A theory for marine source arrays

Geophysics ◽  
1988 ◽  
Vol 53 (5) ◽  
pp. 650-658 ◽  
Author(s):  
Richard E. Duren
Keyword(s):  
Energy Density ◽  
Solid Angle ◽  
Large Element ◽  
Far Field ◽  
Linear Superposition ◽  
Frequency Spectra ◽  
Analysis And Design ◽  
Unit Solid Angle ◽  
Radiated Energy ◽  
Marine Source

General mathematical expressions for a marine source array’s (1) far‐field pulse spectrum, (2) radiated energy density, and (3) directivity are developed for both a source in an infinite homogeneous medium and a source operating near the ocean surface. These results, intended to assist the analysis and design of marine source arrays, apply to any marine source array when (1) individual elements radiate isotropically, (2) their individual waveforms are specified, and (3) the array geometry is specified. Arbitrary geometry and arbitrary isotropic waveforms are allowed. The theory assumes linear superposition of the individually specified waveforms, and is consistent with the “square law effect” for identical elements. For an array of small elements, expended energy agrees with the array’s radiated energy found using far‐field methods. Also, the energy radiated from an array with large element spacing is equal to the sum of the independently radiated energies. Two closely spaced identical elements radiate four times the energy contained in a single outgoing waveform over all space. The appropriate directivity definition for marine seismic sources is the ratio of the radiated energy density per unit solid angle in a particular direction to the average radiated energy density per unit solid angle. This definition allows directivity to be expressed explicitly in terms of the individual frequency spectra and geometry.

scholarly journals Laser generated plasma as a source for real time studies in X-ray crystal research: Part I: Fundamental remarks about source characteristics and requirements

1984 ◽  
Vol 2 (2) ◽  
pp. 167-185 ◽  
Author(s):  
E. Förster ◽  
K. Goetz ◽  
K. Schäfer ◽  
W. D. Zimmer
Keyword(s):  
Solid State ◽  
Real Time ◽  
Solid Angle ◽  
Wavelength Interval ◽  
Time Resolved ◽  
X Ray ◽  
Source Characteristics ◽  
Unit Solid Angle ◽  
State Research ◽  
Laser Plasmas

Because of the large number of X-ray photons which will be emitted per unit solid angle and wavelength interval, laser generated plasmas have good prospects as X-ray sources for time-resolved diffraction experiments in solid state research. Starting from this a modified two-crystal diffractometer will be described, which uses the particular advantages of laser plasmas as X-ray flash sources. Requirements for the source will be determined and discussed.

Note on the Unit Solid Angle

1964 ◽  
Vol 54 (6) ◽  
pp. 845_1
Author(s):  
Fritz Kasten
Keyword(s):  
Solid Angle ◽  
Unit Solid Angle

scholarly journals The scattering of electrons by metal vapours. I.—cadmium

1933 ◽  
Vol 141 (844) ◽  
pp. 473-483 ◽  
Keyword(s):  
Angular Distribution ◽  
Solid Angle ◽  
Alkali Metal Atom ◽  
Wave Length ◽  
Theoretical Work ◽  
Angular Distributions ◽  
Unit Solid Angle ◽  
Slow Electrons ◽  
Diffraction Effects ◽  
Simple Picture

Since the discovery of the diffraction of electrons by gas atoms* a large amount of experimental and theoretical work has been devoted to the study of electron scattering in gases. As a result it is now possible to recognize the main processes occurring in the collisions with the gas atoms and it has been found that it is usually only necessary to calculate the scattering by the undisturbed field of the atom in order to explain the experimental results. As a consequence considerable simplification is introduced in the theory of the phenomena and it follows that the diffraction effects are mainly determined by the ratio of the wave-length of the incident electrons to the distance from the centre of the atom at which the magnitude of the potential energy of the electron in the atomic field is comparable with its kinetic energy. When this ratio is large (very slow electrons) the angular distribution per unit solid angle of the scattered electrons is independent of angle. As the ratio decreases maxima and minima appear and the diffraction effects become more and more complicated until such electron energies are reached that the ratio begins to increase again. For such energies the simple picture fails but Born’s approximation applies and the angular distribution per unit solid angle decreases uniformly with increase of angle. Thus one would expect potassium and argon to give similar angular distributions for electrons with energies considerably greater than the ionization energy of the N electron of potassium but, when the electron energy becomes comparable with this energy, the presence of the outer electron in the alkali metal atom should produce much more complicated angular distributions than are observed for electrons of the same energy scattered by argon. If the above view of the phenomena is correct, it follows that the field of an atom may be approximately determined merely by comparison of the diffraction effects which it produces in scattering electrons with those produced by atoms whose fields are known. All that is necessary is to effect this comparison at a series of different electron energies. A generalization of this method to molecules which have approximately spherically symmetrical fields would also be possible.

Optimizing conditions for x-ray microchemical analysis in analytical electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 548-549 ◽  
Author(s):  
N. J. Zaluzec
Keyword(s):  
Solid Angle ◽  
Analytical Electron Microscopy ◽  
Incident Beam ◽  
Thin Foil ◽  
Experimental Conditions ◽  
X Ray ◽  
Microchemical Analysis ◽  
Analytical Electron ◽  
Image Position ◽  
Incident Beam Energy

The ultimate sensitivity of microchemical analysis using x-ray emission rests in selecting those experimental conditions which will maximize the measured peak-to-background (P/B) ratio. This paper presents the results of calculations aimed at determining the influence of incident beam energy, detector/specimen geometry and specimen composition on the P/B ratio for ideally thin samples (i.e., the effects of scattering and absorption are considered negligible). As such it is assumed that the complications resulting from system peaks, bremsstrahlung fluorescence, electron tails and specimen contamination have been eliminated and that one needs only to consider the physics of the generation/emission process.The number of characteristic x-ray photons (Ip) emitted from a thin foil of thickness dt into the solid angle dΩ is given by the well-known equation

Contrast in Scanning Images of Thin Crystals

1972 ◽  
Vol 30 ◽  
pp. 520-521
Author(s):  
S. Kimoto ◽  
H. Hashimoto ◽  
S. Takashima ◽  
R. M. Stern ◽  
T. Ichinokawa
Keyword(s):  
Crystal Surface ◽  
Solid Angle ◽  
Incident Angle ◽  
Intensity Variation ◽  
Lattice Defects ◽  
Scanning Microscope ◽  
Electron Detector ◽  
Backscattered Electrons ◽  
Electron Image ◽  
Backscattered Electron

The most well known application of the scanning microscope to the crystals is known as Coates pattern. The contrast of this image depends on the variation of the incident angle of the beam to the crystal surface. The defect in the crystal surface causes to make contrast in normal scanning image with constant incident angle. The intensity variation of the backscattered electrons in the scanning microscopy was calculated for the defect in the crystals by Clarke and Howie. Clarke also observed the defect using a scanning microscope.This paper reports the observation of lattice defects appears in thin crystals through backscattered, secondary and transmitted electron image. As a backscattered electron detector, a p-n junction detector of 0.9 π solid angle has been prepared for JSM-50A. The gain of the detector itself is 1.2 x 104 at 50 kV and the gain of additional AC amplifier using band width 100 Hz ∼ 10 kHz is 106.

High spatial resolution x-ray microanalysis of interfaces

1995 ◽  
Vol 53 ◽  
pp. 284-285
Author(s):  
J. R. Michael
Keyword(s):  
Spatial Resolution ◽  
Electron Probe ◽  
Solid Angle ◽  
Collection Efficiency ◽  
Spatial Scales ◽  
Energy Dispersive Spectrometer ◽  
X Rays ◽  
X Ray ◽  
Probe Size ◽  
Brightness Field

X-ray microanalysis in the analytical electron microscope (AEM) refers to a technique by which chemical composition can be determined on spatial scales of less than 10 nm. There are many factors that influence the quality of x-ray microanalysis. The minimum probe size with sufficient current for microanalysis that can be generated determines the ultimate spatial resolution of each individual microanalysis. However, it is also necessary to collect efficiently the x-rays generated. Modern high brightness field emission gun equipped AEMs can now generate probes that are less than 1 nm in diameter with high probe currents. Improving the x-ray collection solid angle of the solid state energy dispersive spectrometer (EDS) results in more efficient collection of x-ray generated by the interaction of the electron probe with the specimen, thus reducing the minimum detectability limit. The combination of decreased interaction volume due to smaller electron probe size and the increased collection efficiency due to larger solid angle of x-ray collection should enhance our ability to study interfacial segregation.

Angular Resolved Electron Spectroscopy with Parallel Recording

1990 ◽  
Vol 48 (2) ◽  
pp. 370-371
Author(s):  
Huang Min ◽  
P.S. Flora ◽  
C.J. Harland ◽  
J.A. Venables
Keyword(s):  
Electron Spectroscopy ◽  
Low Voltage ◽  
Solid Angle ◽  
Detection System ◽  
Voltage Electron ◽  
Cylindrical Mirror ◽  
Inner Radius ◽  
Channel Plate ◽  
And Performance ◽  
Type Detector

A cylindrical mirror analyser (CMA) has been built with a parallel recording detection system. It is being used for angular resolved electron spectroscopy (ARES) within a SEM. The CMA has been optimised for imaging applications; the inner cylinder contains a magnetically focused and scanned, 30kV, SEM electron-optical column. The CMA has a large inner radius (50.8mm) and a large collection solid angle (Ω > 1sterad). An energy resolution (ΔE/E) of 1-2% has been achieved. The design and performance of the combination SEM/CMA instrument has been described previously and the CMA and detector system has been used for low voltage electron spectroscopy. Here we discuss the use of the CMA for ARES and present some preliminary results.The CMA has been designed for an axis-to-ring focus and uses an annular type detector. This detector consists of a channel-plate/YAG/mirror assembly which is optically coupled to either a photomultiplier for spectroscopy or a TV camera for parallel detection.

Comparison of high-angle take-off and low-angle take-off EDX detector geometry of the HF-2000 FE-TEM

1993 ◽  
Vol 51 ◽  
pp. 252-253
Author(s):  
Y. Sato ◽  
T. Hashimoto ◽  
M. Ichihashi ◽  
Y. Ueki ◽  
K. Hirose ◽  
...  
Keyword(s):  
Quantitative Analysis ◽  
Field Emission ◽  
Solid Angle ◽  
Energy Dispersive ◽  
Objective Lens ◽  
X Rays ◽  
High Angle ◽  
X Ray ◽  
Detector Geometry

Analytical TEMs have two variations in x-ray detector geometry, high and low angle take off. The high take off angle is advantageous for accuracy of quantitative analysis, because the x rays are less absorbed when they go through the sample. The low take off angle geometry enables better sensitivity because of larger detector solid angle.Hitachi HF-2000 cold field emission TEM has two versions; high angle take off and low angle take off. The former allows an energy dispersive x-ray detector above the objective lens. The latter allows the detector beside the objective lens. The x-ray take off angle is 68° for the high take off angle with the specimen held at right angles to the beam, and 22° for the low angle take off. The solid angle is 0.037 sr for the high angle take off, and 0.12 sr for the low angle take off, using a 30 mm2 detector.

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