Determining an obstacle by far-field data measured at a few spots

Qi Wang; Yanren Hou

doi:10.3934/ipi.2015.9.591

Article Contents

2015, Volume 9, Issue 2: 591-600. Doi: 10.3934/ipi.2015.9.591

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Determining an obstacle by far-field data measured at a few spots

Qi Wang^1, and
Yanren Hou^2,

1.
Department of Computing Sciences, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049
2.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an,710049

Received: December 31, 2013

Revised: April 30, 2014

Published: April 2015

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Abstract

We consider the inverse scattering problem of determining an acoustic sound-soft obstacle by using the far-field data. It is shown that if the shape of the obstacle is known in advance, then the far-field data measured at four different spots can uniquely determine the location and size of the obstacle. If the shape of the obstacle is unknown, we show that the location of the obstacle can be approximately determined by using the far-field data measured at four appropriately chosen spots.

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Mathematics Subject Classification: Primary: 78A46; Secondary: 81U40.

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