法进行改进;然后,利用改进的 HAF-ICPF 方法估计三次相位信号的参数。改进的 HAF-ICPF 方法由于避免了复杂的搜索过程,在保持原有高抗噪声性能的基础上,大大降低了计算复杂度。仿真结果验证了方法的有效性。     

弹光调制干涉图的预处理及相位校正方法

弹光调制傅里叶变换干涉信号是高速、连续非线性变化。为了实现等时间采样干涉信号的准确光谱重建,有必要对弹光调制干涉信号的预处理技术和相位校正方法进行研究。为了从连续的干涉数据中获取一幅完整的干涉图,文中利用干涉图零光程差点的幅值最大特性,获取一幅完整的干涉图。同时,为了克服干涉图的非对称性,提出将改进的Mertz相位校正方法与非均匀快速傅里叶变换算法（NUFFT）相结合,提高重建光谱的速度和准确度。在实验中,通过仿真产生300 K红外黑体的非对称弹光调制干涉图,采用该数据处理方法提高了重建光谱的精度,并以大气窗口为被测对象,比较准确地重建了大气光谱曲线,实现了气体成分的定性分析。     

Fourier-based forward and back-projectors in iterative fan-beam tomographic image reconstruction

Fourier-based forward and back-projection methods can reduce computation in iterative tomographic image reconstruction. Recently, an optimized nonuniform fast Fourier transform (NUFFT) approach was shown to yield accurate parallel-beam projections. In this paper, we extend the NUFFT approach to describe an O (N2 log N) projector/backprojector pair for fan-beam transmission tomography. Simulations and experiments with real CT data show that fan-beam Fourier-based forward and back-projection methods can reduce computation for iterative reconstruction while still providing accuracy comparable to their O (N3) space-based counterparts.     

Two-dimensional and three-dimensional NUFFT migration method for landmine detection using ground-penetrating Radar

Ground-penetrating radar (GPR) has been widely used for landmine detection due to its high signal-to-noise ratio (SNR) and superior ability to image nonmetallic landmines. Processing GPR data to obtain better target images and to assist further object detection has been an active research area. Phase-shift migration is a widely used method; however, its wavenumber space is nonuniformly sampled because of the nonlinear relationship between the uniform frequency samples and the wavenumbers. Conventional methods use linear interpolation to obtain uniform wavenumber samples and compute the fast Fourier transform (FFT). This paper develops two- and three-dimensional migration methods that process GPR data to obtain images close to the actual target geometries using a nonuniform fast Fourier transform (NUFFT) algorithm. The proposed method is first compared to the conventional migration approaches on simulated data and then applied to landmine field data sets. Results suggest that the NUFFT migration method is useful in focusing images, estimating landmine structure, and retaining relatively high signal-to-noise ratio in the migrated data. The processed data sets are then fed to the normalized energy and least-mean-square-based anomaly detectors. Receiver operating characteristic curves of data sets processed by different migration methods are compared. The NUFFT migration shows potential improvements on both classifiers with a reduced false alarm rate at most probabilities of detection.     

基于改进型快速双线性参数估计的复杂运动目标ISAR成像

针对复杂运动目标的逆合成孔径雷达(ISAR)成像中多普勒扩散导致的成像质量下降,该文在建立方位回波信号为立方相位信号(CPS)的基础上,提出一种基于改进型快速双线性参数估计的复杂运动目标ISAR成像方法。该方法通过利用双线性立方相位函数,非均匀快速傅里叶变换(NUFFT),基于Chirp-z的尺度变换以及快速傅里叶变换(FFT)等操作,能够快速实现CPS参数估计和复杂运动目标的ISAR成像。由于实现过程均采用NUFFT和FFT快速实现,该方法计算量小,并且双线性操作可以保证其具有较好的抗噪声性能和交叉项抑制性能。理论分析和仿真结果验证了该ISAR成像算法的有效性。