Determination of structure of weak scatterers from holographic images

For a weak scatterer a three dimensional Fourier transform of the image formed by a generalized hologram is shown to yield directly the Fourier transform of the scattering potential evaluated on the Ewald sphere. The entire scattering potential can be approximately determined if the object is illuminated from all directions in a series of experiments and if the scattering potential is essentially bandlimited to within a sphere of radius 4π/λ.     

The representation of waist-to-waist transformation of Gaussian beams by the scaled fractional Fourier transform

The beam waist-to-waist transformation of Gaussian beams between input and output reference planes described by the scaled fractional Fourier transform is analyzed in this paper. We obtain the transfer matrix of ABCD optical system that corresponds to the scaled fractional Fourier transform. The results show that the beam waist-to-waist transformation of Gaussian beams can be described by the scaled fractional Fourier transform when the ABCD optical system has a suitable transfer matrix. The relationship between the input and output waist planes and some particular cases when a Gaussian beam passes through a thin lens is also discussed.     

Post-annealing effect on the structural and mechanical properties of multiphase zirconia films deposited by a plasma focus device

Nanostructured multiphase zirconia films （MZFs） are deposited on Zr substrate by the irradiation of energetic oxygen ions emanated from a plasma focus device. The oxygen operating gas pressure of 1 mbar （1 bar=105 Pa） provides the most appropriate ion energy flux to deposit crystalline ZrO2 films. X-ray diffraction （XRD） patterns reveal the formation of polycrystalline ZrO2 films. The crystallite size （CS）, crystal growth, and dislocation densities are attributed to increasing focus shots, sample axial distances, and working gas pressures. Phase and orientation transformations from t-ZrO2 to m-ZrO2 and c-ZrO2 are associated with increasing focus shots and continuous annealing. For lower （200 ℃） annealing temperature （AT）, full width at half maximum （FWHM） of diffraction peak, CS, and dislocation density （δ） for （020） plane are found to be 0.494, 16.6 nm, and 3.63×10-3 nm-2 while for higher （400 ℃） AT, these parameters for （111） plane are found to be 0.388, 20.87 nm, and 2.29×10-3 nm-2, respectively. Scanning electron microscope （SEM） results demonstrate the formation of rounded grains with uniform distribution. The estimated values of atomic ratio （O/Zr） in ZrO2 films deposited for different axial distances （6 cm, 9 cm, and 12 cm） are found to be 2.1, 2.2, and 2.3, respectively. Fourier transform infrared （FTIR） analysis reveals that the bands appearing at 441 cm-1 and 480 cm-1 belong to m-ZrO2 and t-ZrO2 phases, respectively. Maximum microhardness （8.65±0.45 GPa） of ZrO2 film is ～ 6.7 times higher than the microhardness of virgin Zr.     

离焦模糊图像中汉字识别技术研究

提出了辐射投影变换(RPT),给出了数学模型和实现方法以及相应的投影函数(RPTF)。为了进一步提高其性能,对原始投影变换进行了优化改进,即累加原始函数的值并作旋转变换,从而得到了改进投影累加函数(IPAF),它可直接用于离焦模糊图像中汉字的识别。将傅里叶变换应用到IPAF上,使描述和识别用的特征量大为减少。采用基于IPAF的傅里叶子(前8个傅里叶系数)作为特征量,对离焦模糊的一级汉字进行识别,总识别率达到了97 4%。     

ZnO thin film characterization by X-ray reflectivity optimization using genetic algorithm and Fourier transformation

Zinc oxide (ZnO) thin film was fabricated by sol-gel spin coating method on glass substrate. X-ray reflectivity (XRR) and its optimization have been used for characterization and extracting physical parameters of the film. Genetic algorithm (GA) has been applied for this optimization process. The model independent information was needed to establish data analyzing process for X-ray reflectivity before optimization process. Independent information was exploited from Fourier transform of Fresnel reflectivity normalized X-ray reflectivity. This Fourier transformation (Auto Correlation Function) yields thickness of each coated layer on substrate. This information is a keynote for constructing optimization process. Specular X-ray reflectivity optimization yields structural parameters such as thickness, roughness of surface and interface and electron density profile of the film. Acceptable agreement exists between results obtained from Fourier transformation and X-ray reflectivity fitting.     

傅里叶-梅林变换(FMT)在畸变-不变图像识别中的应用

针对尺度缩放和角度旋转变化目标相关识别率低的问题,在联合相关识别中加入傅里叶-梅林变换方法.采用傅里叶-梅林变换(FMT)中的对数极坐标变换、梅林变换、傅里叶变换具有的旋转、尺度、平移(RST)不变性,可以提高JTC图像识别的性能,实现畸变-不变图像的识别.利用联合变换相关器对角度旋转0°～40°、尺度变化0～20%的目标进行计算机仿真实验.实验结果表明:在JTC中采用FMT可以实现畸变-不变图像的识别.     

New Poisson Sum Formula Derived by Squeezing Transformation in Quantum Optics

Using squeezing transform in the context of quantum optics and based on the Fourier series expansion we rigorously derive a new Poisson sum formula. Application of this new formula to the representation transformation of kq-wave function for describing electrons in periodic lattice is demonstrated. In so doing, the transition matrix element of harmonic oscillator in kq representation is derived.     

基于希尔伯特变换的干涉条纹相位解调新算法

提出了一种新的应用希尔伯特变换解调干涉条纹相位的算法,可以从单幅干涉条纹图中解调出全场相位分布.在实际应用中,常借助傅里叶变换实现希尔伯特变换算法,但是会忽略负频率成分,造成相位信息的丢失.对于相位分布非单调变化的干涉条纹,提出了一种判断函数,用来计算相位信息零频率点的分布.利用相位的零频率点分布构造了一个二元模板,使用该模板对本文提出的两次希尔伯特变换法产生的包裹相位图进行修正.对修正后的包裹相位图进行解包裹处理,可以得到连续的全场相位分布.对该方法用计算机模拟进行了验证.     

Invariant Joint Transform CorrelatorⅠ: Mapping Filter

l.IntroductionAVanderLugtcomp1exlnatchingspatialcorreIator[1jandajointtransformcorrela-tor[z~ejaret``omaJorkindsofcorrelators,however,theyaresensitivetoscalingandro-tationvariance.Thisdisadvantageisaseverelimitationforthemtobeusedinpracticalapplications-Invariantprocessingwiththeclassicalopticalcorre1atorwithproPertiesotherthanPOsitiondemandsthatthepropertyisrepresentedasashift.WithaIog-POlarmafrping[="j,thesizeandorientationw'il1beexpressedasshiftparameters,orratherrotationascyc1icshift.…     

傅里叶思想的精髓及其伟大之处

介绍了傅里叶级数和傅里叶变换的基本思想,从哲学、物理学和数学的角度阐述了其深刻涵义和伟大之处.指出了傅里叶的思想和牛顿-莱布尼茨的思想的不同之处.导出了四维协变的傅里叶变换公式.简要介绍了傅里叶级数和变换在物理学中的应用.     

光学傅里叶变换系统频谱位置的一种简单推导方法

以不同光照条件下各种光学傅里叶变换系统为研究对象,利用光学变换矩阵和柯林斯公式推导了其频谱位置所满足的条件.推导过程表明,该方法具有简单、便捷和容易在有限的课堂教学时间内讲解清楚的特点.     

光束分数傅里叶变换几何特性的相空间束矩阵分析方法

提出一种分析傍轴光束分数傅里叶变换几何特性的相空间束矩阵变换的简单方法. 以分析椭圆高斯光束分数傅里叶变换几何特性为例，研究表明，利用本方法讨论傍轴束分数傅里叶变换的几何特性简单可靠、从几何图像理解傍轴束分数傅里叶变换清晰直观. 为研究光束传输变换的特性提供了一种简单方便的新途径. 关键词： 相空间束矩阵 分数傅里叶变换 椭圆高斯光束     

铁磁形状记忆合金Ni52.2Mn23.8Ga24的马氏体相变及其物理表征

对Ni52.2Mn23.8Ga24的单晶样品在马氏体相变过程中的相变潜热、磁性、电阻以及应变等物理序参量进行了测量.测量结果表明:不同的物理机制表征的相变温度有所不同.利用马氏体相变的GT关系予以分析,解释了不同测量方法获得的相变温度差别的原因.研究指出,Heusler合金Ni2MnGa的相变是分布晶格畸变类型,磁结构的变化发生在第二步晶格的非均匀切变,但相变应变与GT模型有区别. 关键词： 马氏体相变 Ni52.2Mn23.8Ga24     

Ultrasonic imaging of an object at the presence of Fourier and non-Fourier transformation in the transmitted through the object acoustic field

A metal object is computer visualized by registration of the amplitudes of the transmitted through the object short acoustic pulses. The pulses are separated by time, because of the presence of holes and internal compact components in the longitudinal section (structure along the propagation direction of acoustic wave). The acoustic field transmitted through the object is composited from a field presenting Fourier transformation of the hole shape and field, transmitted through the metal components in the longitudinal section of the object. A computer Fourier transformation of the digital data of the amplitude fields transmitted through the object components is performed instead of converging lens. The Fourier series of the object obtained as digital data after the transformation is multiplied with a term, describing the angle distribution of the field on spatial frequencies. The reconstruction of the image of the metal components is performed by reverse transformation, i.e. summing up in all spatial frequencies. 3D visualization of the transmitted through the hole acoustic field determines the hole geometry (circular, square, rectangular).It is shown that at the transmission of a short acoustic pulse through the components with different thicknesses and holes, presenting Fourier and non-Fourier transformation can be registered separately in contrast to the optics.     

Three-dimensional weight-accumulation algorithm for generating multiple excitation spots in fast optical stimulation

We report here an algorithm for calculating a hologram to be employed in a high-access speed microscope for observing sensory-driven synaptic activity across all inputs to single living neurons in an intact cerebral cortex. The system is based on holographic multi-beam generation using a two-dimensional phase-only spatial light modulator to excite multiple locations in three dimensions with a single hologram. The hologram was calculated with a three-dimensional weighted iterative Fourier transform method using the Ewald sphere restriction to increase the calculation speed. Our algorithm achieved good uniformity of three dimensionally generated excitation spots; the standard deviation of the spot intensities was reduced by a factor of two compared with a conventional algorithm.     

Particle-Mesh Ewald(PME)算法的GPU加速

讨论在NVIDIACUDA开发环境下,用GPU加速分子动力学模拟中静电作用的长程受力计算部分.采用Particle-Mesh Ewald(PME)方法,将其分解为参数确定、点电荷网格离散、离散网格的傅立叶变换、静电热能求解与静电力求解5个部分,并分别分析各部分的GPU实现.此方法已成功用于7个不同大小的生物分子体系的模拟计算,达到了7倍左右的加速.该程序可耦合到现有分子动力学模拟软件中,或作为进一步开发的GPU分子动力学程序的一部分,显著加速传统分子动力学程序.     

In situ monitoring of the solution‐mediated polymorphic transformation of glycine: characterization of the polymorphs and observation of the transformation rate using Raman spectroscopy and microscopy

The aim of this work was to investigate the mechanism and progression of the solution‐mediated polymorphic transformation and crystallization of glycine. The identification of the α‐ and γ‐forms of glycine crystals was performed using powder X‐ray diffraction (PXRD), Raman microscopy and in situ probe Raman spectroscopy. The influence of the addition of NaCl and of the process parameters such as saturation temperature, seed size and stirring speed on the transformation behavior from the metastable α‐ form to the stable γ‐ form was examined. In situ probe Raman spectroscopy was used to monitor the solid‐phase properties—polymorphic composition. Fourier transform infrared spectroscopy (FTIR) with a ZnSe window was used to track the liquid‐phase concentration at different times. Besides, the polymorphic transformation of glycine in the solvent was also examined in situ using a microscope with a heating/cooling stage. The integration of the different offline and in situ analytical measurement techniques greatly assisted in accurately and quantitatively perceiving the fundamental phenomena that govern the transformation process. Copyright © 2008 John Wiley & Sons, Ltd.     

基于线性调频Z变换的差分吸收光谱数据处理方法研究

差分吸收光谱法(differential optical absorption spectroscopy,DOAS)是一种常用的污染气体监测方法,对所监测的光谱数据去噪可以提高反演精度。可采用傅里叶变换(fast Fourier transform, FFT)滤波法滤除光谱数据中的噪声,但该算法本身会引入误差。提出一种线性调频Z变换法(chirp Z transform,CZT),通过对傅里叶变换之后的频谱进行局部细化,能够在保留傅里叶变换滤波法去噪效果的基础上,对算法的误差进行补偿,从而进一步提高反演精度。实验配置了SO₂及NO₂进行浓度反演,结果表明,直接采用相除法反演浓度时误差较大且很不稳定,线性调频Z变换法能够获得比傅里叶变换滤波法更高的反演精度。模拟了SO₂和NO₂混合气体实验,频谱分析结果表明FFT算法无法解决特征吸收结构被扭曲、削弱等问题,CZT算法能完成特定频段频谱的精细化重构。     

Polar Fourier transforms of radially sampled NMR data

Radial sampling of the NMR time domain has recently been introduced to speed up data collection significantly. Here, we show that radially sampled data can be processed directly using Fourier transforms in polar coordinates. We present a comprehensive theoretical analysis of the discrete polar Fourier transform, and derive the consequences of its application to radially sampled data using linear response theory. With adequate sampling, the resulting spectrum using a polar Fourier transform is indistinguishable from conventionally processed spectra with Cartesian sampling. In the case of undersampling in azimuth--the condition that provides significant savings in measurement time-the correct spectrum is still produced, but with limited distortion of the baseline away from the peaks, taking the form of a summation of high-order Bessel functions. Finally, we describe an intrinsic connection between the polar Fourier transform and the filtered backprojection method that has recently been introduced to process projection-reconstruction NOESY data. Direct polar Fourier transformation holds great potential for producing quantitatively accurate spectra from radially sampled NMR data.     

X-ray coherent diffraction interpreted through the fractional Fourier transform

Diffraction of coherent X-ray beams is treated through the fractional Fourier transform. The transformation allow us to deal with coherent diffraction experiments from the Fresnel to the Fraunhofer regime. The analogy with the Huygens-Fresnel theory is first discussed, a generalized uncertainty principle is introduced and the successive diffraction of two objects is interpreted through the fractional Fourier transform.