Extended ptychography in the transmission electron microscope: possibilities and limitations

The extended-ptychographical iterative engine (e-PIE) is a recently developed powerful phase retrieval algorithm which can be used to measure the phase transfer function of a specimen and overcome conventional lens resolution limits. The major improvement over PIE is the ability to reconstruct simultaneously both the object and illumination functions, robustness to noise and speed of convergence. The technique has proven to be successful at optical and X-ray wavelengths and we describe here experimental results in transmission electron microscopy supported by corresponding simulations. These simulations show the possibilities - even with strong phase objects - and limitations of ptychography; in particular issues arising from poorly-defined probe positions.     

点衍射波前位相的测评

提出一种检测点衍射干涉仪关键部件针孔所产生的衍射光学波前的方法。介绍了点衍射波前的产生原理,分析了小孔质量状态、照明光路调整状态与波前各个像差分量之间的关系。基于信息光学基础理论,采用傅里叶变换和迭代算法,采集针孔衍射图像并进行计算分析,实现对衍射波前的位相复原以获得波前信息。阐述了测试方法的理论依据和计算公式,应用研制的位相复原分析计算软件测试并分析了实际采集的点衍射图像,通过15次的迭代,输出的位相值逐渐收敛,图像误差因子下降到0.12。目前,该方法已用于对针孔的筛选和针孔照明系统的装调中,实验结果证明了该测试方法的可行性。     

位相复原技术在光学成像质量测评中的应用

对于大口径或特殊波段成像的光学系统,采用常规测试手段难以实现对光学系统成像质量的评估。而光学系统波像差是表征光学系统成像质量的重要指标之一。本文基于信息光学基础理论采用傅立叶变换和迭代算法通过对光学成像系统星点图像（光强点扩散函数PSF）计算分析,从而实现对光学成像系统位相的复原获得波像差信息。本文论述了有关的理论依据和分析计算公式;并研制了位相复原分析计算软件。通过计算机仿真与误差分析论证了研制的位相复原计算方法的正确性,复原误差小于5%。提出了在实际应用中采用此方法时减少复原误差的一种途径。通过实际采集的光学系统星点图像的位相复原实验验证了位相复原分析软件的适用性。此方法为非常规光学成像系统波相差的评估工作提供了新途径。     

Error tolerance of an iterative phase retrieval algorithm for moveable illumination microscopy

This paper examines the behaviour of the new Ptychographical Iterative Engine (PIE) algorithm when part of the initial information it requires is inaccurately known. This could be the parameters describing the illuminating wavefunction, the precise location of the specimen relative to the illuminating wavefunction, or other information that is assumed about the physical system. The tolerance of the algorithm for unavoidable problems such as noise and source incoherence is also investigated, leading to the conclusion that this approach to phase retrieval is very robust. It can not only tolerate errors in the assumed parameters, but can often be used as a method of characterising the parameters more accurately.     

Influence of thick crystal effects on ptychographic image reconstruction with moveable illumination

The properties of the iterative phase-retrieval ptychographical imaging technique are modelled. We use the multi-slice method to generate a series of diffraction patterns when a small convergent illumination spot is moved across a silicon crystal orientated in the 1 0 0 direction. These are then used to reconstruct the transmission function of the sample by solving the phase of diffraction patterns using the ptychographical iterative engine (PIE) algorithm [H.M.L. Faulkner, J.M. Rodenburg, Physical Review Letters 93 (2004) 023903], which assumes the object is a thin, two-dimensional grating. It is found that to obtain lattice-resolved reconstructions, the thickness of the crystal should be smaller than half of the corresponding extinction distance, the probe should be highly defocused to obtain a planar enough wave front and the movements of the probe should be as small as possible to minimize the changes in the transmission function of the sample for two adjacent illumination positions     

A method for correcting the effect of specimen drift on coherent diffractive imaging

Coherent diffractive imaging involves the inversion of a diffraction pattern to find the wave function at the exit-surface plane of the specimen. It is a promising technique for imaging, for example, nanoparticles with electrons and biological molecules with X-rays. If the illumination is not a plane wave of infinite extent, then a relative drift between the illumination and the object introduces errors into the diffraction pattern; an issue which is often overlooked. This may be of particular importance for applications with electron microscopes which use nanoscale probes. Here we show that beams which are uniform over a sufficiently large region can be used to pose a phase retrieval problem that is immune from specimen drift, provided suitable analysis of the diffraction data is undertaken. The method only applies to objects contained within a support that is smaller than a uniform region of the beam.     

Phase resolving microscopy by multi-plane diffraction detection

An easily applicable quantitative phase-contrast microscopy is presented. A bright-field microscope with a coherent illumination is used. Only a series of diffraction images is taken in different distances from the sample. For reconstruction, a conjugate gradient technique as a new variant of phase retrieval technique is developed. The technique is experimentally investigated in detail. A phase accuracy up to 0.07 rad or a height accuracy of 13 nm in transmission for a binary test sample is reached, respectively.     

基于松下电工FP1型PLC的直线插补程序设计

PLC在机械设备自动控制中有着广泛的应用,在PLC上开发直线及圆弧插补功能将拓展PLC在数控机床等领域的应用范围。介绍了在松下电工FP1型PLC上开发直线插补程序实现对二维数控平台控制的方法。     

Phase retrieval and aberration correction in the presence of vortices in high-resolution transmission electron microscopy.

We discuss phase retrieval and the correction of images for aberrations, in particular defocus and spherical aberration, in high-resolution transmission electron microscopy. Non-interferometric phase retrieval requires at least two intensity measurements in different planes. Vortices in the phase may occur in the image plane or the other planes involved in the phase retrieval. We discuss the performance of various methods of phase retrieval in that case. After retrieval of the phase, the aberrations can be corrected in the Fraunhofer diffraction space (the wave function in the diffraction space is related to that in the image space by a Fourier transform). The aberration-corrected image is obtained from the aberration-corrected wave function in the diffraction plane by inverse Fourier transformation.     

Coherent nano-area electron diffraction

We describe the new coherent nano-area electron diffraction (NED) and its application for structure determination of individual nanostructures. The study is motivated by the challenge and the general lack of analytical techniques for characterizing nanometer-sized, heterogeneous phases. We show that by focusing electrons on the focal plane of the pre-objective lens using a 3rd condenser lens and a small condense aperture, it is possible to achieve a nanometer-sized highly parallel illumination or probe. The high angular resolution of diffraction pattern from the parallel illumination allows over-sampling and consequently the solution of phase problem based on the recently developed ab initio phase retrieval technique. From this, a high-contrast and high-resolution image can be reconstructed at resolution beyond the performance limit of the image-forming objective lens. The significance of NED for nanostructure characterization will be exemplified by single-wall carbon nanotubes and small metallic clusters. Imaging from diffraction patterns, or diffractive imaging, will be demonstrated using double-wall carbon nanotubes.     

Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging

We outline a new approach to X‐ray projection microscopy in a scanning electron microscope (SEM), which exploits phase contrast to boost the quality and information content of images. These developments have been made possible by the combination of a high‐brightness field‐emission gun (FEG)‐based SEM, direct detection CCD technology and new phase retrieval algorithms. Using this approach we have been able to obtain spatial resolution of < 0.2 µm and have demonstrated novel features such as: (i) phase‐contrast enhanced visibility of high spatial frequency image features (e.g. edges and boundaries) over a wide energy range; (ii) energy‐resolved imaging to simultaneously produce multiple quasi‐monochromatic images using broad‐band polychromatic illumination; (iii) easy implementation of microtomography; (iv) rapid and robust phase/amplitude‐retrieval algorithms to enable new real‐time and quantitative modes of microscopic imaging. These algorithms can also be applied successfully to recover object–plane information from intermediate‐field images, unlocking the potentially greater contrast and resolution of the intermediate‐field regime. Widespread applications are envisaged for fields such as materials science, biological and biomedical research and microelectronics device inspection. Some illustrative examples are presented. The quantitative methods described here are also very relevant to projection microscopy using other sources of radiation, such as visible light and electrons.     

Axial Phase-Darkfield-Contrast (APDC), a new technique for variable optical contrasting in light microscopy

Axial phase-darkfield-contrast (APDC) has been developed as an illumination technique in light microscopy which promises significant improvements and a higher variability in imaging of several transparent 'problem specimens'. With this method, a phase contrast image is optically superimposed on an axial darkfield image so that a partial image based on the principal zeroth order maximum (phase contrast) interferes with an image, which is based on the secondary maxima (axial darkfield). The background brightness and character of the resulting image can be continuously modulated from a phase contrast-dominated to a darkfield-dominated character. In order to achieve this illumination mode, normal objectives for phase contrast have to be fitted with an additional central light stopper needed for axial (central) darkfield illumination. In corresponding condenser light masks, a small perforation has to be added in the centre of the phase contrast providing light annulus. These light modulating elements are properly aligned when the central perforation is congruent with the objective's light stop and the light annulus is conjugate with the phase ring. The breadth of the condenser light annulus and thus the intensity of the phase contrast partial image can be regulated with the aperture diaphragm. Additional contrast effects can be achieved when both illuminating light components are filtered at different colours. In this technique, the axial resolution (depth of field) is significantly enhanced and the specimen's three-dimensional appearance is accentuated with improved clarity as well as fine details at the given resolution limit. Typical artefacts associated with phase contrast and darkfield illumination are reduced in our methods.     

PLC在注聚站中的应用

介绍了注聚站的工艺流程及控制要求，并针对该要求设计了控制系统。系统采用PLC作为控制中心。对该系统的功能、硬件配置和软件编写进行了讨论，分析了各I／O模块的功能，并给出了结构框图。该系统具有较好的通用性和扩展性，并已成功地运用在实际生产中。     

卷烟主流烟气中几种醛酮的光电离质谱研究

为了对卷烟主流烟气中的成分进行定性和定量检测,利用同步辐射光电离-飞行时间质谱装置,对卷烟主流烟气气相成分中的甲醛、乙烯酮、乙醛、丙醛和丙酮进行研究。通过实时获得烟气在不同光子能量下的质谱图,可以获得这些成分的质荷比信息;改变光子能量,对潜在的醛、酮质谱峰扫描光电离效率曲线,与其标准光电离曲线和电离能比对,可以进行准确的定性。     

Effective phase correction function for high-resolution exit wave reconstruction by a three-dimensional Fourier filtering method

The phase correction function used in the three-dimensional Fourier filtering method (3D-FFM) for compensating lens aberrations was investigated to reconstruct a high-resolution exit wave of a sample. An appropriate function, which hardly suffered from imperfect illumination conditions, was determined by comparing two types of phase correction functions with numerical calculations and experiments using through-focus images of an amorphous thin film and a [110]-oriented Si single crystal taken under tilted illumination or partially coherent illumination. Theoretical calculations indicated that a function in terms of w (an axial Fourier component), available uniquely in the 3D Fourier space, compensated for the phase shift due to the spherical aberration more precisely than did a conventional function in terms of g (the two-dimensional (2D) planar Fourier components). Experimentally, exit waves reconstructed using the w-function showed sample structures at approximately 20% higher resolution than those reconstructed using the g-function. Image contrast simulations proved that the w-function had a significant advantage over the g-function: the former canceled out the effect of illumination divergence, resulting in a high-resolution exit wave. These results demonstrated that exit waves, which are uniquely realized in the 3D-FFM, should be reconstructed using the w-type phase correction function.     

Evanescent-wave microscopy: A simple optical configuration

Under suitable conditions, the region of the aqueous phase immediately adjacent to a glass-water interface can be selectively illuminated using the evanescent wave created when total internal reflection occurs at the interface. Objects in the aqueous phase away from the glass become effectively invisible, since the intensity of the evanescent wave decays exponentially with distance from the interface. Previous methods of generating evanescent waves for light microscopy have employed accessory light sources and optical components that directed the illumination on the specimen from one side. The asymmetric illumination creates a surprising orientation dependence of visibility for some specimens. Objects such as microtubules are totally invisible unless they are orientated nearly perpendicular to the direction of illumination. An explanation of this phenomenon is provided in terms of the geometry of diffraction of light by long thin objects. A simple method of achieving evanescent-wave illumination is described and shown to be useful in practice for biological specimens. In contrast to previously described methods, the present arrangement has the advantage of producing circularly symmetric illumination, and of utilizing only standard optical microscope components. The system has been used for imaging specimens both by light scattering and by fluorescence. It has proved useful for following the fragmentation of flagella into isolated microtubules, observing microtubules gliding over dynein adsorbed to a surface, and also for determining the arrangement of vinculin and alpha-actinin in cell-substratum attachment sites and termini of growing myofibrils in cardiac cells.     

数字全息干涉测量的时域和复数空间处理法

描写了一种新颖的在复数域处理数字全息干涉的方法.不同于一般的直接处理相位信息的数字相位相减法,本文提出的方法处理的是可以直接得出相位的复数信号.基于这种概念,本文提出了两种时域相位提取的算法.在这两种算法中,CCD相机感光原件的每一个像素做为一个新的独立的传感器,然后每个像素的复数信号作为时间的函数被测量和处理.这两种算法被应用于有台阶的物体的形貌检测,试验的结果证明,本文提出的算法优越于现在的数字全息通用的算法.     

Phase‐retrieved pupil function and coherent transfer function in confocal microscopy

This work reports on the retrieval of the pupil function and coherent transfer function of a coherent reflection type confocal microscope from simulated measurements of the intensity point spread function. Two phase retrieval algorithms are presented in this vein, which incorporate the multiple pupil dependence of image formation in confocal microscopy. Verification of the algorithms follows by numerical simulations.     

相位恢复算法在仿真与实验上的研究

相位恢复算法一直存在着精确度不高,收敛速度慢甚至停滞不前等问题。将基于光强传输方程(TIE)法与G-S迭代算法混合提高了相位恢复的精确度,梯度算法的提出加大了迭代步长,使得收敛速度加快。采用GS-TIE算法和振幅加成梯度算法分别从仿真和实验的角度去比较分析恢复的效果。通过对二维图像仿真得出,振幅加成梯度算法在收敛速度上是GSTIE迭代算法的3倍,精确度是GS-TIE迭代算法的10倍。从实验结果得知,GS-TIE恢复的相位清晰可见,轮廓明显,在边缘处过度均匀,而振幅加成梯度算法相对比较模糊,在轮廓边缘处过度不均匀,悬差较大。     

Structure determination at the atomic level from dynamical electron diffraction data under systematic row conditions.

We discuss a method to obtain structural information on crystals at the atomic level in high-resolution transmission electron microscopy from dynamical diffraction data under systematic row conditions. Working at a fixed incident energy and within an N-beam approximation, data is required at a well defined set of N incident beam orientations to determine the scattering matrix, one orientation for each column in the matrix. At each orientation the corresponding column of the scattering-matrix is obtained by Fourier transformation of the exit surface wave function. Thus, in addition to each exit surface image, we must recover the phase of the wave function for that orientation in the image plane. We show that retrieval of the phase using algorithms based on conservation of flux, which assume continuity of the phase, can yield incorrect solutions for the phase. This is because singularities can occur in the phase of the wave field at points where the intensity is zero, which can lead to edge dislocations in the phase. We demonstrate, using a model example, how these edge dislocations arise. We will show that phase retrieval from a through focal series of measurements or using the Gerchberg-Saxton algorithm (starting from measurements of an image and the corresponding diffraction pattern), correctly retrieves the phase and hence the exit surface wave function for all the orientations required to obtain the scattering-matrix. The dynamical (multiple) scattering can then be inverted to uniquely obtain the projected potential.