A study on orthogonality sampling.
Potthast, R. (2010) A study on orthogonality sampling. Inverse Problems, 26 (7). 074015. ISSN 1361-6420
Full text not archived in this repository.
To link to this article DOI: 10.1088/0266-5611/26/7/074015
The goal of this paper is to study and further develop the orthogonality sampling or stationary waves algorithm for the detection of the location and shape of objects from the far field pattern of scattered waves in electromagnetics or acoustics. Orthogonality sampling can be seen as a special beam forming algorithm with some links to the point source method and to the linear sampling method. The basic idea of orthogonality sampling is to sample the space under consideration by calculating scalar products of the measured far field pattern , with a test function for all y in a subset Q of the space , m = 2, 3. The way in which this is carried out is important to extract the information which the scattered fields contain. The theoretical foundation of orthogonality sampling is only partly resolved, and the goal of this work is to initiate further research by numerical demonstration of the high potential of the approach. We implement the method for a two-dimensional setting for the Helmholtz equation, which represents electromagnetic scattering when the setup is independent of the third coordinate. We show reconstructions of the location and shape of objects from measurements of the scattered field for one or several directions of incidence and one or many frequencies or wave numbers, respectively. In particular, we visualize the indicator function both with the Dirichlet and Neumann boundary condition and for complicated inhomogeneous media.
 Ammari H and Kang H 2004 Reconstruction of Small Inhomogeneities from Boundary Measurements (Lecture Notes in Mathematics vol 1846) (Berlin: Springer)  BurkardCand PotthastR2009Atime-domain probe method for three-dimensional rough surface reconstructions Inverse Problems Imaging 3 259274  Cheney M 2001 The linear sampling method and the MUSIC algorithm Inverse Problems 17 591–5  Chiao R Y and Thomas J 1994 Analytic evaluation of sampled aperture ultrasonic imaging techniques for NDE IEEE Trans. Ultrason. Ferroelectr. Freq. Control 41 484–93  Colton D and Cakoni F 2006 Qualitative Methods in Inverse Scattering Theory (Series on Interaction of Mathematics and Mechanics) (Berlin: Springer)  Colton D and Kress R 1983 Integral Equation Methods in Scattering Theory (New York: Wiley)  Colton D and Kress R 1998 Inverse Acoustic and Electromagnetic Scattering Theory 2nd edn (Berlin: Springer)  Dorn O, Miller E L and Rappaport C M 2001 Shape reconstruction in 2D from limited-view multifrequency electromagnetic data Radon Transform and Tomography (AMS series Contemporary Mathematics vol 278) pp 97–122  Dorn O, Miller E L and Rappaport C M 2000 A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets Inverse Problems 16 1119–56  Holmes C, DrinkwaterBWandWilcox PD2005 Post-processing of the fullmatrix of ultrasonic transmit-receive array data for non-destructive evaluation NDT&E Int. 38 701–11  Karaman M, Li P-C and O’Donnell M 1995 Synthetic aperture imaging for small scale systems IEEE Trans. Ultrason. Ferroelectr. Freq. Control 42 429–42  Kirsch A and Grinberg N 2008 The Factorization Method for Inverse Problems (Oxford Lecture Series in Mathematics & Its Applications 36) (Oxford: Oxford University Press)  Kress R 1989 Linear Integral Equations (Berlin: Springer)  Krim H and Viberg M 1996 Two decades of array signal processing research IEEE Signal Process. Mag. 57–94  Kusiak S, Potthast R and Sylvester J 2003 A ‘range test’ for determining scatterers with unknown physical properties Inverse Problems 19 533–47  Lax P and Phillips R S 1967 Scattering Theory (New York: Academic)  Luke D R and Potthast R 2003 The no response test—a sampling method for inverse scattering problems SIAM J. Appl. Math. 63 1292–312  Luke D R 2004 Multifrequency inverse obstacle scattering: the point source method and generalized filtered backprojection Math. Comput. Simul. 66 297–314  Potthast R 2006 A survey about sampling and probe methods for inverse problems Inverse Problems 22 R1–47  Potthast R 2001 Point-sources and Multipoles in Inverse Scattering (London: Chapman & Hall)  Potthast R 2008 Acoustic Tomography by Orthogonality Sampling (Reading, UK: Institute of Acoustics Spring Conference)  Simonetti F and Huang L 2008 From beamforming to diffraction tomography J. Appl. Phys. 103  Vanska S 2008 Stationary waves method for inverse scattering problems Inverse Problems Imaging 2 577–86
Centaur Editors: Update this record