Electron Holography at Atomic Dimensions—Present State

An electron microscope is a wave optical instrument where the object information is carried by an electron wave. However, an important information, the phase of the electron wave, is lost, because only intensities can be recorded in a conventional electron micrograph. Off-axis electron holography solves this “phase problem” by encoding amplitude and phase information in an interference pattern, the so-called hologram. After reconstruction, a rather unrestricted wave optical analysis can be performed on a computer. The possibilities as well as the current limitations of off-axis electron holography at atomic dimensions are discussed, and they are illustrated at two applications of structure characterization of ε-NbN and YBCO-1237. Finally, an electron microscope equipped with a Cs-corrector, a monochromator, and a Möllenstedt biprism is outlined for subangstrom holography.     

统计最优柱面近场声全息识别声发射源研究

植物在受到病害胁迫时会发出声发射信号。通过声发射信号的采集,以统计最优柱面近场声全息技术为理论依据,进行植物的声源信号识别和声场分析。对单声源和多声源分别进行了仿真分析,通过不断修改全息柱面半径、重建柱面半径和测量点间距等参数,探索获得最佳重建效果的参数范围,同时探讨了窗函数对重建效果的影响。将基于统计最优算法的柱面近场声全息与基于空间傅里叶变换算法的柱面近场声全息进行了比较,仿真结果表明,单声源时基于空间傅里叶变换技术计算的重建面声压幅值相对误差均在10dB以下,而统计最优柱面声全息技术计算的重建面声压幅值相对误差均在15dB以下,多声源时基于空间傅里叶变换技术计算的重建面声压幅值相对误差基本在2dB左右,而统计最优柱面声全息技术计算的重建面声压幅值相对误差在26dB以下,充分表明了统计最优柱面声全息技术的优越性。     

Eliminating the Influence of the Perturbed Reference Wave in Electron Holography

Abstract

A method is developed to eliminate the influence of the perturbed reference wave when long-range electromagnetic fields are investigated by electron holography. Based on phase relationships between the reference wave and the object wave, with digital reconstruction and data processing, we can extract the phase of an object wave from the phase difference between the object wave and the perturbed wave, which is always obtained in normal reconstruction. An example of one-dimension electromagnetic fields is given to verify this method.     

Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field

The recording of the volume speckle field from an object at different planes combined with the wave propagation equation allows the reconstruction of the wavefront phase and amplitude without requiring a reference wave. The main advantage of this single-beam multiple-intensity reconstruction (SBMIR) technique is the simple experimental setup because no reference wave is required as in the case of holography. The phase retrieval technique is applied to the investigation of diffusely transmitting and reflecting objects. The effects of different parameters on the quality of reconstructions are investigated by simulation and experiment. Significant enhancements of the reconstructions are observed when the number of intensity measurements is 15 or more and the sequential measurement distance is 0.5 mm or larger. Performing two iterations during the reconstruction process using the calculated phase also leads to better reconstruction. The results from computer simulations confirm the experiments. Analysis of transverse and longitudinal intensity distributions of a volume speckle field for the SBMIR technique is presented. Enhancing the resolution method by shifting the camera a distance of a half-pixel in the lateral direction improves the sampling of speckle patterns and leads to better quality reconstructions. This allows the possibility of recording wave fields from larger test objects.     

俄歇电子全息的计算机模拟研究和数值重现

原子的芯能级电子吸收能量后被激发 ,经过退激发过程发射出的俄歇电子波在传播过程中被周围的原子散射 ,带有周围原子结构信息的散射波 (物波 )与未被散射的电子波 (参考波 )相干涉形成的衍射图即俄歇电子全息图 ,通过全息图的重现 ,可获得原子级分辨率的三维结构信息。本文在合理的物理模型下 ,以Cu单晶以及高温超导YBCO中的Y原子近邻的一些原子簇为计算实例 ,首次就受激原子周围单层近邻原子散射和多层原子散射产生的俄歇电子全息进行了计算机模拟和数值重现 ,获得了三维晶格结构参量 ,并讨论了不同原子序数的原子在全息图形成及重现中的作用。本工作有助于材料微结构的研究     

波叠加联合波束形成的局部声场重建技术研究

传统近场声全息是以快速傅里叶变换为基础的,在有限测量孔径条件下将产生窗效应和卷绕误差,因此一定程度上制约了其在工程上的应用。基于此,提出了一种基于波叠加联合波束形成的局部声场重建技术。首先利用波束形成对传声器阵列采集的声场信息进行分析计算,获得声源的具体位置;然后在该位置配置等效源,并利用迭代算法对局部声场的数据扩展;最后应用扩展后获得的声场数据进行重构。该技术只需要少量的传声器就可以方便快速的实现声场重建。在半消声室内采用两个音箱模拟声源进行研究,实验结果表明:在小测量孔径下该方法可以准确的重构外部声场,拓宽了近场声全息在工程中的应用范围。     

Phase recovery and lensless imaging by iterative methods in optical,X-ray and electron diffraction

Thomas Young's quantitative analysis of interference effects provided the confidence needed to revive the wave theory of light, and firmly established the concept of phase in optics. Phase plays a similarly fundamental role in matter-wave interferometry, for which the field-emission electron microscope provides ideal instrumentation. The wave-particle duality is vividly demonstrated by experimental 'Young's fringes' using coherent electron beams under conditions in which the flight time is less than the time between particle emission. A brief historical review is given of electron interferometry and holography, including the Aharonov-Bohm effect and the electron Sagnac interferometer. The simultaneous development of phase-contrast imaging at subnanometre spatial resolution has greatly deepened our understanding of atomic processes in biology, materials science and condensed-matter physics, while electron holography has become a routine tool for the mapping of electrostatic and magnetic fields in materials on a nanometre scale. The encoding of phase information in scattered farfield intensities is discussed, and non-interferometric, non-crystallographic methods for phase retrieval are reviewed in relationship to electron holography. Examples of phase measurement and diffraction-limited imaging using the hybrid input-output iterative algorithm are given, including simulations for soft X-ray imaging, and new experimental results for coherent electron and visible-light scattering. Image reconstruction is demonstrated from experimental electron and visible-light Fraunhofer diffraction patterns. The prospects this provides for lensless imaging using particles for which no lenses exist (such as neutrons, condensates, coherent atom beams and X-rays) are discussed. These new interactions can be expected to provide new information, perhaps, for example, in biology, with the advantage of less damage to samples.     

Computerized tomography technique for reconstruction of obstructed phase data in shearography

Shearography is an interferometric method that overcomes several limitations of holography by eliminating the reference beam. It greatly simplifies the optical setup and has much higher tolerance to environmental disturbances. Consequently, the technique has received considerable industrial acceptance, particularly for nondestructive testing. Shearography, however, is generally not applicable to the measurement of an obstructed area, as the area to be measured must be accessible to both illumination and imaging. We present an algorithm based on the principle of tomography that permits the reconstruction of the unavailable phase distribution in an obstructed area from the measured boundary phase distribution. In the process, a set of imaginary rays is projected from many different directions across the area. For each ray, integration of the phase directional derivative along the ray is equal to the phase difference between the boundary points intercepted by the ray. Therefore, a set of linear equations can be established by considering the multiple rays. Each equation expresses the unknown phase derivatives in the obstructed area in terms of the measured boundary phase. Solution of the set of simultaneous equations yields the unknown phase distribution in the blind area. While its applications to shearography are demonstrated, the technique is potentially applicable to all full-field optical measurement techniques such as holography, speckle interferometry, classical interferometry, thermography, moiré, photoelasticity, and speckle correlation techniques.     

Image reconstruction for in-line holography with the Yang-Gu algorithm

A new approach to the numerical reconstruction of wave fronts stored by in-line holography is presented. The new algorithm can achieve good reconstructed results in both unitary and nonunitary systems. The influences of recording distance and noise as well as of digitalization errors on the quality of reconstruction are numerically investigated. The experimental results demonstrate the validity of this new approach.     

Rainbow holography of a diffuse three-dimensional object with a synthetic slit

Abstract

A study of rainbow holography with a movable synthetic slit in three-dimensional (3D) space is presented. A diffuse 3D object and an imaging lens are translated uniformly along the same direction with different (or identical) speeds in the X-Y plane. The spatial frequencies of the coherent wave illuminating the object are α, 0 and γ. As a result, the synthetic slit in rainbow holography is presented at a position which depends on the translational direction of the object and the imaging lens, their relative speeds, the spatial frequency of the illuminating wave in the X ₀ direction, and the relative distance of the reference source and the reconstruction source from the holographic plate. Theoretical analysis and some experimental results are presented.     

Information Processing with Coherent Light

In any plane of an optical tract coherent light is fully described by the complex amplitude, that is to say by a two-valued function. Nevertheless, it can be also described by a one-valued or real function, such as photographic density plus a known, coherent reference wave. This is the basis of wavefront reconstruction or holography. The history of holography is presented, and some of its applications, such as holographic interferometry, contour mapping and three-dimensional pictures in monochrome or in natural colours are discussed. Some prospective applications are holographic panoramas and three-dimensional projection of moving pictures. Information coding and storage are very promising applications, but held up by the phenomenon of ‘laser speckle’. Finally it is pointed out that holographic coding, which is a very complicated and multi-dimensional type of coding, has greater potentiality than expected on the basis of Shannon's communication theory. With a code of blocks consisting of N data only N data can be transmitted exactly, but a much greater number can be transmitted with a tolerable error. J. P. Wild's Culgoora radioheliograph, which maps 3000 points with only 96 aerials by a method which could be (though for economy reasons is not) simultaneous, can be considered as the first practical application of this principle.     

基于近场声全息的重建算法分析与研究

针对声全息算法种类繁多及应用场合不同需求,通过有限元仿真和数值仿真相结合,对基于傅里叶变换、统计最优和等效源3种算法进行分析,寻找声源频率、重建距离、采样间距及正则化方法对重建精度的影响,并对其计算效率进行对比。在开阔水域进行实验验证。结果表明:随着声源频率增大,重建距离增加,采样点数减少,声全息算法的重建精度逐渐降低。在低频区域,结合L-曲线正则化法的统计最优近场声全息具有最佳的声场重建效果;基于等效源法的声全息重建精度最高,但容易产生虚像;基于傅里叶变换的声全息算法受重建距离影响严重,但重建速度优异,且声源定位准确。     

基于压缩感知和快速波叠加谱方法的近场声全息

在等效源法近场声全息理论的基础上,将等效源强和积分核函数在轴对称虚拟面上进行双向傅里叶级数展开,使待求的源强向量转化为稀疏的傅里叶展开系数向量,并结合压缩感知重构算法中的基追踪降噪算法建立了一种基于压缩感知和快速波叠加谱的半解析、半数值等效源近场声全息方法.利用脉动球源与长条形声源对比了所提方法与传统压缩等效源法的声场...     

Pseudocolour encoding by lensless one-step rainbow holography with a synthesized slit

Abstract

Pseudocolour encoding of holographic images by lensless one-step rainbow holography with a synthesized slit is proposed. When a different portion of the object is recorded the reference wave is incident at a different angle θ and during each exposure the incident angle changes continuously around this angle θ. The pseudocolour holographic image is obtained by white-light reconstruction of the lensless one-step rainbow hologram with synthesized slit. The basic advantage of this technique is the elimination of a narrow slit and a lens in the encoding process. The theoretical analysis and experimental result are presented.     

Electron holographic tomography

The exact knowledge about intrinsic electrostatic potentials and in particular their three-dimensional distribution at the nanometer scale is a key prerequisite for understanding the solid state properties. Electron holographic tomography (EHT), the combination of off-axis holography with tomography in the transmission electron microscope, provides a unique access to this information. We review the development and application of automated EHT to reconstruct 3D potentials in nanostructures such as the mean inner potential of a material or the diffusion potential across p–n junctions in semiconductors. We also discuss future challenges of the 3D reconstruction of electric crystal potentials at atomic resolution and magnetostatic fields as well as ways to overcome present limitations of the method.     

Scheme to improve the reconstructed image in parallel quasi-phase-shifting digital holography

We propose a scheme to improve the reconstructed image in parallel quasi-phase-shifting digital holography. Parallel quasi-phase-shifting digital holography is a technique capable of noiseless instantaneous measurement of three-dimensional objects, and it implements four kinds of phase shifting at a time with an array of 2 x 2 phase-shifting devices located in the reference wave. In the phase-shifting calculation in the reconstruction process of the technique, the scheme assigns the 2 x 2 cell configuration for each pixel in the vertical direction and for each 1-pixel interval in the horizontal direction of the hologram recorded by the image sensor. We conduct both a numerical simulation and a preliminary experiment. The results show that the proposed scheme can improve the quality of the reconstructed image calculated by the conventional scheme of parallel quasi-phase-shifting digital holography we previously proposed, and then the effectiveness of the proposed scheme is verified.     

Quantum-implementable selective reconstruction of high-resolution images

This paper, written for interdisciplinary audience, presents computational image reconstruction implementable by quantum optics. The input-triggered selection of a high-resolution image among many stored ones, and its reconstruction if the input is occluded or noisy, has been successfully simulated. The original algorithm, based on the Hopfield associative neural net, was transformed in order to enable its quantum-wave implementation based on holography. The main limitations of the classical Hopfield net are much reduced with the simulated new quantum-optical implementation.     

Digital recording and numerical reconstruction of holograms: an optical diagnostic for combustion

Holographic interferometry (HI) has proved to be a useful tool for nonintrusive temperature measurements in flames (and thereafter for inference of the local composition based on the state relationship approach) with high spatial and temporal resolution. Digital holographic interferometry (DHI) is a relatively new imaging and measurement technique that electronically records a hologram (e.g., on a CCD) and reconstructs it by a numerical method. Cumbersome chemical processing of the hologram is avoided in DHI, which thereby provides greater flexibility, speed, and the potential for real-time processing. In conventional holography, fringes that are neither bright nor dark on a hologram cannot be accurately resolved. The DHI technique has not yet to our knowledge been used for combustion applications. Herein we evaluate its efficacy for making temperature measurements in flames and assess its applicability through a simulation. Each part of a double exposure associated with the holographic technique is considered to be recorded by a hypothetical CCD sensor at a separate time from the other part. We applied the principles of Fourier optics to develop two numerical methods for hologram reconstruction, and we show that both methods provide an accurate reconstruction of the phase image associated with a flame. Because of the periodic nature of the wave function, the reconstructed phase values are limited to the interval [-pi/2, pi/2]. Thus an unwrapping algorithm is provided that produces a continuous phase distribution based on the condition that the reconstructed phase is jumped by a value of -pi or pi. We have also developed an iterative calculation method to adjust the value of the digital reference wave parameters that determines the phase imaging reconstruction in DHI.     

基于混合波叠加法的声源识别理论与试验研究

波叠加法作为噪声源识别的一种技术，克服了基于边界元法的声全息中的奇异值积分和解的非唯一性难题，但在测量面上要求足够多的传声器数目以满足重建精度，这样导致测量成本高、工作耗时且也不利实际实施。针对波叠加法的此缺点，提出将波叠加法和HELS方法相结合的方法，此法是基于Helmholtz方程最小二乘法，用相对少量的测点数据获得包围源的最小球面上或之外的任意一假想球面上的声压数据，然后将这些数据作为输入，计算出辐射体内混合内域虚源强的强度值，通过解离散波叠加的方程，重建出在重建面上离散点的声压值。达到用相对少量的测点数据重建表面为任意形状的振源辐射声压的目的。数值仿真与试验结果表明：它具有计算速度快、重建精度高、测量成本低和容易实施等优点，可以精确地识别和定位机械噪声源，在工程实践中具有广泛的应用前景。