Probe retrieval in ptychographic coherent diffractive imaging

Ptychography is a coherent diffractive imaging method that uses multiple diffraction patterns obtained through the scan of a localized illumination on the specimen. Until recently, reconstruction algorithms for ptychographic datasets needed the a priori knowledge of the incident illumination. A new reconstruction procedure that retrieves both the specimen's image and the illumination profile was recently demonstrated with hard X-ray data. We present here the algorithm in greater details and illustrate its practical applicability with a visible light dataset. Improvements in the quality of the reconstruction are shown and compared to previous reconstruction techniques. Implications for future applications with other types of radiation are 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.     

Correlation of the orientation of stacked aragonite platelets in nacre and their connection via mineral bridges

In this work, we studied the correlation of the orientation of stacked aragonite platelets of Haliotis laevigata nacre, using selected area diffraction (SAD) in transmission electron microscopy (TEM). From the position of the center of Laue circle (COLC) within the diffraction patterns the tilt angles of the investigated platelets relatively to a reference platelet (oriented in zone axis) are determined. The strong correlation of the platelets supports the existence of mineral bridges, which connect the stacked platelets and enable a transfer of the platelet orientation during growth. Electron tomography and subsequent reconstruction of the obtained data yield information about the shape of the mineral bridges. The crystalline structure of the material within the mineral bridges was investigated by high resolution TEM (HRTEM).     

Characterization of JEOL 2100F Lorentz-TEM for low-magnification electron holography and magnetic imaging

We present results that characterize the performance and capabilities of the JEOL 2100F-LM electron microscope to carry out holography and quantitative magnetic imaging. We find the microscope is well-suited for studies of magnetic materials, or for semi-conductor dopant profiling, where a large hologram width ( approximately 1 microm) and fine fringe spacing ( approximately 1.5 nm) are obtained with good contrast ( approximately 20%). We present, as well, measurements of the spherical aberration coefficient Cs=(108.7+/-9.6)mm and minimum achievable focal step delta f=(87.6+/-1.4)nm for the specially designed long-focal-length objective lens of this microscope. Further, we detail experiments to accurately measure the optical parameters of the imaging system typical of conventional holography setup in a transmission electron microscope. The role played by astigmatic illumination in the hologram formation is also assessed with a wave-optical model, which we present and discuss. The measurements obtained for our microscope are used to simulate realistic holograms, which we compare directly to experimental holograms finding good agreement. These results indicate the usefulness of measuring these optical parameters to guide the optimization of the experimental setup for a given microscope, and to provide an additional degree of practical experimental possibility.     

Quantitative TEM-based phase retrieval of MgO nano-cubes using the transport of intensity equation

Through focus series of images are collected from MgO nano-cube crystals in the transmission electron microscope (TEM). The experimental data is used to solve the transport of intensity equation (TIE) to retrieve phase maps, which portray the morphology of the cubes and are quantified by the mean inner potential V(0). Particular attention is given to the practical difficulties associated with TIE phase retrieval of non-conducting polyhedron particles.     

Refinement of the 200 structure factor for GaAs using parallel and convergent beam electron nanodiffraction data

We present a new method to measure structure factors from electron spot diffraction patterns recorded under almost parallel illumination in transmission electron microscopes. Bloch wave refinement routines have been developed to refine the crystal thickness, its orientation and structure factors by comparison of experimentally recorded and calculated intensities. Our method requires a modicum of computational effort, making it suitable for contemporary personal computers. Frozen lattice and Bloch wave simulations of GaAs diffraction patterns are used to derive optimised experimental conditions. Systematic errors are estimated from the application of the method to simulated diffraction patterns and rules for the recognition of physically reasonable initial refinement conditions are derived. The method is applied to the measurement of the 200 structure factor for GaAs. We found that the influence of inelastically scattered electrons is negligible. Additionally, we measured the 200 structure factor from zero loss filtered two-dimensional convergent beam electron diffraction patterns. The precision of both methods is found to be comparable and the results agree well with each other. A deviation of more than 20% from isolated atom scattering data is observed, whereas close agreement is found with structure factors obtained from density functional theory [A. Rosenauer, M. Schowalter, F. Glas, D. Lamoen, Phys. Rev. B 72 (2005), 085326-1], which account for the redistribution of electrons due to chemical bonding via modified atomic scattering amplitudes.     

Atom probe analysis of titanium hydride precipitates

It is expected that the three-dimensional atom probe (3DAP) will be used as a tool to visualize the atomic scale of hydrogen atoms in steel is expected, due to its high spatial resolution and very low detection limit. In this paper, the first 3DAP analysis of titanium hydride precipitates in metal titanium is reported in terms of the quantitative detection of hydrogen. FIB fabrication techniques using the lift-out method have enabled the production of needle tips of hydride precipitates, of several tens of microns in size, within a titanium matrix. The hydrogen concentration estimated from 3DAP analysis was slightly smaller than that of the hydride phase predicted from the phase diagram. We discuss the origin of the difference between the experimental and predicted values and the performance of 3DAP for the quantitative detection of hydrogen.     

The study of quantitativeness in atom probe analysis of alloying elements in steel

The quantitativeness in atom probe analysis of dilute solute alloying elements in steel was systematically investigated. The samples of binary Fe–Si, Fe–Ti, Fe–Cr, Fe–Cu, Fe–Mn and Fe–Mo alloys were prepared for present study. The apparent compositions of alloying elements were examined by three-dimensional atom probe (3DAP) under various experimental conditions. The temperature dependence of the apparent compositions varied largely with the alloys, which indicated that the degree of preferential evaporation or retention varied with the alloying elements. Furthermore, the analysis direction dependence of the apparent Mn composition was examined in the Fe–Mn alloy. The experimental results indicated that the order of the field evaporation rate of elements in steel was Cu>Cr>Mn∼Mo>Fe>Ti∼Si. The field evaporability of alloying elements in steel was discussed in terms of the solution enthalpy of the alloying elements and the phase types of the binary Fe alloys.     

Transmission electron microtomography without the "missing wedge" for quantitative structural analysis

A three-dimensional (3D) visualization and structural analysis of a rod-shaped specimen of a zirconia/polymer nanocomposite material were carried out by transmission electron microtomography (TEMT) with particular emphasis on complete rotation of the specimen (tilt angular range: +/-90 degrees ). In order to achieve such an ideal experimental condition for the TEMT, improvements in the specimen as well as the sample holder were made. A rod-shaped specimen was necessary in order to obtain a high transmission of the specimen upon tilting to large angles. The image resolution of the reconstructed tomogram was isotropic, in sharp contrast to the anisotropic image resolution of the conventional TEMT with a limited angular range (the "missing wedge" problem). A volume fraction of zirconia, phi, evaluated from the 3D reconstruction was in quantitative agreement with the known composition of the nanocomposite. A series of 3D reconstructions was made from the tilt series with complete rotation by limiting the maximum tilt angle, alpha, from which a couple of structural parameters, the volume fraction and surface area per unit volume, Sigma, of the zirconia, were evaluated as a function of alpha. It was confirmed from actual experimental data that both phi and Sigma slightly decreased with the increasing alpha and reached constant values at around alpha=80 degrees , suggesting that the specimen may have to be tilted to +/-80 degrees for truly quantitative measurements.     

New approach for the dynamical simulation of CBED patterns in heavily strained specimens

A new method for the dynamical simulation of convergent beam electron diffraction (CBED) patterns is proposed. In this method, the three-dimensional stationary Schrödinger equation is replaced by a two-dimensional time-dependent equation, in which the direction of propagation of the electron beam, variable z, stands as a time. We demonstrate that this approach is particularly well-suited for the calculation of the diffracted intensities in the case of a z-dependent crystal potential. The corresponding software has been developed and implemented for simulating CBED patterns of various specimens, from perfect crystals to heavily strained cross-sectional specimens. Evidence is given for the remarkable agreement between simulated and experimental patterns.     

Mapping inelastic intensities in diffraction patterns of magnetic samples using the energy spectrum imaging technique

We present the quantitative measurement of inelastic intensity distributions in diffraction patterns with the aim of studying magnetic materials. The relevant theory based on the mixed dynamic form factor (MDFF) is outlined. Experimentally, the challenge is to obtain sufficient signal for core losses of 3d magnetic materials (in the 700-900eV energy-loss range). We compare two experimental settings in diffraction mode, i.e. the parallel diffraction and the large-angle convergent-beam electron diffraction configurations, and demonstrate the interest of using a spherical aberration corrector. We show how the energy spectrum imaging (ESI) technique can be used to map the inelastic signal in a data cube of scattering angle and energy loss. The magnetic chiral dichroic signal is measured for a magnetite sample and compared with theory.     

Tomographic spectroscopic imaging; an experimental proof of concept

Recording the electron energy loss spectroscopy data cube with a series of energy filtered images is a dose inefficient process because the energy slit blocks most of the electrons. When recording the data cube by scanning an electron probe over the sample, perfect dose efficiency is attained; but due to the low current in nanoprobes, this often is slower, with a smaller field of view. In W. Van den Broek et al. [Ultramicroscopy, 106 (2006) 269], we proposed a new method to record the data cube, which is more dose efficient than an energy filtered series. It produces a set of projections of the data cube and then tomographically reconstructs it. In this article, we demonstrate these projections in practice, we present a simple geometrical model that allows for quantification of the projection angles and we present the first successful experimental reconstruction, all on a standard post-column instrument.     

A practical method to detect and correct for lens distortion in the TEM

A practical, offline method for experimental detection and correction for projector lens distortion in the transmission electron microscope (TEM) operating in high-resolution (HR) and selected area electron diffraction (SAED) modes is described. Typical TEM works show that, in the simplest case, the distortion transforms on the recording device, which would be a circle into an ellipse. The first goal of the procedure described here is to determine the elongation and orientation of the ellipse. The second goal is to correct for the distortion using an ordinary graphic program. The same experimental data set may also be used to determine the actual microscope magnification and the rotation between SAED patterns and HR images. The procedure may be helpful in several quantitative applications of electron diffraction and HR imaging, for instance while performing accurate lattice parameter determination, or while determining possible metrical deviations (cell edges and angles) from a given symmetry.     

Simulation of partially coherent image formation in a compact soft X-ray microscope

In this paper, we describe a numerical method of simulating two-dimensional images in a compact soft X-ray microscope using partially coherent illumination considerations. The work was motivated by recent test object images obtained by the latest generation in-house compact soft X-ray microscope, which showed diffraction-like artifacts not observed previously. The numerical model approximates the condenser zone plate as a secondary incoherent source represented by individually coherent but mutually incoherent source points, each giving rise to a separate image. A final image is obtained by adding up all the individual source point contributions. The results are compared with the microscope images and show qualitative agreement, indicating that the observed effects are caused by partially coherent illumination.     

Low-dose performance of parallel-beam nanodiffraction

We evaluate the low-dose performance of parallel nano-beam diffraction (NBD) in the transmission electron microscope as a method for characterizing radiation sensitive materials at low electron irradiation dose. A criterion, analogous to Rose's, is established for detecting a diffraction spot with desired signal-to-noise ratio. Our experimental data show that a dose substantially lower than in high-resolution bright-field imaging is sufficient to determine structure and orientation of individual nanoscale objects embedded in amorphous matrix. In an instrument equipped with a cold field-emission gun it is possible to form a probe with sub-3 nm diameter and sub-0.3 mrad convergence angle with sufficient beam current to record a diffraction pattern with less than 0.2 s acquisition time. The interpretation of NBD patterns is identical to that of selected area diffraction patterns. We illustrate the physical principles underlying good low-dose performance of NBD by means of a phase grating. The electron irradiation dose needed to detect a diffraction peak in NBD is found proportional to 1/N2, where N is the number of lattice planes contributing to the peak.     

Surface structural sensitivity of convergent-beam RHEED: Si (0 0 1) 2 x 1 models compared with dynamical simulations

The aim of this work is to evaluate the sensitivity of convergent-beam RHEED for the refinement of surface atomic structure. We have compared experimental and theoretical convergent-beam RHEED patterns from the silicon (0 0 1) reconstructed surface. The experiment was carried out in a custom designed UHV diffraction camera,using a micron sized probe. Both experimental and theoretical CB-RHEED patterns show complex details, highly sensitive to the surface structure. The multiple scattering simulations were based on two experimental structural models which make different assumptions for dimer tilt, one derived from X-ray diffraction results, and another from LEED data. The simulated CB-RHEED patterns using the X-ray model were found to be in closer agreement with our experiment than the LEED model. However, the agreement is not entirely satisfactory, suggesting that further improvement on this model is necessary.     

Accuracy and precision in model based EELS quantification

We present results on model based quantification of electron energy loss spectra (EELS), focusing on the factors that influence accuracy and precision in determining chemical concentrations. Several sources of systematical errors are investigated. The spectrometer entrance aperture determines the collection angle, and the effects of its position with respect to the transmitted beam are investigated, taking into account the diffraction by the crystal structure. The effect of the orientation of the sample is tested experimentally and theoretically on SrTiO3, and finally, a simulated experiment on c-BN at different thicknesses confirms the superior results of the model based method with respect to the conventional method. A test on a set of experimental reference compounds is presented, showing that remarkably good accuracy can be obtained. Recommendations are given to achieve high accuracy and precision in practice.     

High-resolution wave field reconstruction using a through-focus series of images taken under limited electron dose

The three-dimensional Fourier filtering method and Schiske's Wiener filtering method are compared with the aim of high-resolution wave field reconstruction of an unstained deoxyribonucleic acid (DNA) molecular fiber using a through-focus series of images taken under a limited electron dose. There were some definite differences between the two reconstructed images, although the two kinds of processing are essentially equivalent except for the dimension and the filter used for processing. Through theoretical analyses together with computer simulations, the differences were proved to be primarily due to specimen drift during the experiment. Although the observed structure of the DNA molecular fiber was heavily damaged by electron beam irradiation, reconstructed images by the three-dimensional Fourier filtering method provided higher resolution information on the molecular structure even when relatively large specimen drift was included in the through-focus series. In contrast, in Schiske's Wiener filtering method, the detailed information of the structure was lost because of the drift, although the reconstructed image showed a higher signal-to-noise ratio. The three dimensional Fourier filtering method seems to be more applicable for observing radiation-sensitive materials under an extremely low electron dose, because specimen drift cannot be completely avoided.     

Three-dimensional atom probe analysis of heavily drawn steel wires by probing perpendicular to the pearlitic lamellae

Three-dimensional atom probe analysis of heavily drawn pearlitic steel wires was conducted by probing in the direction perpendicular to the pearlitic lamellae. A needle tip perpendicularly intersecting the lamellar structure was prepared using focused ion beam (FIB) milling combined with the lift-out method. The specimen preparation technique enabled the analysis of many lamellae and their interfaces with higher depth spatial resolution, which was suitable for drawn pearlitic steel wires having inhomogeneous and fine lamellar structure. Carbon concentration peaks at the cementite lamellae appeared higher and narrower than those obtained by probing parallel to the lamellae, which implies that the conventional analysis overestimated the extent of cementite decomposition in drawn pearlitic steel wires.