Image Reconstruction with Acoustic Measurement Using Distorted Born Iteration Method

1996 ◽  
Vol 18 (2) ◽  
pp. 140-156 ◽  
Author(s):  
C. Lu ◽  
J. Lin ◽  
W. Chew ◽  
G. Otto
Keyword(s):  
Cross Section ◽  
Born Approximation ◽  
Measurement Data ◽  
Arbitrary Cross Section ◽  
Ultrasonic Measurement ◽  
Diffraction Tomography ◽  
Two Dimensional ◽  
Scattering Problems ◽  
First Order ◽  
Scattered Fields

The distorted Born iterative method (DBIM) is applied to solve electromagnetics and ultrasonics inverse scattering problems. First, we use the DBIM to process the data, which are the scattered fields from two-dimensional cylinders with arbitrary cross section. From this simulation, we confirmed that the first-order Born approximation can be applied to larger objects as long as the phase change of a wave passing through the object due to its presence is smaller than a limit. Then we applied DBIM to process the ultrasonic measurement data. Images for a balloon and an egg that are immersed in water have been reconstructed and compared with those from the first-order diffraction tomography (DT).

Application of coordinate transformation to two-dimensional scattering and diffraction problems

1969 ◽  
Vol 47 (7) ◽  
pp. 795-804 ◽  
Author(s):  
L. Shafai
Keyword(s):  
Electromagnetic Field ◽  
Differential Equations ◽  
Cross Section ◽  
Coordinate Transformation ◽  
Scattered Field ◽  
Arbitrary Cross Section ◽  
Surface Currents ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
First Order

The two-dimensional problem of determining the electromagnetic field scattered by a cylinder of arbitrary cross section is reduced to the solution of first-order, coupled differential equations. The procedure for finding the surface currents, scattered field, and the scattering cross section for a perfectly-conducting cylinder is given in detail. A brief study of the scattering by a polygonal cylinder and n identical strips equally spaced azimuthally around the z axis is used to examine the behavior of the differential equations.

Long waves in a uniform channel of arbitrary cross-section

1968 ◽  
Vol 32 (2) ◽  
pp. 353-365 ◽  
Author(s):  
D. H. Peregrine
Keyword(s):  
Solitary Wave ◽  
Cross Section ◽  
Gravity Waves ◽  
Equations Of Motion ◽  
Rectangular Channel ◽  
Arbitrary Cross Section ◽  
Long Waves ◽  
Order Of Approximation ◽  
Two Dimensional ◽  
Uniform Channel

Equations of motion are derived for long gravity waves in a straight uniform channel. The cross-section of the channel may be of any shape provided that it does not have gently sloping banks and it is not very wide compared with its depth. The equations may be reduced to those for two-dimensional motion such as occurs in a rectangular channel. The order of approximation in these equations is sufficient to give the solitary wave as a solution.

Two-dimensional toroidal MHD equilibria of arbitrary cross-section

1983 ◽  
Vol 29 (1) ◽  
pp. 173-175 ◽  
Author(s):  
Ferdinand F. Cap
Keyword(s):  
Equilibrium Problem ◽  
Cross Section ◽  
Arbitrary Cross Section ◽  
Two Dimensional ◽  
New Approach ◽  
Mhd Equilibrium ◽  
Mhd Equilibria

A new approach to the solution of the MHD equilibrium problem is outlined.

Second-Order Diffraction Forces on an Array of Vertical Cylinders in Bichromatic Bidirectional Waves

1995 ◽  
Vol 117 (1) ◽  
pp. 12-18 ◽  
Author(s):  
J. H. Vazquez ◽  
A. N. Williams
Keyword(s):  
Cross Section ◽  
Finite Depth ◽  
Hydrodynamic Forces ◽  
Arbitrary Cross Section ◽  
Second Order ◽  
Order Problem ◽  
First Order ◽  
Wave Directionality ◽  
Vertical Cylinders ◽  
Green Function Approach

A complete second-order solution is presented for the hydrodynamic forces due to the action of bichromatic, bidirectional waves on an array of bottom-mounted, surface-piercing cylinders of arbitrary cross section in water of uniform finite depth. Based on the constant structural cross section, the first-order problem is solved utilizing a two-dimensional Green function approach, while an assisting radiation potential approach is used to obtain the hydrodynamic loads due to the second-order potential. Results are presented which illustrate the influence of wave directionality on the second-order sum and difference frequency hydrodynamic forces on a two-cylinder array. It is found that wave directionality may have a significant influence on the second-order hydrodynamic forces on these arrays and that the assumption of unidirectional waves does not always lead to conservative estimates of the second-order loading.

scholarly journals Estimation of reliability of seismic and electromagnetic monitoring in seismic active areas by diffraction tomography

2001 ◽  
Vol 1 (1/2) ◽  
pp. 69-73 ◽  
Author(s):  
V. N. Troyan ◽  
Yu. V. Kiselev
Keyword(s):  
Numerical Simulation ◽  
Born Approximation ◽  
Maxwell Equations ◽  
Diffraction Tomography ◽  
Seismic Parameters ◽  
First Order ◽  
The Finite Difference Method ◽  
Tomography Method ◽  
Electromagnetic Monitoring ◽  
Direct Problems

Abstract. This paper presents the algorithms and results of the numerical simulation of the solution of a 2-D inverse problem on the restoration of seismic parameters and electrical conductivity of local inhomogeneities by the diffraction tomography method based upon the first order Born approximation. The direct problems for the Lame and Maxwell equations are solved by the finite difference method. Restoration of inhomogeneities which are not very weak is implemented with the use of a small number of receivers (source-receiver pairs).

The theory of deep holograms

1968 ◽  
Vol 304 (1478) ◽  
pp. 275-289 ◽  
Keyword(s):  
Born Approximation ◽  
Random Noise ◽  
Directional Selectivity ◽  
Two Dimensional ◽  
First Order ◽  
Auto Correlation ◽  
Auto Correlation Function ◽  
Colour Photography ◽  
Photographic Emulsions ◽  
Second Wave

A simple theory of the first-order properties of holograms in thick photographic emulsions is presented. Following a combination by Denisyuk of the basic method of wavefront recon­struction with Lippmann’s method of colour photography, such holograms are produced by the interference of an object wave with a coherent reference wave, falling on the emulsion from opposite sides. It is shown, by using the first Born approximation, that such deep holograms have three properties which distinguish them from two-dimensional or ‘plane’ holograms: (1) They have directional selectivity, that is to say the image will appear only if the hologram is illuminated in the reconstruction within a certain angular zone. (2) They have colour selectivity, that is to say they will reflect only within a certain narrow waveband close to the original wavelength. (3) The second wave, which is a disturbance in two-dimensional holograms is as good as completely suppressed. All three are of great practical value. It is shown that holograms which are produced by strongly diffused, wide-angle illumina­tion, and which have a random, noise-like appearance, contain the information in the form of the auto-correlation function of densities or scattering powers between different space-elements in the emulsion.

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