| 1. |
- Cheney, Margaret, et al.
(författare)
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Optimal electromagnetic measurements
- 2001
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Ingår i: Journal Electromagnetic Waves and Applications. - 1569-3937. ; 15:10, s. 1323-1336
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Tidskriftsartikel (refereegranskat)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 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.
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| 2. |
- Cheney, Margaret, et al.
(författare)
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Optimal Electromagnetic Measurements
- 2000
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 3. |
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| 4. |
- Cheney, Margaret, et al.
(författare)
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Resonance Enhancement in Noise
- 2023
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This document compares two approaches to finding resonance peaks from asingle sensor: 1) averaging multiple measurements of the transfer function orfrequency-domain scattering matrix, versus 2) using the iterative time-reversalprocess, which involves iteratively re-transmitting a time-reversed version ofthe scattered field at the previous iterations. The averaging method has theadvantage of handling arbitrarily much noise if sufficiently many averages areused. On the other hand, up to a certain level of noise, the time-reversalmethod has dramatic advantages over the averaging method; but it also requires more complex equipment. This document discusses the tradeoffs involved, with the goal of providing information that may be useful in the system design process.
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| 5. |
- Cheney, Margaret, et al.
(författare)
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Three-dimensional inverse scattering: layer-stripping formulas and ill-posedness results
- 1988
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Ingår i: Inverse Problems. - : IOP Publishing. - 0266-5611 .- 1361-6420. ; 4:3, s. 625-642
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Tidskriftsartikel (refereegranskat)abstract
- The authors consider the three-dimensional direct and inverse scattering problems for the Schrodinger equation and for the reduced wave equation with variable velocity. The scatterer is probed with either point sources or plane waves of fixed frequency. They ask the question, 'How does the wave field change when the scatterer is truncated?' Simple formulae for the derivative of the wave field with respect to the truncation parameter are obtained. Similar formulae are obtained for the scattering amplitudes. These formulae are used to derive ill-posedness results for various inverse scattering problems. The ill-posedness results apply when data are collected over a range of frequencies.
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| 6. |
- Kristensson, Gerhard, et al.
(författare)
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Resonance Enhancement with Antenna Modeling
- 2018
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This paper develops theory for an iterative experimental approach to use one or more antennas to identify resonances of a scattering system, which could consist of the antennas and one or more scattering objects. We include realistic mathematical models for the antennas and for target(s), and we show that the resonances include effects from the antennas and wave propagation as well as the target scattering operator and its poles. We show how the effects of the antennas and wave propagation paths can be removed, to leave only the effect of the target scattering operator. We include simulations for the case of one and two cylindrical dipole antennas probing a dielectric sphere, and we show the effect of antenna resonances on the iterative experimental process.
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