{
  "id": "1401.0083",
  "version": "v4",
  "published": "2013-12-31T03:51:06.000Z",
  "updated": "2014-10-27T01:16:48.000Z",
  "title": "The enclosure method for inverse obstacle scattering using a single electromagnetic wave in time domain",
  "authors": [
    "Masaru Ikehata"
  ],
  "comment": "Thoroughly revised version",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, a time domain enclosure method for an inverse obstacle scattering problem of electromagnetic wave is introduced. The wave as a solution of Maxwell's equations is generated by an applied volumetric current having an {\\it orientation} and supported outside an unknown obstacle and observed on the same support over a finite time interval. It is assumed that the obstacle is a perfect conductor. Two types of analytical formulae which employ a {\\it single} observed wave and explicitly contain information about the geometry of the obstacle are given. In particular, an effect of the orientation of the current is catched in one of two formulae. Two corollaries concerning with the detection of the points on the surface of the obstacle nearest to the centre of the current support and curvatures at the points are also given.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-04-28T04:10:23.000Z",
      "abstract": "In this paper, a time domain enclosure method for an inverse obstacle scattering problem of electromagnetic wave is introduced. The wave as a solution of Maxwell's equations is produced by an applied volumetric current supported outside an unknown obstacle and observed on the same support over a finite time interval. It is assumed that the obstacle is a perfect conductor. Two types of analytical formulae which explicitly contains information about the geometry of the obstacle from a {\\it single} observed wave are given. As corollaries, one gets: (i) a {\\it maximum sphere} centred at a give point $p$ outside the obstacle whose exterior encloses the unknown obstacle using a {\\it single} observed wave; (ii) all the points on the intersection of the maximum sphere in (i) with the boundary of the obstacle, which is called the {\\it first reflection point}, going from $p$ in this paper, using infinitely many observed waves corresponding to infinitely many input sources; (iii) both the Gauss and mean curvatures of the boundary of the obstacle at an arbitrary {\\it known} first reflection point, going from $p$ using suitably chosen {\\it two} observed waves.",
      "comment": "resubmitted to Inverse Problems on 28 April 2014",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-10-27T01:16:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35L50",
      "35Q61",
      "78A46",
      "78M35"
    ],
    "keywords": [
      "inverse obstacle scattering",
      "single electromagnetic wave",
      "enclosure method",
      "time domain",
      "volumetric current supported outside"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.0083I"
    }
  }
}