1,721,125 research outputs found
A formula for the image intensity of phase objects in Zernike mode
No full textI present an analytical expression for the image intensity of a phase object visualized in Zernike phase contrast mode. The formula is valid for periodic and non-periodic weak and strong objects, and accounts for the effects of finite illumination. The expression provided is intended as a generalization of the standard reference formula given in the Born and Wolf [Principles of Optics, sixth ed., Pergamon Press, New York, 1980, p. 427] textbook as well as of the formalism employed to evaluate imaging doses in Zernike mode [M. Malac, M. Beleggia, R. Egerton, Y. Zhu, Ultramicroscopy 108 (2008) 126]. 1 illustrate the usefulness of the improved expression by means of three examples: a sinusoidal phase grating, a Gaussian object, and a phase step. The optimal Zernike phase angle yielding maximum image contrast is found to be object-dependent and not necessarily equal to pi/2. Phase plate optimization criteria are derived and presented for two of the examples considered. (c) 2008 Elsevier B.V. All rights reserved
A Fourier-space approach for the computation of magnetostatic interactions between arbitrarily shaped particles
No full textA new formalism has been developed to describe the magnetostatic energy associated with particles of arbitrary shape and magnetization state. The formalism relies on a Fourier space description of the particle shape, through the so-called shape amplitude, which can be used to obtain explicit expressions for the demagnetization tensor field, magnetic field, magnetic induction and magnetostatic energy of a particle for a given magnetization state. Moreover, the interaction energy between particles, located at arbitrary positions in space, which may have different shapes and magnetization states can also be computed. These results may contribute to a deeper understanding of magnetostatic coupling in nanostructures and of the role of shape anisotropy
Electron-optical phase shift of a Josephson vortex
No full textThe possibility of directly observing Josephson vortices in a superconducting material by transmission electron microscopy is here investigated. First, the anisotropic London equation for the magnetic field of a Josephson vortex is solved in Fourier space. Then, from the knowledge of the magnetic field, the vector potential and the Aharonov-Bohm phase shift are derived. Finally, phase contrast image simulations are presented. It will be shown that, with current technology, the direct observation of a Josephson vortex is possible
Phase shift of charged metallic nanoparticles
No full textWe calculate the electrostatic potential generated by a charged conducting sphere located at some distance over a conducting substrate by means of two complementary approaches. The potential is then projected along the electron beam direction yielding the electron-optical phase shift. The scenario is compared with a uniformly charged sphere over the same substrate, a model that has been widely employed to interpret phase images of charged particles. We illustrate the implications of our findings in the context of transmission electron microscopy experiments performed on metallic nanoparticles, where this classical analysis can be considered as a useful and insightful starting point towards more accurate, yet more complicate, quantum mechanical approaches. (C) 2009 Elsevier B.V. All rights reserved
Forces between arrays of permanent magnets of basic geometric shapes
No full textWe provide formulas for evaluating the magnetic force between two permanent magnet arrays, regularly spaced over a square lattice. We focus on three basic shapes of magnets constituting the arrays: cylinder, sphere and rectangular prism. When the lattice parameter is large, the expressions can be used to calculate the force between two single magnets in a computationally efficient way. The calculations are validated experimentally by measuring the attraction force between two single permanent magnets, where we demonstrate a fair agreement within about 15%. (C) 2013 Elsevier B.V. All rights reserved
Observation of superconducting fluxons by transmission electron microscopy: A Fourier space approach to calculate the electron optical phase shifts and images
No full textAn approach is presented for the calculation of the electron optical phase shift experienced by high-energy electrons in a transmission electron microscope, when they interact with the magnetic field associated with superconducting fluxons in a thin specimen tilted with respect to the beam. It is shown that by decomposing the vector potential in its Fourier components and by calculating the phase shift of each component separately, it is possible to obtain the Fourier transform of the electron optical phase shift, which can be inverted either analytically or numerically. It will be shown how this method can be used to recover the result, previously obtained by the real-space approach, relative to the case of a straight flux tube perpendicular to the specimen surfaces. Then the method is applied to the case of a London fluxon in a thin film, where the bending and the broadening of the magnetic-field lines due to the finite specimen thickness are now correctly taken into account and not treated approximately by means of a parabolic fit. Finally, it will be shown how simple models for the pancake structure of the fluxon can be analyzed within this framework and the main features of electron transmission images predicted
Electron-optical phase shift of magnetic nanoparticles I. Basic concepts
No full textThe electron-optical phase shift induced in the electron beam due to the interaction with the electromagnetic field of magnetized nanoparticles of defined shape and arbitrary dimensions is calculated, presented and discussed. Together with the computable knowledge of vector potential and magnetic induction, including the demagnetizing field, and with the extension to more realistic geometries which will be presented in part II, this theoretical framework can be employed for the interpretation of transmission electron microscopy experiments on magnetic particles on the nanometre scale
Phase-shift and phase-contrast images of pancake superconducting vortices
Full text linkRecently, a Fourier space approach has been developed, which can be fruitfully applied for calculating the phase-shift and phase-contrast transmission electron microscope images of superconducting pancake fluxons in high-T-c layered specimens. in this work, the results obtained by a very simplified model, where the specimen is approximated by three thin layers, are presented and discussed. These model calculations, although oversimplified, can nonetheless give useful hints on the expected images of pancake vortices not piercing the specimen but residing in it or near its surfaces, or pinned by a tilted columnar defect. Furthermore, the model calculations motivate more elaborate and accurate, but time and memory consuming, calculations, which can be carried out by increasing the number of layers
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