Optimal electromagnetic measurements
Författare
Summary, in English
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.
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.
Publiceringsår
2001
Språk
Engelska
Sidor
1323-1336
Publikation/Tidskrift/Serie
Journal Electromagnetic Waves and Applications
Volym
15
Issue
10
Dokumenttyp
Artikel i tidskrift
Förlag
VSP BV
Ämne
- Electrical Engineering, Electronic Engineering, Information Engineering
- Other Electrical Engineering, Electronic Engineering, Information Engineering
Status
Published
Forskningsgrupp
- Electromagnetic theory
ISBN/ISSN/Övrigt
- ISSN: 1569-3937