A Time Domain Point Source Method for Inverse Scattering by Rough Surfaces

In this paper we propose a new method to determine the location and shape of an unbounded rough surface from measurements of scattered electromagnetic waves. The proposed method is based on the point source method of Potthast (IMA J. Appl. Math. 61, 119–140, 1998) for inverse scattering by bounded obstacles. We propose a version for inverse rough surface scattering which can reconstruct the total field when the incident field is not necessarily time harmonic. We present numerical results for the case of a perfectly conducting surface in TE polarization, in which case a homogeneous Dirichlet condition applies on the boundary. The results show great accuracy of reconstruction of the total field and of the prediction of the surface location.

[1]  Peter Monk,et al.  Recent Developments in Inverse Acoustic Scattering Theory , 2000, SIAM Rev..

[2]  S. Chandler-Wilde,et al.  Scattering by infinite one-dimensional rough surfaces , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[3]  John A. DeSanto,et al.  The reconstruction of shallow rough-surface profiles from scattered field data , 1991 .

[4]  S. Chandler-Wilde,et al.  Efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane , 1995 .

[5]  Akira Noguchi,et al.  Rough Surface Inverse Scattering Problem with Gaussian Beam Illumination (Special Issue on Electromagnetic Theory) , 1994 .

[6]  N. C. Nigam.  Introduction to Random Vibrations , 1983 .

[7]  C. Sheppard.  Imaging of random surfaces and inverse scattering in the Kirchoff approximation , 1998 .

[8]  S. Chandler-Wilde.  The Impedance Boundary Value Problem for the Helmholtz Equation in a Half‐Plane , 1997 .

[9]  S. Chandler-Wilde,et al.  Scattering by rough surfaces : the Dirichlet problem for the Helmholtz equation in a non-locally perturbed half-plane , 1996 .

[10]  D. Daniels.  Ground Penetrating Radar , 2005 .

[11]  John A. DeSanto,et al.  Reconstruction of rough-surface profiles with the Kirchhoff approximation , 1991 .

[12]  C. Eftimiu.  Scattering by rough surfaces: A simple model , 1986 .

[13]  Masahiro Yamamoto,et al.  An Inverse Problem in Periodic Diffractive Optics: Reconstruction of Lipschitz Grating Profiles , 2002 .

[14]  Roland Potthast,et al.  The No Response Test---A Sampling Method for Inverse Scattering Problems , 2003, SIAM J. Appl. Math..

[15]  T. Arens,et al.  Why linear sampling works , 2004 .

[16]  Roland Potthast,et al.  A 'range test' for determining scatterers with unknown physical properties , 2003 .

[17]  Mark Spivack,et al.  Direct solution of the inverse problem for rough surface scattering at grazing incidence , 1992 .

[18]  Masaru Ikehata,et al.  On reconstruction in the inverse conductivity problem with one measurement , 2000, 1902.05182.

[19]  Simon N. Chandler-Wilde,et al.  A Nyström Method for a Class of Integral Equations on the Real Line with Applications to Scattering by Diffraction Gratings and Rough Surfaces , 2000 .

[20]  R. J. Peppin.  An Introduction to Random Vibrations, Spectral and Wavelet Analysis , 1994 .

[21]  Andreas Kirsch,et al.  Characterization of the shape of a scattering obstacle using the spectral data of the far field operator , 1998 .

[22]  Maxim J. Goldberg,et al.  An improved operator expansion algorithm for direct and inverse scattering computations , 1999 .

[23]  R. Potthast.  Point Sources and Multipoles in Inverse Scattering Theory , 2018 .

[24]  Margaret Cheney,et al.  A Mathematical Tutorial on Synthetic Aperture Radar , 2001, SIAM Rev..

[25]  A. Kirsch,et al.  A simple method for solving inverse scattering problems in the resonance region , 1996 .

[26]  Roland Potthast,et al.  A point source method for inverse acoustic and electromagnetic obstacle scattering problems , 1998 .

[27]  R. Kress.  Linear Integral Equations , 1989 .

[28]  G. Micula,et al.  Numerical Treatment of the Integral Equations , 1999 .

[29]  Dean Goodman,et al.  Ground-Penetrating Radar: An Introduction for Archaeologists , 1997 .

[30]  Andreas Kirsch,et al.  The factorization method in inverse scattering from periodic structures , 2003 .