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Optimal electromagnetic measurements

Cheney, Margaret and Kristensson, Gerhard LU (2001) In Journal Electromagnetic Waves and Applications 15(10). p.1323-1336
Abstract
We consider the problem of obtaining information about an inaccessible half-space from electromagnetic measurements made in the accessible half-space. If the measurements are of limited precision, some scatterers will be undetectable because their scattered fields are below the precision of the measuring instrument. How can we make optimal measurements? In other words, what incident fields should we apply that will result in the biggest measurements?

There are many ways to formulate this question, depending on the measuring instruments. In this paper we consider a formulation involving wave-splitting in the accessible half-space: what downgoing wave will result in an upgoing wave of greatest energy? This formulation is most... (More)
We consider the problem of obtaining information about an inaccessible half-space from electromagnetic measurements made in the accessible half-space. If the measurements are of limited precision, some scatterers will be undetectable because their scattered fields are below the precision of the measuring instrument. How can we make optimal measurements? In other words, what incident fields should we apply that will result in the biggest measurements?

There are many ways to formulate this question, depending on the measuring instruments. In this paper we consider a formulation involving wave-splitting in the accessible half-space: what downgoing wave will result in an upgoing wave of greatest energy? This formulation is most natural for far-field problems.



A closely related question arises in the case when we have a guess about the configuration of the inaccessible half-space. What measurements should we make to determine whether our guess is accurate? In this case we compare the scattered field to the field computed from the guessed configuration. Again we look for the incident field that results in the greatest energy difference.



We show that the optimal incident field can be found by an iterative process involving time reversal "mirrors". For band-limited incident fields and compactly supported scatterers, this iterative process converges to a sum of time-harmonic fields. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal Electromagnetic Waves and Applications
volume
15
issue
10
pages
1323 - 1336
publisher
VSP BV
external identifiers
  • scopus:0035166116
ISSN
1569-3937
DOI
10.1163/156939301X01228
language
English
LU publication?
yes
id
ccba50bd-cb24-42cc-97f8-8f01bf0bd1b5 (old id 143192)
date added to LUP
2007-06-27 11:57:07
date last changed
2018-01-07 09:55:01
@article{ccba50bd-cb24-42cc-97f8-8f01bf0bd1b5,
  abstract     = {We consider the problem of obtaining information about an inaccessible half-space from electromagnetic measurements made in the accessible half-space. If the measurements are of limited precision, some scatterers will be undetectable because their scattered fields are below the precision of the measuring instrument. How can we make optimal measurements? In other words, what incident fields should we apply that will result in the biggest measurements? <br/><br>
There are many ways to formulate this question, depending on the measuring instruments. In this paper we consider a formulation involving wave-splitting in the accessible half-space: what downgoing wave will result in an upgoing wave of greatest energy? This formulation is most natural for far-field problems.<br/><br>
<br/><br>
A closely related question arises in the case when we have a guess about the configuration of the inaccessible half-space. What measurements should we make to determine whether our guess is accurate? In this case we compare the scattered field to the field computed from the guessed configuration. Again we look for the incident field that results in the greatest energy difference.<br/><br>
<br/><br>
We show that the optimal incident field can be found by an iterative process involving time reversal "mirrors". For band-limited incident fields and compactly supported scatterers, this iterative process converges to a sum of time-harmonic fields.},
  author       = {Cheney, Margaret and Kristensson, Gerhard},
  issn         = {1569-3937},
  language     = {eng},
  number       = {10},
  pages        = {1323--1336},
  publisher    = {VSP BV},
  series       = {Journal Electromagnetic Waves and Applications},
  title        = {Optimal electromagnetic measurements},
  url          = {http://dx.doi.org/10.1163/156939301X01228},
  volume       = {15},
  year         = {2001},
}