A time-domain probe method for three-dimensional rough surface reconstructions
Department of Mathematics, University of Reading, Whiteknights, PO Box 220, Berkshire, RG6 6AX, United Kingdom, United Kingdom
In particular, we discuss the reconstruction of the shape of a rough surface in three dimensions from time-domain measurements of the scattered field. In practise, measurement data is collected where the incident field is given by a pulse. We formulate the time-domain field reconstruction problem equivalently via frequency-domain integral equations or via a retarded boundary integral equation based on results of Bamberger, Ha-Duong, Lubich. In contrast to pure frequency domain methods here we use a time-domain characterization of the unknown shape for its reconstruction.
Our paper will describe the Time-Domain Probe Method and relate it to previous frequency-domain approaches on sampling and probe methods by Colton, Kirsch, Ikehata, Potthast, Luke, Sylvester et al. The approach significantly extends recent work of Chandler-Wilde and Lines (2005) and Luke and Potthast (2006) on the time-domain point source method. We provide a complete convergence analysis for the method for the rough surface scattering case and provide numerical simulations and examples.
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