Modified Born approximation for solving scattering problems

2003 ◽  
Vol 113 (4) ◽  
pp. 2284-2284 ◽  
Author(s):  
Igor L. Oboznenko ◽  
Vladimir Genis ◽  
Dat H. Tran
Keyword(s):  
Born Approximation ◽  
Scattering Problems

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).

Numerical Solution of Direct and Inverse Scattering Problems in 1D with a General Nonlinearity

2014 ◽  
Vol 14 (3) ◽  
pp. 347-359 ◽  
Author(s):  
Markus Harju ◽  
Georgios Fotopoulos
Keyword(s):  
Inverse Scattering ◽  
Born Approximation ◽  
Direct Problem ◽  
Regularization Methods ◽  
Scattering Problems ◽  
Numerical Examples ◽  
Method Of Integral Equations ◽  
Inverse Scattering Problems ◽  
General Nonlinearity ◽  
Methods Numerical

Abstract.We consider direct and inverse scattering problems for a general nonlinear Schrödinger equation. The direct problem is solved by the method of integral equations. The inverse problem is solved by the method of Born approximation. The computation of the Born approximation is carried out using regularization methods. Numerical examples are given to illustrate the effectiveness of these methods.

NOTE ON THE RELATION BETWEEN FEYNMAN'S FORMULATION OF SCATTERING PROBLEMS AND THE BORN APPROXIMATION

1951 ◽  
Vol 29 (1) ◽  
pp. 66-71
Author(s):  
J. R. H. Dempster
Keyword(s):  
Wave Function ◽  
Born Approximation ◽  
Second Order ◽  
Scattering Problems ◽  
Scattered Particle ◽  
Particle Wave Function ◽  
Scattering Potential ◽  
Arbitrary Scattering

Feynman's formulation of scattering problems is described briefly, and is compared with Born's approximation. The two procedures are shown to be equivalent and to be valid under the same conditions. Feynman's formulas are used to calculate the first and second order terms of the scattered particle wave function, with an arbitrary scattering potential.

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