光子回声量子存储器中非均匀展宽频谱对存储效率的影响

本文提出了一个利用光子回声技术探究非均匀展宽频谱线形(如高斯、洛伦兹分布)对存储效率影响的简捷方法。我们发现当信号光脉冲的持续时间与介质频谱线宽的乘积远大于1时,可将分布函数的傅里叶变换近似成狄拉克函数,使得研究非均匀展宽频谱对存储效率的影响变得非常容易;通过计算发现不同线形分布达到最佳存储效率的光学深度有所不同,频谱线形趋于均匀时达到最优存储效率的存储介质光学深度最小。该研究对实验上实现最优化光量子态存储具有指导意义。     

基于图像二维小波多尺度分解傅里叶变换轮廓术

应用傅里叶变换轮廓术测量物体三维面形时,当被测物体形状复杂或是被噪声严重污染时,导致频谱分布展宽,发生频谱混叠现象,基频提取困难,无法准确恢复物体的三维面型.提出了基于小波分解的傅里叶变换轮廓术,采用小波变换的方法对变形条纹图进行二维多尺度分解,重构被测物的背景图像,滤出图像的零频成分,得到相对变形条纹.运用小波变换与傅里叶变换轮廓术相结合的方法,只需拍摄一幅变形条纹图,将被测物体与背景分离,不受背景成分的影响,且易于基频信息的提取,降低了对滤波器的要求.实验证明该方法较好地防止了频谱的混叠问题,提高了测量范围与解相精度.     

傅里叶变换基本性质的物理诠释

数学物理方法是物理学专业基础课,其中的积分变换部分也是工程技术专业的基本教学内容.在该课程中,傅里叶变换往往是积分变换法教学的首要内容,而傅里叶变换的基本性质则是该部分的重点,也是其产生广泛应用的关键原因.本文从振动的合成与分解、物理学量纲分析等角度对傅里叶变换的线性定理、延迟定理、位移定理、标度变换定理、微分定理及卷积定理共6条基本性质进行了物理学诠释.对学生深刻理解和灵活运用傅里叶变换法解决物理问题、进行信号频谱分析大有裨益;对学生学习后续的量子力学、信号与系统等课程亦有帮助.     

信息光学 光学滤波与频谱分析

O438.2∥TB92 2006032128窗口傅里叶变换的三维面形测量= Windowed Fouriertransformfor 3-Dshape measurement[刊,中]/付艳华(四川大学电子信息学院光电系.四川,成都(610064)) ,陈文静…∥激光杂志.—2006 ,27(1) .—39 ,41提出在基于频谱分析的三维面形测量中,用窗口傅里叶变换( WFT)代替传统的快速傅里叶变换(FFT)去获取三维物体面形分布。理论分析和实验结果表明,窗口傅里叶变换不但可以减小频谱混叠对测量精度的影响,并且若在窗口傅里叶变换的处理过程中,设置合理的“门限”,还能够有效地抑制噪声,从而在一定程度上保证了基于频谱…     

傅里叶变换轮廓要中频谱泄漏的讨论

讨论了频谱泄漏对傅里叶变换轮廓术测量精度的影响.由于用傅里叶变换轮廓术进行三维面形测量时,测得的变形光场是空间有限函数,故离散傅里叶变换时先要进行周期拓展,如果拓展周期选择不当,拓展后的条纹将不连续,对之进行傅里叶变换会产生频谱泄漏.文章从理论上推导了拓展周期与变形结构光场频谱泄漏之间的关系.给出了由泄漏引起的视场边缘误差的计算模型和定量分析.提出采用条纹外插以减小泄漏误差的方法,计算机模拟及初步实验证实了该方法的有效性.     

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.     

空间外差光谱仪干涉图非均匀性校正研究

空间外差光谱仪在研制加工过程中,由于加工误差及胶合误差会使CCD接收到的干涉图存在光强分布不均匀现象,降低了变换光谱的准确性。基于对空间外差光谱仪干涉图光强非均匀性的产生机制与特点分析基础上,提出了一种干涉图非均匀性校正方法,该方法通过对实际干涉图进行单调分解、分段归一化及重新组合过程求解出光强分布函数,然后将变换光谱与光强分布函数倒数的傅里叶变换结果进行卷积来获得非均匀性校正后的光谱,最后将校正光谱进行逆傅里叶变换从而实现干涉图的非均匀性校正。将此方法应用于空间外差试验仪的近红外实测单色光干涉图的非均匀性校正,结果显示,该方法可以有效改善干涉图光强分布的非均匀性,抑制变换光谱的边频信号,通过与仿真的理想光谱对比,1 571和1 572 nm光谱校正前后噪声的减小率分别达到40.7%和24%,提高了光谱信噪比和准确性。     

相位分布及编码尺度对计算全息再现像的影响

研究了傅里叶变换计算全息编码中相位分布和编码尺度对再现像的影响.基于罗曼Ⅲ型编码原理,用Mat-lab计算得到傅里叶变换计算全息图,通过液晶光阀输出全息图实现再现,研究再现像的特征在物图加随机相位和增大编码尺度前后的变化.结果表明:物图不加随机相位的全息图,其再现像具有高通效果,实现了边缘提取;物图加随机相位,再现相当于低通滤波,再现像被平滑,当物频谱结构丰富时,平滑作用更明显,甚至无法辨识再现像;增大编码单元尺寸,即提高编码精度可使再现像清晰.     

基于图象处理和傅里叶变换的三维多孔介质重构方法

本文基于傅里叶变换的截断高斯场方法的理论,通过从实际多孔介质二维切片的二元化图像中提取孔隙率和自相关函数来构造整个三维多孔结构.模拟结果显示通过傅里叶变换技术得到的随机过程确实满足高斯分布,且构造出的三维多孔结构的统计特性基本与二维切片类似,说明了该技术能够构造出符合要求的三维多孔介质,从而为进一步从孔隙尺度研究其内部传热传质过程奠定了基础.     

透射型体光栅对超短脉冲高斯光束衍射特性研究

采用傅里叶频谱分析法, 将超短脉冲高斯光束展开为单色单角谱成分的线性叠加;利用Kogelnik一维耦合波理论, 分析透射型体光栅对各单色单角谱成分的衍射特性;再通过逆傅里叶变换得出衍射光波的时空分布与光栅各参量的对应关系.结果表明:衍射光束在时域以及在光栅波矢与光栅前表面法向所构成平面内的空域光强分布随光栅周期的减小而呈展宽趋势, 且在空域的展宽趋势较为迅速, 与入射光束在空域进行比较, 衍射光束空域分布发生非常明显的畸变;衍射光束在时域以及在光栅波矢与光栅前表面法向所构成平面内的空域光强分布随光栅厚度的增大亦呈展宽趋势, 且展宽速度相当, 与入射光束在时域和空域比较, 均发生了较明显的畸变.     

Fiber Fourier optics

The Fourier transform of a coherent optical image can be evaluated physically by use of a single lens plus free-space propagation, thereby providing the basis for the field of Fourier optics. I point out that one can similarly evaluate the discrete Fourier transform of a sampled or pixelated optical array physically by passing the discrete array amplitudes through a network of single-mode fibers or optical waveguides. A passive optical network that evaluates the fast Fourier transform of a coherent array can be fabricated by use of (N/2)log(2)[N] optical 3-dB couplers plus small added phase shifts. Implementing such networks in fiber or integrated optical form could provide the basis for a possible technology of fiber Fourier optics.     

Improved differential 3D shape retrieval

Phase unwrapping is a complex step in three-dimensional (3D) surface measurement. To simplify the computation process, Martino et al. proposed a differential algorithm. However, it will result in large error when the orthogonal fringes are not in horizontal or vertical direction. To solve this problem, the relationship between projector׳s and camera׳s coordinate systems is introduced. With the data obtained from coordinate transformation, the improved differential algorithm can be used for orthogonal fringes in any direction. Besides that, taking advantage of Fourier differentiation theorem makes operation and calculation simpler. By contrast, the results of experiments show that the proposed method is applicable to the patterns with orthogonal fringes in every direction. In addition, Fourier differentiation theorem effectively increases the speed of differential process.     

脉冲相干激光雷达测距信号研究

对脉冲激光雷达外差测距信号进行了研究，理论上，采用调Q激光脉冲的数值计算波形，研究了脉冲激光经远处目标漫反向后进行外差接收的波形及其傅里叶变换频谱成分。实验上，研究了可调谐电光调Q射频激励波导CO2激光器脉冲激光经目标反射后的外差波形及其傅里叶变换频谱成分，并计算了目标的距离，理论分析与实验结果一致。     

Interactions of coherent electromagnetic radiation with nuclei

When coherent electromagnetic radiation resonantly couples two levels of a nucleus, the system can emit photons by stimulated and by spontaneous emission. The spontaneous emission spectrum is defined as the Fourier transform of the first-order correlation function of the magnetic or electric field operator. This function can be expressed in terms of one-time and two-time averages of nuclear operators. The one-time averages can be calculated by solving the Bloch-type equations for the matrix elements of the nuclear density operator. Application of the quantum regression theorem permits to calculate two-time averages with the aid of one-time averages and hence the radiated spectrum.     

Three-dimensional generalization of the Van Cittert-Zernike theorem to wave and particle scattering

Coherence properties of primary partially coherent radiations (light, X-rays and particles) elastically scattered from a 3D object consisting of a collection of electrons and nuclei are analyzed in the Fresnel diffraction region and in the far field. The behaviour of the cross-spectral density of the scattered radiation transverse and along to the local direction of propagation is shown to be described by respectively the 3D Fourier and Fresnel transform of the generalized radiance function of a scattering secondary source associated with the object. A relativistic correct expression is derived for the mutual coherence function of radiation which takes account of the dispersive propagation of particle beams in vacuum. An effect of the spatial coherence of radiation on the temporal one is found; in the Fresnel diffraction region, in distinction to the field, both the longitudinal spatial coherence and the spectral width of radiation affect the longitudinal coherence. A solution of the 3D inverse scattering problem for partially coherent radiation is presented. It is shown that squared modulus of the scattering potential and its 2D projections can be reconstructed from measurements of the modulus and phase of the degree of transverse spatial coherence of the scattered radiation. The results provide a theoretical basis for new methods of image formation and structure analysis in X-ray, electron, ion, and neutron optics.     

The 2.5-dimensional equivalent sources method for directly exposed and shielded urban canyons

When a domain in outdoor acoustics is invariant in one direction, an inverse Fourier transform can be used to transform solutions of the two-dimensional Helmholtz equation to a solution of the three-dimensional Helmholtz equation for arbitrary source and observer positions, thereby reducing the computational costs. This previously published approach [D. Duhamel, J. Sound Vib. 197, 547-571 (1996)] is called a 2.5-dimensional method and has here been extended to the urban geometry of parallel canyons, thereby using the equivalent sources method to generate the two-dimensional solutions. No atmospheric effects are considered. To keep the error arising from the transform small, two-dimensional solutions with a very fine frequency resolution are necessary due to the multiple reflections in the canyons. Using the transform, the solution for an incoherent line source can be obtained much more efficiently than by using the three-dimensional solution. It is shown that the use of a coherent line source for shielded urban canyon observer positions leads mostly to an overprediction of levels and can yield erroneous results for noise abatement schemes. Moreover, the importance of multiple facade reflections in shielded urban areas is emphasized by vehicle pass-by calculations, where cases with absorptive and diffusive surfaces have been modeled.     

Spatial Position Detection of Three-Dimensional Objects by Effective Three-Dimensional Correlation Based on Fourier Transform Profilometry

Spatial position detection of a three-dimensional (3D) object by a correlator based on Fourier transform profilometry is discussed. The presence of the 3D object and its precise spatial position can be recognized by the correlator using the position and phase of the correlation peak. The spatial position is obtained by the relative displacement from the position where the reference object is originally placed. The characteristic of the correlator with respect to the moving direction of a 3D object is experimentally verified. Effects of the baseline factor on 3D object recognition are also investigated.     

三维电子散斑干涉载频调制及其在柴油机上的应用

将电子散斑干涉场的三维载波调制技术应用到三维物体变形测量中.用水平方向、竖直方向及垂直试件表面的三路相干光分别照明物体，在水平和竖直方向通过控制反射镜的微小偏转引入载波，实现位移场干涉条纹的调制；利用物体的微小偏转实现离面位移场干涉条纹的调制；结合傅里叶变换法，分别解调出变形场的位相，从而实现了物体三维变形场的精确测量.将该技术应用到柴油机油泵的三维位移测量上，成功测量了油泵的三维位移场.     

Digital in-line holography with a sub-picosecond laser beam

The diffraction of an ultrashort pulsed laser beam by an opaque particle is studied. The case of a pulse with a Gaussian spectrum is investigated analytically by using the steepest descent method. This analytical solution allows us to calculate the intensity distribution of the diffraction field. This result enables to determine the optimal fractional orders Fourier transform to reconstruct digital in-line particle hologram.     

卷积完全匹配层在空爆电磁脉冲2维模拟中的应用

 在分析不同类型完全匹配层特点的基础上，选用了卷积形式完全匹配层（CPML）截断空中核爆电磁脉冲数值模拟的开放边界。从自由空间中电磁波的平面波解和分裂形式的完全匹配层出发，构造了未分裂形式的完全匹配层，应用傅里叶变换的卷积定理，推导出2维旋转椭球-双曲正交坐标系下卷积形式完全匹配层介质中电磁场的迭代形式的离散方程。计算表明，采用CPML吸收边界方法使得截断的外边界处的场的计算误差大大减少。