| 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. |
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| 6. |
- 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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| 7. |
- Cheney, Margaret
(författare)
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Tomography problems arising in Synthetic Aperture Radar
- 2000
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This paper gives a mathematical tutorial on Synthetic Aperture Radar (SAR). We see that with the usual mathematical model, the SAR reconstruction problem reduces to a problem in integral geometry. A number of mathematical problems are posed; the paper concludes with a short description of the basic idea underlying the algorithms used in most present systems. The challenge to the mathematical community is to find algorithms that might be better.
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| 8. |
- 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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| 9. |
- Sjödén, Therese, 1977-
(författare)
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Sensitivity Analysis and Material Parameter Estimation using Electromagnetic Modelling
- 2012
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Estimating parameters is the problem of finding their values from measurements and modelling. Parameters describe properties of a system; material, for instance, are defined by mechanical, electrical, and chemical parameters. Fisher information is an information measure, giving information about how changes in the parameter effect the estimation. The Fisher information includes the physical model of the problem and the statistical model of noise. The Cramér-Rao bound is the inverse of the Fisher information and gives the best possible variance for any unbiased estimator.This thesis considers aspects of sensitivity analysis in two applied material parameter estimation problems. Sensitivity analysis with the Fisher information and the Cramér-Rao bound is used as a tool for evaluation of measurement feasibilities, comparison of measurement set-ups, and as a quantitative measure of the trade-off between accuracy and resolution in inverse imaging.The first application is with estimation of the wood grain angle parameter in trees and logs. The grain angle is the angle between the direction of the wood fibres and the direction of growth; a large grain angle strongly correlates to twist in sawn timber. In the thesis, measurements with microwaves are argued as a fast and robust measurement technique and electromagnetic modelling is applied, exploiting the anisotropic properties of wood. Both two-dimensional and three-dimensional modelling is considered. Mathematical modelling is essential, lowering the complexity and speeding up the computations. According to a sensitivity analysis with the Cramér-Rao bound, estimation of the wood grain angle with microwaves is feasible.The second application is electrical impedance tomography, where the conductivity of an object is estimated from surface measurements. Electrical impedance tomography has applications in, for example, medical imaging, geological surveillance, and wood evaluation. Different configurations and noise models are evaluated with sensitivity analysis for a two-dimensional electrical impedance tomography problem. The relation between the accuracy and resolution is also analysed using the Fisher information.To conclude, sensitivity analysis is employed in this thesis, as a method to enhance material parameter estimation. The sensitivity analysis methods are general and applicable also on other parameter estimation problems.
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