基于快速傅里叶变换和汉克耳变换的逆阿贝尔变换

激光等离子体实验中的轴对称的Ｘ光的体发射强度及光学全息干涉的测量,需要采用逆阿贝尔（Ａｂｅｌ）变换。用快速傅里叶变换（ＦＦＴ）和汉克耳（Ｈａｎｋｅｌ）变换的算法数值求解逆阿贝尔变换,具有精度高、可在频域内滤波的特点。     

傅里叶变换滤波-差分吸收光谱法在烟气SO_2在线监测中的应用研究

差分吸收光谱(DOAS)法是利用气体分子窄带吸收特征来测量气体浓度的一种新型的光谱测量技术。本文分析了紫外差分吸收光谱(DOAS)法检测SO2数值处理上的问题,提出傅里叶变换滤波分析方法。本方法可有效减少各种干扰对SO2浓度计算的影响,特别是对与SO2有重叠差分吸收光谱但有不同频谱特性且未知气体的干扰有很好的效果。     

基于快速傅里叶变换和积分图的快速相关匹配

为克服传统相关匹配算法计算复杂度过大的缺点,基于快速傅里叶变换和积分图提出了一种快速相关匹配算法.在不改变传统相关匹配计算结果的前提下,该算法通过对相关系数公式的分析和化简,用快速傅里叶变换计算模板图像和基准图像的相关,并采用积分图计算基准图像灰度值及其能量的窗口积分,使相关匹配计算量与模板图像大小近似无关,从而大大降低了计算复杂度.不同光照条件下图像匹配实验和复杂环境下目标跟踪实验结果表明,该算法具有很强的抗干扰能力,其执行效率比传统相关匹配提高1～2个数量级.     

基于GPU和分块技术的巨幅影像快速傅里叶变换算法研究(英文)

快速傅里叶变换(FFT)是遥感影像处理的基础方法,随着高光谱、高空间和高时间分辨率遥感影像获取能力的提升,如何利用快速傅里叶变换技术快速有效地处理巨幅遥感影像是当前遥感影像处理技术中的重要环节和研究热点。傅里叶变换算法FFT是基本的图像处理算法之一,该算法可进行遥感影像的条带噪声去除、影像压缩和影像配准处理等多种用途。CUFFT函数库是NVIDIA公司提供的基于GPU的FFT算法库,FFTW是由MIT科学实验室计算机组在PC平台上开发的基于CPU的FFT算法,是目前在基于CPU的运行速度最快的FFT算法函数库,这两种实现共有的问题是当可用内存或显存的容量小于图像容量时,就会出现内存或显存溢出。针对这种问题,提出了一种基于GPU和分块技术的巨幅遥感影像快速傅里叶变换(huge remote fast Fourier transform,HRFFT)算法。通过对CUDA的CUFFT函数库中的FFT算法进行改进,解决了巨幅图像内存或显存溢出的问题,并结合HJ-1A卫星的CCD影像,通过实验与其他算法进行了对比,证明了该方法的合理性。在实际应用中,利用本文提出的HRFFT算法,改善了影像处理的效果,提高了遥感影像的质量,同时加快了影像处理的速度,节省了计算时间,取得了较好的效果。     

含介质的单透镜和双透镜分数傅里叶变换光学系统

根据菲涅耳衍射公式,导出了含介质的单透镜与双透镜系统输出面的光场复振幅分布,并与分数傅里叶变换定义式比较,得到了实现分数傅里叶变换的系统结构参量.运用矩阵光学方法,导出上述系统的ABCD矩阵,并与分数傅里叶变换矩阵比较,研究发现两种方法所得结果一致.     

光纤法布里-珀罗传感器腔长的傅里叶变换解调原理研究

在宽带光源条件下对光纤法布里-珀罗传感器腔长的傅里叶变换解调原理进行了详细的理论推导,在此基础上给出了具体的实现算法和仿真对比实验.仿真结果表明:采用傅里叶变换可以有效地对光纤法布里-珀罗传感器进行腔长解调.     

基于稀疏相位和可调傅里叶变换的图像加密

针对光学图像加密的轮廓显现问题,提出了一种基于稀疏相位和可调傅里叶变换的图像加密方法。将可调傅里叶变换引入光学图像加密程序中,运用二维可调傅里叶变换实现像素混淆处理,相比基于复数或实数的变换域方案,计算复杂度较低;从加密函数提取相位值并获得加密数据的相位函数,再提取相位加密函数的稀疏数据,从而避免将密文相位信息主要集中在纯相位掩码内,以解决轮廓显现问题;完成了单图像加密实验和双图像加密实验,结果表明实现了较好的安全性,解决了光学图像加密的轮廓显现问题。     

无透镜傅里叶变换全息图在欠采样条件下的数值再现分析

在理论分析无透镜傅里叶变换全息图记录的基础上,结合CCD的结构特点,用傅里叶频谱方法具体研究了无透镜傅里叶变换全息图在欠采样条件下的再现问题.指出在无透镜傅里叶变换全息术中,对有限尺寸物体而言,在记录过程不满足申农（Shannon）采样定理的条件下,仍能完整再现出物体的像.同时对再现像的变化特点进行了理论说明.所得的实验结果与理论分析一致.     

复化辛普森法和傅里叶法在衍射计算上的比较

通过快速傅里叶变换(FFT)法和复化辛普森法对衍射的数值进行计算,可以看出快速傅里叶变换法是一种积分变换法,而复化辛普森法则是迭代相加的方法.通过计算得出了FFT法的计算速度高于复化辛普森法,计算精度则远低于复化辛普森法;复化辛普森法适合近距离菲涅尔衍射和近场衍射,而FFT法不适合.     

Validity of the time-dependent variational approximation to the Gaussian wavepacket method applied to double-well systems

We have examined the validity of the time-dependent variational approximation (TDVA) to the Gaussian wavepacket method (GWM) for quantum double-well (DW) systems, by using the quasi-exact spectral method (SM). Comparisons between results of wavefunctions, averages of position and momentum, the auto-correlation function, and an uncertainty product calculated by SM and TDVA have been made. It has been shown that a given initial Gaussian wavepacket in SM is quickly deformed at t>0$t>0$ where a wavepacket cannot be expressed by a single Gaussian, and that assumptions on averages of higher-order fluctuations in TDVA are not justified. These results cast some doubt on an application of TDVA to DW systems. Gaussian wavepacket dynamics in anharmonic potential systems is studied also.     

On the accuracy of wavefunctions obtained by the Fourier grid Hamiltonian method

The quality of wavefunctions obtained by the Fourier grid Hamiltonian (FGH) method is analyzed. The criteria used for judging the quality are the extent to which virial, hypervirial and Hellmann-Feynman theorems are satisfied by the numerically computed FGH-wavefunction. The quality of the FGH-wavefunction is also examined from the point of view of local error in the wavefunction. It is shown that high quality wavefunctions can be obtained from the FGH recipe if the grid length (L) and grid spacings are chosen after properly examining the range of the potential and its nature.     

飞秒激光脉冲作用下氢原子径向和角向波包的产生与演化

采用劈裂-伪谱方法求解激光场中的含时薛定谔方程,探讨飞秒激光脉冲中氢原子波包的演化过程.研究了氢原子激发态的径向分布,角向分布、各态布居和电子云密度随时间的变化关系.在用共振激光脉冲控制氢原子波包演化的过程中径向分布、角向分布、各态布居和电子云密度随时间发生变化,但发现径向分布和角向分布在变化的过程中始终经过一些特殊点,并从理论上分析了存在这些特殊点的原因.     

Treatment of Dirac Fields in Light—Front Coordinates by Dirac‘s Method for Constrained Hamiltonian Systems

Dirac‘s method which itself is for constrained Boson fields and particle systems is followed and developed to treat Dirac fields in light-front coordinates.     

用Sin-DVR方法求解在绝热表象下锥形交叉分子振动本征态

在波恩-奥本海默近似中,分子中原子核的运动通常采用绝热表象的基态势能面来描述,一般情况下这样是比较好的近似. 然而当势能面上存在锥形交叉时,即使体系的能量远远低于锥形交叉点,绝热基态势能面近似将不再有效. 锥形交叉的出现,使得绝热表象下描述核运动的哈密顿中出现了两个额外的附加项：对角波恩－奥本海默近似校正(DBOC)项和几何相位(GP)项. 尤其GP项,使得基态绝热势能面近似失效. 这两项在锥形交叉点处的数值是发散的,因此在绝热表象中来严格描述核运动,会使量子动力学的计算存在数值收敛的困难. 在量子分子动力学计算中,最常用的数值方法是分离变量表象方法(DVR). 本文通过在绝热表象和透热表象下求解涉及两个电子态且包含锥形交叉的二维的薛定谔方程来验证Sinc-DVR的数值收敛性. 计算结果显示,在绝热表象中采用通常格点密度分布的Sinc-DVR方法,即使在没有特别的处理DBOC和GP项时,也可以得到比较可靠的结果. 此时的数值不确定性并没有比引入任意的向量势来纠正GP效应的不确定性更差. 需要特别注意的是,纠正GP效应的任意向量势的精确形式,通常是不易得到其精确形式的.     

Estimating leaf chlorophyll and nitrogen content of wetland emergent plants using hyperspectral data in the visible domain

Increasing amounts of recycled water have been used in wetlands; as such, monitoring the growth status of wetland plants with remote sensing technology is of great significance to restore and reconstruct wetland added by recycled water. In this paper, Phragmites australis and Typha angustifolia were selected. Spectral reflectance was determined in the visible domain to avoid the influence of leaf water on the established model; chlorophyll and nitrogen contents were measured as data sources. Statistical analysis, including correlation analysis and stepwise regression analysis, was conducted to estimate chlorophyll and nitrogen contents with different derivative transform spectra, namely, first derivative reflectance spectrum (FDS), band depth (BD), continuum-removed derivative reflectance (CRDR), band depth ratio (BDR), and normalized band depth index (NBDI). After the selected bands were statistically analyzed, we found that the range of 550–750 nm, particularly 700–750 nm (red edge range), was the key range to estimate biochemical parameters. Single removal cross-validation results showed that the optimum models of chlorophyll content inversion in reeds, cattails, and combined samples were BD, CRDR, and NBDI, respectively; the corresponding R² were 0.87, 0.83, and 0.81. The respective RMSE values were 0.16, 0.15, and 0.33; the optimal models of nitrogen content inversion in reeds, cattails, and combined samples were BD, CRDR, and BD, respectively; the corresponding R² were 0.69, 0.72, and 0.79. The respective RMSE values were 0.15, 0.11, and 0.17. Kruskal–Wallis non-parametric test and multi-way ANOVA were then performed; results revealed that data types and biological differences greatly influence the inversion model; by contrast, spectral derivative transform and vegetation type difference did not significantly affect the inversion model. Our results could be used as a scientific basis of the non-destructive growth status monitoring of wetland plants. It also provided a reference for restoration and management of wetlands supplied with recycled water.     

Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere-ocean system

A vector radiative transfer model has been developed for a coupled atmosphere-ocean system. The radiative transfer scheme is based on the discrete ordinate and matrix operator methods. The reflection/transmission matrices and source vectors are obtained for each atmospheric or oceanic layer through the discrete ordinate solution. The vertically inhomogeneous system is constructed using the matrix operator method, which combines the radiative interaction between the layers. This radiative transfer scheme is flexible for a vertically inhomogeneous system including the oceanic layers as well as the ocean surface. Compared with the benchmark results, the computational error attributable to the radiative transfer scheme has been less than 0.1% in the case of eight discrete ordinate directions. Furthermore, increasing the number of discrete ordinate directions has produced computations with higher accuracy. Based on our radiative transfer scheme, simulations of sun glint radiation have been presented for wavelengths of 670 nm and 1.6 μm. Results of simulations have shown reasonable characteristics of the sun glint radiation such as the strongly peaked, but slightly smoothed radiation by the rough ocean surface and depolarization through multiple scattering by the aerosol-loaded atmosphere. The radiative transfer scheme of this paper has been implemented to the numerical model named Pstar as one of the OpenCLASTR/STAR radiative transfer code systems, which are widely applied to many radiative transfer problems, including the polarization effect.     

Study on the absorption characteristics and birefringence of Ce-doped SBN

Cerium-doped Sr_0.60Ba_0.40Nb₂O₆ (SBN:60) crystals were obtained by Czochralski method. Optical transmission spectra were measured and the absorption coefficients were calculated in the visible range. The results showed that Ce-doped crystals were transparent for wavelengths more than and the fundamental absorption edge shifted towards the longer wavelength direction with increasing Ce concentrations. In addition, the birefringence of crystals were investigated based on the theory of interference between extraordinarily and ordinarily polarized light, and the birefringence values were determined in the long wavelength region. As a result, the birefringence becomes larger by doping of SBN crystals with cerium.     

Fourier transform of single eigenvalue probability density function using ensemble-averaged traces of the Hamiltonian

A determinantal identity is used to calculate the ensemble-averaged traces of the Hamiltonian. Using these averages a general expression is obtained for the Fourier transform of the single eigenvalue probability density function for all the three Gaussian ensembles for the two-dimensional case. It is shown how one can use the familiar step-up operators for the representation of a determinant. The ensemble-averaged traces are also used to derive the Fourier transform of the non-zero mean ensemble.     

傅里叶变换轮廓术物体三维形貌测量的系统分析及其坐标校准方法

对非共面以及非平行度下的傅里叶变换轮廓术(FTP)物体三维形貌的测最系统进行了分析,采用两个参考平面辅助分析系统光路结构,引入了一个能使双光轴共面的等效虚拟投影出瞳中心.基于光线跟踪原理给出了相位与高度的映射关系,给出了满足平等度的系统参数特性并借助于摄像机坐标系同时获取校准平面的高度以及相应的相位数据,实现了高度和横向坐标的简易校准.实验结果表明了该方法的有效性与可行性.