Coordinate Systems and Integration Limits for Global Flame Transfer Function Calculations

This paper discusses the problem of determining a kinematics (in terms of transfer function, as far as possible) of parameters of the motion of an aircraft expressed in the curvilinear coordinate system and control accelerations expressed in a rectangular coordinate system. Examples of curvilinear coordinate systems using in practice can be polar, biangular, two-center bipolar, elliptic, parabolic cylindrical, spherical, ellipsoidal, coordinate systems. A technique for obtaining a kinematic link for the control problem of an unmanned aerial vehicle in the elliptic coordinate system was described. It allowed to obtain simpler view of the kinematic link which could provide navigation an aircraft along the hyperbola deriving from the time difference of arrival navigation system. It can. As a result, it is possible to reduce the number of the navigation radio beacons.

Download Full-text

Multidimensional Wave Field Signal Theory: Transfer Function Relationships

Mathematical Problems in Engineering ◽

10.1155/2012/478295 ◽

2012 ◽

Vol 2012 ◽

pp. 1-27 ◽

Cited By ~ 1

Author(s):

Natalie Baddour

Keyword(s):

Transfer Function ◽

Signal Theory ◽

Fourier Domain ◽

Theoretic Approach ◽

Input Output ◽

Coordinate Systems ◽

Fourier Inversion ◽

Inversion Formulas ◽

Transmission Of Information ◽

Physical Phenomena

The transmission of information by propagating or diffusive waves is common to many fields of engineering and physics. Such physical phenomena are governed by a Helmholtz (real wavenumber) or pseudo-Helmholtz (complex wavenumber) equation. Since these equations are linear, it would be useful to be able to use tools from signal theory in solving related problems. The aim of this paper is to derive multidimensional input/output transfer function relationships in the spatial domain for these equations in order to permit such a signal theoretic approach to problem solving. This paper presents such transfer function relationships for the spatial (not Fourier) domain within appropriate coordinate systems. It is shown that the relationships assume particularly simple and computationally useful forms once the appropriate curvilinear version of a multidimensional spatial Fourier transform is used. These results are shown for both real and complex wavenumbers. Fourier inversion of these formulas would have applications for tomographic problems in various modalities. In the case of real wavenumbers, these inversion formulas are presented in closed form, whereby an input can be calculated from a given or measured wavefield.

Download Full-text

Reference Coordinate System Requirements for Geophysics

International Astronomical Union Colloquium ◽

10.1017/s0252921100050946 ◽

1975 ◽

Vol 26 ◽

pp. 87-92

Author(s):

P. L. Bender

Keyword(s):

Coordinate System ◽

Polar Motion ◽

Main Part ◽

Measurement Techniques ◽

Reference Points ◽

Angular Motion ◽

Coordinate Systems ◽

Axis Of Rotation ◽

The Earth ◽

Fixed System

AbstractFive important geodynamical quantities which are closely linked are: 1) motions of points on the Earth’s surface; 2)polar motion; 3) changes in UT1-UTC; 4) nutation; and 5) motion of the geocenter. For each of these we expect to achieve measurements in the near future which have an accuracy of 1 to 3 cm or 0.3 to 1 milliarcsec.From a metrological point of view, one can say simply: “Measure each quantity against whichever coordinate system you can make the most accurate measurements with respect to”. I believe that this statement should serve as a guiding principle for the recommendations of the colloquium. However, it also is important that the coordinate systems help to provide a clear separation between the different phenomena of interest, and correspond closely to the conceptual definitions in terms of which geophysicists think about the phenomena.In any discussion of angular motion in space, both a “body-fixed” system and a “space-fixed” system are used. Some relevant types of coordinate systems, reference directions, or reference points which have been considered are: 1) celestial systems based on optical star catalogs, distant galaxies, radio source catalogs, or the Moon and inner planets; 2) the Earth’s axis of rotation, which defines a line through the Earth as well as a celestial reference direction; 3) the geocenter; and 4) “quasi-Earth-fixed” coordinate systems.When a geophysicists discusses UT1 and polar motion, he usually is thinking of the angular motion of the main part of the mantle with respect to an inertial frame and to the direction of the spin axis. Since the velocities of relative motion in most of the mantle are expectd to be extremely small, even if “substantial” deep convection is occurring, the conceptual “quasi-Earth-fixed” reference frame seems well defined. Methods for realizing a close approximation to this frame fortunately exist. Hopefully, this colloquium will recommend procedures for establishing and maintaining such a system for use in geodynamics. Motion of points on the Earth’s surface and of the geocenter can be measured against such a system with the full accuracy of the new techniques.The situation with respect to celestial reference frames is different. The various measurement techniques give changes in the orientation of the Earth, relative to different systems, so that we would like to know the relative motions of the systems in order to compare the results. However, there does not appear to be a need for defining any new system. Subjective figures of merit for the various system dependon both the accuracy with which measurements can be made against them and the degree to which they can be related to inertial systems.The main coordinate system requirement related to the 5 geodynamic quantities discussed in this talk is thus for the establishment and maintenance of a “quasi-Earth-fixed” coordinate system which closely approximates the motion of the main part of the mantle. Changes in the orientation of this system with respect to the various celestial systems can be determined by both the new and the conventional techniques, provided that some knowledge of changes in the local vertical is available. Changes in the axis of rotation and in the geocenter with respect to this system also can be obtained, as well as measurements of nutation.

Download Full-text

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

International Astronomical Union Colloquium ◽

10.1017/s0252921100050867 ◽

1975 ◽

Vol 26 ◽

pp. 21-26

Keyword(s):

Coordinate System ◽

Working Group ◽

General Character ◽

Coordinate Systems ◽

Reference Coordinate System ◽

Group 2 ◽

Definition Of ◽

Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

Download Full-text

Note on Selection of Coordinate Systems for Geodynamics

International Astronomical Union Colloquium ◽

10.1017/s0252921100051174 ◽

1975 ◽

Vol 26 ◽

pp. 395-407

Author(s):

S. Henriksen

Keyword(s):

Sea Level ◽

The Other ◽

Coordinate Systems ◽

Mean Sea Level ◽

The Earth ◽

The One ◽

Static Systems ◽

Selection Of

The first question to be answered, in seeking coordinate systems for geodynamics, is: what is geodynamics? The answer is, of course, that geodynamics is that part of geophysics which is concerned with movements of the Earth, as opposed to geostatics which is the physics of the stationary Earth. But as far as we know, there is no stationary Earth – epur sic monere. So geodynamics is actually coextensive with geophysics, and coordinate systems suitable for the one should be suitable for the other. At the present time, there are not many coordinate systems, if any, that can be identified with a static Earth. Certainly the only coordinate of aeronomic (atmospheric) interest is the height, and this is usually either as geodynamic height or as pressure. In oceanology, the most important coordinate is depth, and this, like heights in the atmosphere, is expressed as metric depth from mean sea level, as geodynamic depth, or as pressure. Only for the earth do we find “static” systems in use, ana even here there is real question as to whether the systems are dynamic or static. So it would seem that our answer to the question, of what kind, of coordinate systems are we seeking, must be that we are looking for the same systems as are used in geophysics, and these systems are dynamic in nature already – that is, their definition involvestime.

Download Full-text

The Role of VLBI in the Establishment of Coordinate Systems

International Astronomical Union Colloquium ◽

10.1017/s0252921100051083 ◽

1975 ◽

Vol 26 ◽

pp. 293-295 ◽

Cited By ~ 1

Author(s):

I. Zhongolovitch

Keyword(s):

General Solution ◽

Future Development ◽

Rational Approach ◽

Radio Telescopes ◽

Coordinate Systems ◽

Tectonic Plates ◽

Astronomical Observations ◽

Optical Instruments ◽

Fundamental Polyhedron

Considering the future development and general solution of the problem under consideration and also the high precision attainable by astronomical observations, the following procedure may be the most rational approach:1. On the main tectonic plates of the Earth’s crust, powerful movable radio telescopes should be mounted at the same points where standard optical instruments are installed. There should be two stations separated by a distance of about 6 to 8000 kilometers on each plate. Thus, we obtain a fundamental polyhedron embracing the whole Earth with about 10 to 12 apexes, and with its sides represented by VLBI.

Download Full-text

Radiation Damage of Support Films

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100096862 ◽

1981 ◽

Vol 39 ◽

pp. 28-29

Author(s):

H.A. Cohen ◽

W. Chiu

Keyword(s):

Transfer Function ◽

Low Temperatures ◽

Carbon Support ◽

Contrast Transfer Function ◽

Electron Dose ◽

Imaging Parameters ◽

Negative Stain ◽

Phase Corrections ◽

Two Parameters ◽

Medium Dose

The goal of imaging the finest detail possible in biological specimens leads to contradictory requirements for the choice of an electron dose. The dose should be as low as possible to minimize object damage, yet as high as possible to optimize image statistics. For specimens that are protected by low temperatures or for which the low resolution associated with negative stain is acceptable, the first condition may be partially relaxed, allowing the use of (for example) 6 to 10 e/Å2. However, this medium dose is marginal for obtaining the contrast transfer function (CTF) of the microscope, which is necessary to allow phase corrections to the image. We have explored two parameters that affect the CTF under medium dose conditions.Figure 1 displays the CTF for carbon (C, row 1) and triafol plus carbon (T+C, row 2). For any column, the images to which the CTF correspond were from a carbon covered hole (C) and the adjacent triafol plus carbon support film (T+C), both recorded on the same micrograph; therefore the imaging parameters of defocus, illumination angle, and electron statistics were identical.

Download Full-text

Possible applications of fraunhofer holography in high resolution electron microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100108258 ◽

1978 ◽

Vol 36 (1) ◽

pp. 222-223 ◽

Cited By ~ 1

Author(s):

N. Bonnet ◽

M. Troyon ◽

P. Gallion

Keyword(s):

Electron Microscopy ◽

High Resolution ◽

Transfer Function ◽

Radiation Damage ◽

High Resolution Electron Microscopy ◽

Far Field ◽

Field Region ◽

Crystalline Materials ◽

Resolution Electron ◽

The Ideal

Two main problems in high resolution electron microscopy are first, the existence of gaps in the transfer function, and then the difficulty to find complex amplitude of the diffracted wawe from registered intensity. The solution of this second problem is in most cases only intended by the realization of several micrographs in different conditions (defocusing distance, illuminating angle, complementary objective apertures…) which can lead to severe problems of contamination or radiation damage for certain specimens.Fraunhofer holography can in principle solve both problems stated above (1,2). The microscope objective is strongly defocused (far-field region) so that the two diffracted beams do not interfere. The ideal transfer function after reconstruction is then unity and the twin image do not overlap on the reconstructed one.We show some applications of the method and results of preliminary tests.Possible application to the study of cavitiesSmall voids (or gas-filled bubbles) created by irradiation in crystalline materials can be observed near the Scherzer focus, but it is then difficult to extract other informations than the approximated size.

Download Full-text

Ultimate resolution and information in electron microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100086787 ◽

1991 ◽

Vol 49 ◽

pp. 496-497

Author(s):

D. Van Dyck

Keyword(s):

Electron Microscopy ◽

Electron Microscope ◽

Transfer Function ◽

Information Transfer ◽

Communication Channel ◽

Structural Information ◽

Information Rate ◽

Noise Power ◽

Signal Power ◽

Imaging Device

An (electron) microscope can be considered as a communication channel that transfers structural information between an object and an observer. In electron microscopy this information is carried by electrons. According to the theory of Shannon the maximal information rate (or capacity) of a communication channel is given by C = B log2 (1 + S/N) bits/sec., where B is the band width, and S and N the average signal power, respectively noise power at the output. We will now apply to study the information transfer in an electron microscope. For simplicity we will assume the object and the image to be onedimensional (the results can straightforwardly be generalized). An imaging device can be characterized by its transfer function, which describes the magnitude with which a spatial frequency g is transferred through the device, n is the noise. Usually, the resolution of the instrument ᑭ is defined from the cut-off 1/ᑭ beyond which no spadal information is transferred.

Download Full-text

Analytic integration of contrast transfer functions

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010010617x ◽

1988 ◽

Vol 46 ◽

pp. 822-823

Author(s):

Peter Rez

Keyword(s):

Wave Function ◽

Transfer Function ◽

Transfer Functions ◽

Spherical Aberration ◽

Continuous Distribution ◽

Objective Lens ◽

Direction Parallel ◽

Scattering Angle ◽

Analytic Integration ◽

Image Position

In high resolution microscopy the image amplitude is given by the convolution of the specimen exit surface wave function and the microscope objective lens transfer function. This is usually done by multiplying the wave function and the transfer function in reciprocal space and integrating over the effective aperture. For very thin specimens the scattering can be represented by a weak phase object and the amplitude observed in the image plane is1where fe (Θ) is the electron scattering factor, r is a postition variable, Θ a scattering angle and x(Θ) the lens transfer function. x(Θ) is given by2where Cs is the objective lens spherical aberration coefficient, the wavelength, and f the defocus.We shall consider one dimensional scattering that might arise from a cross sectional specimen containing disordered planes of a heavy element stacked in a regular sequence among planes of lighter elements. In a direction parallel to the disordered planes there will be a continuous distribution of scattering angle.

Download Full-text