Optimal Electromagnetic Measurements
Author
Summary, in English
We consider the problem of obtaining information about an inaccessible halfspace
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 wavesplitting
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.
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 wavesplitting
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.
Publishing year
2000
Language
English
Publication/Series
Technical Report LUTEDX/(TEAT-7091)/1-24/(2000)
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Document type
Report
Publisher
[Publisher information missing]
Topic
- Electrical Engineering, Electronic Engineering, Information Engineering
Status
Published
Report number
TEAT-7091
Research group
- Electromagnetic theory