基于数字全息技术的变形测量

全息技术在测量、防伪中有大量应用.数字全息技术采用数字记录和计算机处理,实现测量的方法上有其特点.本文重点对数字全息技术实现变形测量的方法和具体算法开展了研究.论文首先总结了数字全息技术应用中的基本问题,包括数字全息算法问题和噪声抑制问题等.叙述了基于数字全息技术的变形测量基本思想,及相位恢复算法,同时分析了几种变形测量的实现方法,并提出了"2+2"步变形测量方法.该方法相对于"1+1"步变形测量方法,提高了测量精度,同时比"4+4"步变形测量法提高了动态性.本文建立了实验系统,获得了硬币的数字全息图,实现了常用的"1+1"步变形测量方法、相移算法的变形测量方法以及"2+2"步变形测量方法,给出了"2+2"变形测量的实验结果.实验结果表明在数字全息技术中结合相移技术进行测量,可以提高物波再现精度,进而提高变形等的测量精度.     

Performance limits of electron holography

Transmission electron microscopy is wave optics. The object exit wave contains the full object information. However, in the usual intensity images, recorded either in real space or in Fourier space, the phases are missing. In many applications at medium and at high resolution, electron holography has shown its unique ability of solving the “missing phase problem” and utilizing the recovered phase for complete interpretation of the object structure. The question is “What are the performance limits?” with respect to field of view, lateral resolution and signal resolution. In this article, the performance limits are derived and discussed.     

机械噪声源识别的混合波叠加法

提出了一种稳健声场的全息变换算法——混合波叠加法，它结合了波叠加法和Helmholtz方程最小二乘（HELS）方法的优点，用相对少量的测点数据就可重建任意形状源表面的声场。在半消声室里，运用29个传声器组成的“＋”字形平面传声器阵列，对一运转的电机进行噪声源识别，得到声源的空间声压场分布及声源位置，显示出混合波叠加法在工程实践中广泛的应用前景。     

混合波叠加法识别噪声源的理论与试验研究

针对基于边界元法的声全息中的奇异值积分和解的非惟一性难题及其基于Helmholtz方程最小二乘法（HELS）特殊函数选择计算问题，提出以一种稳健的声场的全息变换算法——混合波叠加法，此法用相对少量的测点数据就可重建任意形状源表面的声场。在对典型声源进行数值仿真并验证该技术重建空间声压场精度高、精确地识别和定位噪声源后，在半消声室里，运用29个传声器组成的“＋”字型平面传声器阵列，得到音箱声源的空间声压场分布及声源位置，显示出混合波叠加法在工程实践中广泛的应用前景。     

Resolution extension and exit wave reconstruction in complex HREM

Direct methods in real and reciprocal space are developed for structural reversion. The direct method in real space involves the use of a novel method to retrieve the phase in the image plane using transport of intensity equation/maximum entropy method (TIE/MEM) and exit wave reconstruction by self-consistent propagation. Since the exit wave is restored from the complex signal in the image planes, no image model between the exit wave and image is assumed. The structural information in the reconstructed exit wave is then further extended by a "complex" maximum entropy method as a direct method in reciprocal space to extrapolate the phase to higher frequencies.     

Influence of the elliptical illumination on acquisition and correction of coherent aberrations in high-resolution electron holography

In high-resolution off-axis electron holography, the interpretable lateral resolution is extended up to the information limit of the electron microscope by means of a correcting phase plate in Fourier space. A plane illuminating electron wave is generally assumed. However, in order to improve spatial coherence, which is essential for holography, the object under investigation is illuminated with an elliptically shaped electron source. This special illumination imposes a variation of beam directions over the field of view. Therefore, due to the interaction of beam tilt and coherent wave aberration, the effective aberrations vary over the field of view yielding a loss of isoplanicity. Consequently, in the past the aberrations were only corrected successfully for a small part of the field of view. However, a thorough analysis of the holographic imaging process shows that the imaging artifacts introduced by the elliptical illumination can be corrected under reconstruction by means of a phase curvature, which models the illuminating wave front. Applied in real space, this phase curvature is seamlessly incorporated into the correction process for coherent wave aberration resulting in an improvement of interpretable lateral resolution up to the information limit for the whole field of view.     

基于传递函数估计的近场声全息的噪声源识别

在近场声全息(NAH)声场测量中,噪声的存在使近场声全息重建精度降低,影响声场重建的实现。本文提出一种基于传递函数估计的双测量面NAH技术,首先采用双测量面对噪声源信号进行测量,然后基于传递函数法引入一种合理的传递函数估计,结合参考传声器信号来求解全息面复声压,最后利用前后测量面数据相位差异来求解格林函数,根据声场重建公式进行近场声全息声场重建。数值仿真及重建误差分析表明,存在测量噪声影响的情况下,本文提出的方法相比传递函数法NAH重建误差更小,能够更准确地识别声源位置并提高声全息重建精度。最后对某型拖拉机前端进行近场阵列扫描试验,验证基于传递函数估计的双测量面NAH的有效性。     

Dark-field electron holography for the measurement of geometric phase

The genesis, theoretical basis and practical application of the new electron holographic dark-field technique for mapping strain in nanostructures are presented. The development places geometric phase within a unified theoretical framework for phase measurements by electron holography. The total phase of the transmitted and diffracted beams is described as a sum of four contributions: crystalline, electrostatic, magnetic and geometric. Each contribution is outlined briefly and leads to the proposal to measure geometric phase by dark-field electron holography (DFEH). The experimental conditions, phase reconstruction and analysis are detailed for off-axis electron holography using examples from the field of semiconductors. A method for correcting for thickness variations will be proposed and demonstrated using the phase from the corresponding bright-field electron hologram.     

Retrieval of object information by inverse problems in electron diffraction

The imaging of crystal defects by high-resolution transmission electron microscopy or with the help of the electron diffraction contrast technique is well known and routinely used. However, a direct and phenomenological analysis of electron micrographs is mostly not possible, but requires the application of image simulation and matching techniques. The trial-and-error matching technique is the indirect solution to the direct scattering problem applied to analyse the nature of the object under investigation. Alternatively, inverse problems as direct solutions of electron scattering equations can be deduced using either an invertible linearized eigenvalue system or a discretized form of the diffraction equations. This analysis is based on the knowledge of the complex electron wave at the exit plane of an object reconstructed for the surrounding of single reflections by electron holography or other wave reconstruction techniques. In principle, it enables directly the retrieval of the local thickness and orientation of a sample as well as the refinement of potential coefficients or the determination of the atomic displacements, caused by a crystal lattice defect, relative to the atom positions of the perfect lattice. Considering especially the sample orientation as perturbation the solution is given by a generalized and regularized Moore–Penrose inverse, where the resulting numerical algorithms imply ill-posed inverse problems.     

Off-axis and inline electron holography: Experimental comparison

Electron holography is a very powerful technique for mapping static electric and magnetic potentials down to atomic resolution. While electron holography is commonly considered synonymous with its off-axis variant in the high energy electron microscopy community, inline electron holography is widely applied in low-energy electron microscopy, where the realization of the off-axis setup is still an experimental challenge. This paper demonstrates that both inline and off-axis holography may be used to recover amplitude and phase shift of the very same object, in our example latex spheres of 90 and 200 nm in diameter, producing very similar results, provided the object does not charge under the electron beam.     

Exit wave reconstruction at atomic resolution

An iterative method for exit wave function reconstruction based on wave function propagation in free space is presented. The method, which has the potential for application to many forms of microscopy, has been tailored to work with a through focal series of images measured in a high-resolution transmission electron microscope. Practical difficulties for exit wave reconstruction which are pertinent in this experimental environment are the slight incoherence of the electron beam, sample drift and its effect upon the defocus step size that can be utilised, and the number of image measurements that need to be made. To gauge the effectiveness of the method it is applied to experimental data that has been analysed previously using a maximum likelihood formalism (the MAL method).     

光学元件表面的数字全息在线检测

针对光学元件表面质量在线检测的特点,设计了基于数字全息的三维再现检测系统.该系统采用离轴光路,避开了被测元件的光轴,在数字全息再现过程中应用倾斜相差补偿技术去除了由于离轴检测引入的倾斜相位畸变.在检测过程中,利用围绕光轴旋转被测元件的方法来改变入射照明光方向矢量和相应的观察方向,实现了多照明矢量合成孔径技术的应用,扩展了系统的检测距离,提高了系统分辨率.同时,多照明角度下检测数据的叠加,还有效地抑制了检测过程中出现的散斑噪声对结果准确度的影响.通过对分辨率板、高精度玻璃反射镜的检测实验,验证了该系统在光学元件表面检测中的作用.当记录距离为40 cm时,其分辨率能够达到10 μm,满足光学元件表面检测的需要.     

显微数字全息图相位的滤波法提取

显微数字全息的关键技术之一是其相位信息的提取。通过分析显微数字全息图的空间频谱特点,提出了一种新的相位提取方法。将数字全息图频谱进行搬移,使物光频谱中心移到频域坐标原点;设计有限脉冲响应(FIR)数字滤波器滤出物光频谱;求解滤波后信号的辐角得到全息图相位。对设计的实验系统进行了验证,实验结果表明采用提出的方法提取显微数字全息相位,完全可行,效果良好。     

数字全息相位再现误差分析及抑制技术

为实现基于数字全息的三维轮廓测量,本文探讨了菲涅耳近似算法实现数字全息相位再现的误差及抑制技术。首先理论分析了基于菲涅耳近似算法实现全息相位再现所包含的误差项,然后计算机模拟了数字离轴全息图的记录和相位再现结果,在此基础,模拟分析了离焦误差、数字再现光波误差及样本深度对相位再现的影响。针对记录参考光波和光学器件所引入的相位误差及其不定性,本文提出利用相位相减全息图处理方法加以消除,并给出了实验结果加以验证。模拟分析结果表明,菲涅耳近似算法误差、离焦误差、数字再现光波倾斜误差、解包裹错误对相位再现结果都有不同程度的影响。若获得高精度的再现结果,对记录过程、再现参数选择和处理方法都要进行严格控制或适当的选取。     

计算全息图的基本理论与制作

与传统光学全息相比,计算全息图因具有极高灵活性,制作简单并且能够记录实际不存在物体的特点而被广泛应用。越来越多的专家和学者致力于研究计算全息图。在介绍计算全息基本理论后,采用四阶迂回相位编码方法,基于MatLab平台分别制作了傅里叶二元计算全息图和菲涅耳二元计算全息图。再现实验中得到的再现像直观明显,对研究和开拓计算全息图更广泛的应用具有参考价值。     

Reconstruction of the projected crystal potential from a periodic high-resolution electron microscopy exit plane wave function

A method based on a simulated annealing algorithm is applied for the reconstruction of the projected crystal potential belonging to a periodic high-resolution electron microscopy exit plane wave function. Using simulated exit plane wave functions of GaAs at different specimen thicknesses, the convergence behaviour and the accuracy of the algorithm are investigated. It is demonstrated that the reconstruction is possible even under strongly non-linear scattering conditions at small specimen thicknesses. Further, the convergence of the algorithm to an ambiguous solution beyond a certain specimen thickness is discussed.     

Projected potential profiles across interfaces obtained by reconstructing the exit face wave function from through focal series

An iterative method for reconstructing the exit face wave function from a through focal series of transmission electron microscopy image line profiles across an interface is presented. Apart from high-resolution images recorded with small changes in defocus, this method works also well for a large defocus range as used for Fresnel imaging. Using the phase-object approximation the projected electrostatic as well as the absorptive potential profiles across an interface are determined from this exit face wave function. A new experimental image alignment procedure was developed in order to align images with large relative defocus shift. The performance of this procedure is shown to be superior to other image alignment procedures existing in the literature. The reconstruction method is applied to both simulated and experimental images.     

Ultrahigh resolution imaging of local structural distortions in intergrowth tungsten bronzes

Details of the local structure of a complex tungsten bronze, K(x)WO(3) have been determined using focal series exit wave reconstruction. Octahedral rotations in different structural regions of the same crystal have been directly measured from the exit wave phase and correlated with variations in cation occupancy determined from the exit wave modulus.     

Determining the radial pair-distribution function within intergranular amorphous films by numerical nanodiffraction

We report on an alternative method to electron nanodiffraction and fluctuation microscopy for the determination of the reduced density function G(r) of amorphous areas with small cross-sections. This method is based on the numerical extraction of diffraction data from the complex-valued exit-face wave function as obtained by HRTEM focal series reconstruction or electron holography. Since it is thus possible to obtain "diffraction data" from rectangular areas of any aspect ratio, this method is particularly suited for intergranular glassy films of only 1-2 nm width, but lengths of several 100 nm. A critical comparison of this method with the already established nanodiffraction and fluctuation microscopy will be made.     

In-line holographic electron microscopy in the presence of external magnetic fields

It is now a well-known fact that the phase of electron waves is altered by external magnetic fields via the Aharonov-Bohm effect. This implies that any electron interference effects will be to some degree affected by the presence of such fields. In this study we examine the distortion effects of external (constant and variable) magnetic fields on electron interference and holography. For digital holography, the reconstruction of the object is done via numerical calculations and this leaves the door open for correcting phase distortions in the hologram reconstruction. We design and quantitatively assess such correction schemes, which decidedly depend on our knowledge of the magnetic field values in the holographic recording process. For constant fields of known value we are able to correct for magnetic distortions to a great extent. We find that variable fields are more destructive to the holographic process than constant fields. We define two criteria, related respectively to global and local contrast of the hologram to establish the maximum allowed external field which does not significantly hinder the accuracy of in-line holographic microscopy with electrons.