Modified Born approximation for solving scattering problems

2003 ◽  
Vol 113 (4) ◽  
pp. 2284-2284 ◽  
Author(s):  
Igor L. Oboznenko ◽  
Vladimir Genis ◽  
Dat H. Tran
1996 ◽  
Vol 18 (2) ◽  
pp. 140-156 ◽  
Author(s):  
C. Lu ◽  
J. Lin ◽  
W. Chew ◽  
G. Otto

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).


2014 ◽  
Vol 14 (3) ◽  
pp. 347-359 ◽  
Author(s):  
Markus Harju ◽  
Georgios Fotopoulos

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.


1951 ◽  
Vol 29 (1) ◽  
pp. 66-71
Author(s):  
J. R. H. Dempster

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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