Showing papers on "Contrast transfer function published in 2004"

Direct Sub-Angstrom Imaging of a Crystal Lattice

Abstract: Despite the use of electrons with wavelengths of just a few picometers, spatial resolution in a transmission electron microscope (TEM) has been limited by spherical aberration to typically around 0.15 nanometer. Individual atomic columns in a crystalline lattice can therefore only be imaged for a few low-order orientations, limiting the range of defects that can be imaged at atomic resolution. The recent development of spherical aberration correctors for transmission electron microscopy allows this limit to be overcome. We present direct images from an aberration-corrected scanning TEM that resolve a lattice in which the atomic columns are separated by less than 0.1 nanometer.

High-Resolution Transmission Electron Microscopy Using Negative Spherical Aberration

Abstract: A novel imaging mode for high-resolution transmission electron microscopy is described. It is based on the adjustment of a negative value of the spherical aberration C S of the objective lens of a transmission electron microscope equipped with a multipole aberration corrector system. Negative spherical aberration applied together with an overfocus yields high-resolution images with bright-atom contrast. Compared to all kinds of images taken in conventional transmission electron microscopes, where the then unavoidable positive spherical aberration is combined with an underfocus, the contrast is dramatically increased. This effect can only be understood on the basis of a full nonlinear imaging theory. Calculations show that the nonlinear contrast contributions diminish the image contrast relative to the linear image for a positive-C S setting whereas they reinforce the image contrast relative to the linear image for a negative-C S setting. The application of the new mode to the imaging of oxygen in SrTiO3 and YBa2Cu3O7 demonstrates the benefit to materials science investigations. It allows us to image directly, without further image processing, strongly scattering heavy-atom columns together with weakly scattering light-atom columns.

Defocused transfer function for a partially coherent microscope and application to phase retrieval.

Abstract: The defocused weak-object transfer function of a partially coherent bright-field microscope is calculated. For weak defocus, this can be expressed analytically. Use of this transfer function for phase restoration (quantitative phase retrieval) from images of weak mixed phase-amplitude objects is discussed.

Depth-Dependent Imaging of Individual Dopant Atoms in Silicon

Abstract: We have achieved atomic-resolution imaging of single dopant atoms buried inside a crystal, a key goal for microelectronic device characterization, in Sb-doped Si using annular dark-field scanning transmission electron microscopy. In an amorphous material, the dopant signal is largely independent of depth, but in a crystal, channeling of the electron probe causes the image intensity of the atomic columns to vary with the depths of the dopants in each column. We can determine the average dopant concentration in small volumes, and, at low concentrations, the depth in a column of a single dopant. Dopant atoms can also serve as tags for experimental measurements of probe spreading and channeling. Both effects remain crucial even with spherical aberration correction of the probe. Parameters are given for a corrected Bloch-wave model that qualitatively describes the channeling at thicknesses <20 nm, but does not account for probe spreading at larger thicknesses. In thick samples, column-to-column coupling of the probe can make a dopant atom appear in the image in a different atom column than its physical position.

"Indirect" high-resolution transmission electron microscopy: aberration measurement and wavefunction reconstruction

Abstract: Improvements in instrumentation and image processing techniques mean that methods involving reconstruction of focal or beam-tilt series of images are now realizing the promise they have long offered. This indirect approach recovers both the phase and the modulus of the specimen exit plane wave function and can extend the interpretable resolution. However, such reconstructions require the a posteriori determination of the objective lens aberrations, including the actual beam tilt, defocus, and twofold and threefold astigmatism. In this review, we outline the theory behind exit plane wavefunction reconstruction and describe methods for the accurate and automated determination of the required coefficients of the wave aberration function. Finally, recent applications of indirect reconstruction in the structural analysis of complex oxides are presented.

Spherical aberration correction in tandem with exit-plane wave function reconstruction : interlocking tools for the atomic scale imaging of lattice defects in GaAs

Abstract: With the availability of resolution boosting and delocalization minimizing techniques, for example, spherical aberration correction and exit-plane wave function reconstruction, high-resolution transmission electron microscopy is drawing to a breakthrough with respect to the atomic-scale imaging of common semiconductor materials. In the present study, we apply a combination of these two state-of-the-art techniques to investigate lattice defects in GaAs-based heterostructures at atomic resolution. Focusing on the direct imaging of stacking faults as well as the core structure of edge and partial dislocations, the practical capabilities of both techniques are illustrated. For the first time, we apply the technique of bright-atom contrast imaging at negative spherical aberration together with an appropriate overfocus setting for the investigation of lattice defects in a semiconductor material. For these purposes, the elastic displacements associated with lattice defects in GaAs viewed along the [110] zone axis are measured from experimental images using reciprocal space strain map algorithms. Moreover, we demonstrate the benefits of the retrieval of the exit-plane wave function not only for the elimination of residual imaging artefacts but also for the proper on-line alignment of specimens during operation of the electron microscope—a basic prerequisite to obtain a fair agreement between simulated images and experimental micrographs.

Full contrast transfer function correction in 3D cryo-EM reconstruction

Abstract: Over the past years electron cryo-microscopy (cryo-EM) has established itself as an important tool in studying the three dimensional structure of biological molecules up to the resolution of 6-9 /spl Aring/. However, as we pursue even higher resolution (i.e., 3-4 /spl Aring/), the depth-of-field problem inherent in the contrast transfer function emerges as a limiting factor. This problem has been previously addressed in the research community (Jensen, G.J., 2000; DeRosier, D.J., 2000; Zhou, Z.H. and Chiu, W., 2003; Cohen, H.A. et al., 1984). We develop a full theoretical solution to this problem. We show that the projected image from the electron microscope corresponds to neither a slice, nor an Ewald sphere, in the Fourier space, but a pair of quadratic surfaces in that space. The general solutions to this problem for both single and double defocus exposures are developed. Simulations show the correctness of the theory.

Transfer function restoration in 3D electron microscopy via iterative data refinement

Abstract: Three-dimensional electron microscopy (3D-EM) is a powerful tool for visualizing complex biological systems. As with any other imaging device, the electron microscope introduces a transfer function (called in this field the contrast transfer function, CTF) into the image acquisition process that modulates the various frequencies of the signal. Thus, the 3D reconstructions performed with these CTF-affected projections are also affected by an implicit 3D transfer function. For high-resolution electron microscopy, the effect of the CTF is quite dramatic and limits severely the achievable resolution. In this work we make use of the iterative data refinement (IDR) technique to ameliorate the effect of the CTF. It is demonstrated that the approach can be successfully applied to noisy data.

Methods, system, and program product for the detection and correction of spherical aberration

Abstract: The present invention provides methods, a system, and a program product for the rapid detection and correction of spherical aberration in microscopy systems. More specifically, the present invention empirically derives a pupil function, adaptively corrects PSF parameters, and automatically detects the coefficient for spherical aberration. A first aspect of the invention provides a method for detecting and estimating spherical aberration in an acquired image obtained using an optical system, comprising the steps of deconvolving an image using each of a plurality of point spread functions, wherein each point spread function has a different spherical aberration value, calculating an image energy for each deconvolved image, and choosing as a spherical aberration coefficient the spherical aberration value corresponding to the deconvolved image having the lowest image energy, wherein a spherical aberration coefficient other than 0 indicates the presence of spherical aberration in the acquired image and its distance from 0 is an estimation of the degree and direction of spherical aberration.

Scanning transmission electron microscope, aberration measuring method, and aberration correction method

Abstract: PROBLEM TO BE SOLVED: To provide a scanning transmission electron microscope capable of obtaining a scanning transmission image having a specified resolution by deciding an aberration coefficient from Ronchigram and applying feedback of signals correcting each aberration to a device. SOLUTION: On the scanning transmission electron microscope composed of an electron beam source 1, a conversion lens 3, a scan coil 7, a dark-field image detection device 13, an A/D converter, and a CPU 21 or the like, an aberration correction device 5 is mounted at a front stage of an objective front magnetic field lens 8, and driving current of each lens and the aberration correcting device are calculated and fed back by the aberration coefficient decided by a fitting of the Ronchigram obtained by a camera 15 and a calculated image against optional structure. COPYRIGHT: (C)2006,JPO&NCIPI

Spherical aberration correction control device and optical disc apparatus

Abstract: A spherical aberration correction control device for controlling a spherical aberration correction section for correcting a spherical aberration of an optical beam irradiating an optical disc. The spherical aberration correction control device includes a spherical aberration control signal generation section for generating a spherical aberration control signal; and an output section for outputting the spherical aberration control signal to the spherical aberration correction section. A correction amount by which the spherical aberration is corrected is changed by the spherical aberration correction section in accordance with components of the spherical aberration control signal. The spherical aberration control signal generation section generates the spherical aberration control signal such that a sum of correction amounts corresponding to the respective components of the spherical aberration control signal becomes substantially zero with respect to a target correction amount.

Aberration integrals for the low-voltage foil corrector

Abstract: Foil aberration correctors make use of a transparent foil to correct for the spherical and chromatic aberration of electron lenses. The low-voltage foil corrector is a novel type, in which the electrons are retarded to almost 0 eV at the foil. For designing a system with this corrector, analytical expressions for the aberrations are required. Such aberration integrals allow combinations of the corrector with other lenses to be calculated, even if the fields overlap. Also many different configurations can be calculated within a reasonable time. Most existing aberration integrals for foil correctors are not suitable because of an integration by parts that had been applied to them, such to obtain expressions without the fourth derivative of the axial potential. This simplification is not allowed when the electron energy approaches zero and is not necessary nowadays because the fourth derivative can be calculated accurately. Additionally, for a characterization of the corrector independent of the probe forming system, the aberration coefficients are less suitable and the geometrical and chromatic slope aberrations must be derived. In this paper, integrals have been obtained that describe correctly the spherical and chromatic aberration correction for the low voltage foil corrector. A program for the numerical calculation of the electrostatic potential can use these integrals to calculate the C s , C c and the slope aberrations. The results show that the low-voltage foil corrector can correct for both the spherical and chromatic aberration simultaneously.

Calculation of focussing quality of the electrostatic mirror objective free of the third-order spherical aberration

Abstract: The formulas for the coefficients of spherical aberration of axisymmetrical electrostatic electron mirror have been obtained. The technique of excluding from the integrand of high-order derivatives of the potential axial distribution in mirror systems is given. The conditions of elimination of spherical aberration in a three-electrode axisymmetrical mirror consisting of coaxial cylinders of equal diameter are found. Using a method of direct numerical calculations of the exact equations of trajectories, the fifth-order spherical aberration coefficient of a mirror objective was calculated and its limiting resolution was estimated. The calculations show that the resolution of the electrostatic mirror objective under consideration is not worse than that of the best objectives with magnetic lenses. The schematic diagram of a transmission electron microscope with a dark-field image, the objective of which is an electrostatic electron mirror, is presented.

Image formation in the high-resolution transmission electron microscope.

Abstract: A recent article in these pages compares STEM images with an image obtained with the One-Angstrom Microscope (OAM) at Lawrence Berkeley National Laboratory (LBNL). Although the experimental work is of excellent quality, Diebold et al. (2003) offer an incorrect explanation of the image formation process in the high-resolution transmission electron microscope. It is important that this misinterpretation be corrected before it comes to be accepted as factual by other scientists who are not expert in the field of high-resolution transmission electron microscopy.

The influence of thermal effects in a beam control system and spherical aberration on the laser beam quality

Abstract: With the strehl ratio, power in the bucket, β parameter and beam widths taken as the characteristic parameters of laser beam quality in the far field, the influence of thermal effects in a beam control system and spherical aberration on the laser beam quality in the far field is studied. Detailed calculations are performed using a four-dimensional simulation code, and numerical results are given and analyzed physically. It is shown that the thermal effects in the propagation channel and positive spherical aberration give rise to an expansion of intensity distributions and reduce the focus ability in the far field, and degrade the beam quality. It is interesting that a suitable choice of the negative spherical aberration would result in a higher peak intensity and a better focus abilty at the geometrical focal plane than that of the spherical-aberration-free case, as the emissive power reaches a certain value; whereas a similar result is achieved at the real focal plane due to the focal shift as in the previous work. The physical interpretation is that there exists the nonlinear thermal blooming, which is illustrated with numerical examples.

Optical pick-up having a spherical aberration compensator and a method of compensating for spherical aberration

Abstract: An optical pick-up apparatus and method incorporating a spherical aberration compensator is disclosed. The optical pick-up employs the spherical aberration device that comprises a wave plate for converting the phase of beams entering the wave plate and outputting the phase-converted beams; and a liquid crystal panel having a molecular structure for adjusting the phase of circularly-polarized beams, whereby it is possible to compensate for the spherical aberrations of the laser beams emitted from a light source and entering an optical recording medium, and the laser beams which are reflected from the optical recording medium and reenter the liquid crystal panel. As a result, jitter characteristic of the optical pick-up can be enhanced.

On improving TEM resolution

Abstract: Spherical aberration and chromatic aberrations are two fundamental optical imperfections that restrict the resolution of modern transmission electron microscopes (TEM). Nowadays,it reaches a limit that further development in lens design will inevitably conflict with the increasing demands of the large specimen space for some new applications,such as electron tomography,liquid-He cyro-microscopy and in-situ experiments. The invention of Cs-corrector may solve this dilemma,which greatly increases microscope point-resolution. The further improvement depends on the future Cc-corrector and,partially,the electron monochromator may do its job. After a detailed discussion of the concept of resolutions in transmission electron microscopy and the effects of the optical aberrations,the method of experimentally measuring resolution is introduced. Then the first results based on a 200kV TEM equipped with a Cs-corrector together with a monochromator are shown. Encouragingly,it confirms that the microscope resolution may reach a dimension below 0.1nm in a TEM with mediate voltage.

Detection of iron-oxide layer on the surface of iron nitride using high-resolution electron microscopy and Fourier filtering

Abstract: High-resolution electron microscopy (HREM) was used to detect the surface Fe 3 O 4 iron-oxide layer formed on [011] Fe 4 N iron nitride due to electron irradiation in the transmission electron microscope. The existence of asurface oxide layer was confirmed by both image processing and through-focus observation. Images of the iron oxide were revealed using the process of fast Fourier transformation (FFT) of experimental HREM images, filtering of the FFT patterns and inverse FFT. By through-focus observation, HREM images of iron oxide were obtained based on the tuning of contrast transfer function. Fourier filtering is effective for examining the beginning of phase transformation, because at this stage the diffraction spots of iron oxide are too weak to be detected. At the time when the iron oxide layer has developed to some extent, through-focus observation is useful to obtain an image of oxide layers.

Optical element, lens and optical head device

Abstract: An optical element includes a diffraction grating by which both a first laser beam and a second laser beam are diffracted. A diffraction performance of the diffraction grating is expressed by an optical path difference function, a third spherical aberration SA3 1 of the first laser beam and a third spherical aberration SA3 2 of the second laser beam in a wave front aberration calculated by the optical path difference function satisfy the following conditional expressions: 0.005<|SA3 1 −SA3 2 |<0.015[λrms] SA3 1 ×SA3 2 <0.