Computer analysis of the source image structure in 3D electron-optic systems: II. A stationary electromagnetic system

Computer analysis of the image of an arbitrary (point or extended) source obtained in 3D electron-optic systems is performed. The systems involve magnetostatic and electrostatic fields, which, respectively, focus and deflect the electron beams. Two approaches to image scanning are considered where the scan potentials are applied in two (symmetric and asymmetric) modes. It is shown that the spread function of the source, which characterizes the imaging quality of the system most fully, may serve as a primary computational criterion.     

An analysis of stimulated longitudinal electrostatic bremsstrahlung in a free-electron laser structure

An analysis of stimulated emission of radiation by an electron beam passing through a periodic longitudinal electrostatic field is presented, and its use in a free-electron laser structure is discussed. The analysis is based on a coupled-mode calculation of the interaction between a waveguided electromagnetic mode and an electron-beam plasma with finite cross section. The dispersion equation derived applies to the collective as well as the single electron regime. This research is supported in part by AFOSR Grant, 77-3445.     

Group structure analysis for classical lattice systems with constraints: I. General properties

The group structure associated with lattice systems without constraints is extended to systems with constraints and some of its physical consequences are investigated. In particular low- and high-temperature expansions, equilibrium equations and duality transformations are analyzed within this framework. It is shown that a large class of systems with constraints whose configuration space has a group structure are “equivalent” to systems without constraints. These structures are illustrated with several examples.     

Computer approach to the determination of electrostatic fields and capacitive coefficients for 3D multielement sets of screens

The structural components of a computer handbook on electrostatic fields and capacitive coefficients of 3D multielement sets of screens are described. The computer approach suggested is based on boundary integral equations from the 3D theory of harmonic potentials and fast algorithms of the finite-group method that are realized on a Pentium-Pro 200 MHz 128-MB RAM PC.     

Automatic Young's fringe analysis in the source image plane

Typically Young's fringe pattern automatic analysis from a double-exposure image (e.g. a photograph) passes through an indirect processing stage on some intermediate parameter domain. Here, we propose a method based on a complicated image processing technique, operating directly with the source fringe image pixels, and providing remarkable accuracy and computational time. This method is intended for laser speckle velocimetry (LSV), particle image velovimetry (PIV), and digital image velocimetry (DIV) applications. Assuming a common fringe pattern model, we introduce a pre-processing stage to improve significantly the fringe discernment. A dynamic thresholding segmentation scheme, adjusted to the fringe spatial structure, follows to localize the fringes being quantitatively attributed with the corresponding eigenvectors. The algorithm has been tested on real patterns as well as on a set of artifically simulated images with pre-defined characteristics.     

Measures of complexity for 3D image analysis of trabecular bone

Based on fractal properties and spatial auto-correlation, the measures of complexity lacunarity, Moran's I and Geary's C index are defined for 3D image analysis. Their abilities to investigate translational invariance, characteristic length scales, spatial correlation and shapes of 3D micro-structures are demonstrated on proto-typical examples. Finally, using these measures of complexity, 3D images of trabecular bone are analysed. The main findings are that the complexity of the trabecular structure decreases and the plate-like shapes of the trabeculae change to mainly rod-like shapes during bone loss. These results and the proposed measures could have a great impact for medicine and for space exploration.     

An automatic image analysis system for the evaluation of dielectric track detectors

The automatic image analysis system for scanning solid state nuclear track detectors is designed by utilizing a microdensitometer. The control of the entire system as well as the data analysis are accomplished with the IBM PC computer equipped with a FrameGrabber. The system counts the number of tracks and measures their geometrical parameters. The usage of the system is illustrated by counting rhombic tracks in mica detectors which were used for the investigation of the fusion–fission reaction ¹²C+ ²⁰⁸Pb.     

Electronic structure of high-temperature superconductors I. Y-Ba-Cu-O systems

The electronic structure of high-T _c copper based superconductors has been studied using the quasirelativistic INDO molecular orbital method. Model clusters of YBa₂Cu₃O _y systems have been investigated fory ranging between 6·0 and 7·0. Monomeric units [Ba₈Cu₃O _x ] ^q and [Y₄Ba₈Cu₄O _x ] ^q , dimeric units [Ba₁₂Cu₆O _x ] ^q and [Y₆Ba₁₂Cu₈O _x ] ^q as well as tetrameric units [Ba₁₈Cu₁₂O _x ] ^q over 300 valence orbitals have been studied. From the set of occupied molecular orbitals the density of states (DOS) function has been calculated along with its d-orbital projection. The highest occupied molecular orbitals cover the oxygen p-band whereas the copper d-band lies at lower energies. Superconducting phase models (y=6·75 to 7·0) have a higher d-DOS function at higher energies with respect to the non-superconducting phase (y=6·0).     

Fractal structure of the crystalline-nuclei boundaries in 2D colloidal crystallization: Computer simulations

By performing 2D kinetic Monte Carlo simulations of colloidal crystallization we found that the boundaries of the crystalline nuclei are not only rough, as obtained by experimentalists, but fractal, whose value (_df$d_f$) we calculated. The corresponding boundary for the crystals, above the critical size (_Nc$N_c$), is also fractal but smoother. A knowledge of the particles coordinates during the crystallization process allows us to calculate the _Nc$N_c$, the line tension (γ) and the chemical potential difference (Δμ) between the two phases. However, different from the experimentalists procedure, we found that the boundary fractalities are needed to derive γ and Δμ.     

Symmetry analysis in neutron diffraction studies of magnetic structures: 3. An example: the magnetic structure of spinels

Using the symmetry analysis technique developed in the two earlier papers of this series a study is made of the magnetic structures in spinels (space group O⁷_h). The magnetic structures with the wave vector K = 0 and those with K ≠ 0 are considered in detail. As an example, an analysis is given of the magnetic ordering in MgV₂O₄ which is characterized by the three-arm star {bdK₁₀} (in Kovalev's notation) and of that in HgCr₂S₄ where a helical structure corresponding to the star {bdK₆} has been found. For each of the three stars we have determined the composition of the magnetic representation and calculated the basis functions of the irreducible representations. For the magnetic structures determined experimentally we have specified the irreducible representations by which these structures should be described. The examples furnished illustrate the typical situations liable to occur when performing symmetry analysis of magnetic structures of crystals.     

3D simulation of the ion-beam transport in bending magnets and electrostatic deflectors

The equations and algorithms for calculating the charged-particle-beam dynamics in bending magnets and electrostatic deflectors, which are used in the ion-beam transport lines and spectrometers, are presented. Calculations of the electromagnetic field 3D maps are illustrated. The value of the electromagnetic-field nonlinearities and their effect on the particle dynamics are analyzed. The simulation of the ion dynamics in the axial injection beam line of the DC-280 cyclotron and GALS spectrometer created at the JINR Laboratory of Nuclear Reactions (FLNR) is described.     

Finite-aperture effects for Fourier transform systems with convergent illumination. Part I: 2-D system analysis

The Optical Fourier Transform (OFT) is one of the most fundamental operations in analogue Optical Signal Processing (OSP). There are many optical arrangements for implementing the OFT, however one which is particularly popular is the Scaled Optical Fourier Transform (SOFT) because it offers the user the ability to scale the output Fourier distribution. In this paper we study some of the practical limits introduced by using a converging spherical lens of finite aperture to produce the illuminating field in the implementation of the SOFT. By deriving simple rules of thumb, based on examining phase and intensity deviations from the ideal unapertured case, we define an area inside the geometric shadow, which we refer to as a sub-geometric shadow. Inside this sub-geometric shadow we show that the worst-case errors in the resulting SOFT, arising due to diffraction, can be quantified and avoided.     

Inverse problems in the theory of electrostatic energy analyzers. I

General formulas are derived for reconstructing two-dimensional Laplace fields from specified focusing and dispersion characteristics in the plane of symmetry. The electrode configuration is determined for an energy analyzer with ideal focusing of a fan beam. The parameters of the plane trajectories, their shape, and their energy dispersion are determined. Zh. Tekh. Fiz. 69, 128–131 (September 1999)     

Computer design of electrostatic systems of charge particle optics: Systems with spherical electrodes and a fine-structure grid

Problems in computer-aided design of 3D optical systems for charged particle optics are analyzed. The results of simulation of electron-optical systems of optoelectronic transducers with two cathode packs (spherical cathode-plane fine-structure grid as the accelerating electrode and plane cathode-spherical fine-structure grid) are considered. We note a low technological efficiency of such structures and unsatisfactory quality (as it regards some parameters) of the image being recorded due to spherical electrodes and a fine-structure grid in the cathode pack. Numerical analysis of the effect of adjustment of the design on the quality of the image being recorded is carried out.     

Computer analysis of coherent electric vibrations in biological systems

The Fröhlich condensed state may be created in the system of vibration modes if the energy supply is above the critical one. A model of a vibration system of a limited number of modes in the frequency range 0·1–4 THz with uniform density of state function and limited energy in the condensed state (saturation) is used for computer simulation. Energy stored in particular modes is calculated as a function of energy supply and energy leakage to the heat bath. The energy stored in the condensed state may be greater than the thermal energy of the system. In the saturated condensed state the stored energy is independent of energy supply. In the vicinity of the critical energy supply the change of the supply of the order of 10% switches on or off the condensed state. The interaction between systems with condensed states leads to interaction forces. Dependent on various conditions these forces may be attractive or repulsive.     

Relativistic effects in the calibration of electrostatic electron analyzers. I. Toroidal analyzers

Relativistic correction terms up to the second order are derived for the kinetic energy of an electron travelling along the circular central trajectory of a toroidal analyzer. Furthermore, a practical energy calibration equation of the spherical sector plate analyzer is written for the variable-plate-voltage recording mode. Accurate measurements with a spherical analyzer performed using kinetic energies from 600 to 2100 eV are in good agreement with this theory showing our approximation (neglect of fringing fields, and source and detector geometry) is realistic enough for actual calibration purposes.     

Finite-aperture effects for Fourier transform systems with convergent illumination. Part II: 3-D system analysis

One of the most important optical signal processing operations is the optical Fourier transform (OFT). Of the arrangements for implementation of the OFT, perhaps the most flexible is that for the scaled optical Fourier transform (SOFT), as it allows control over the scale of the output Fourier transform distribution. By means of an analysis in cylindrical coordinates, we examine some of the practical limits introduced by the use of a thin lens of finite aperture in the implementation of the SOFT. Using simple rules of thumb that are based on an examination of the phase and magnitude deviations from the ideal (infinite-lens) diameter case, we define a volume inside the geometric shadow, which we refer to as a sub-geometric shadow. We then show that inside this sub-geometric shadow errors introduced by diffraction can be quantified.