Generalised magnetic polarizability tensors

Ledger, P.D.; Lionheart, William R B

doi:10.1002/mma.4809

Cited by 17 publications

(55 citation statements)

References 16 publications

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“…Still further, using (26), (24) becomes (22a), and in a similar manner, using (25), (27) becomes (22b) as desired. It also follows from (22a), and the linearity of the transmission problem (11)…”

Section: The Following Symmetric Bilinear Forms On Real Vectorsmentioning

confidence: 85%

“…9 We have extended the work of Ammari et al to provide a complete asymptotic expansion for the perturbed magnetic field, which allows an object to be characterised by generalised MPTs of which the rank 2 MPT is the simplest case. 11 In Ledger et al, 12 we have developed asymptotic expansions for the perturbed magnetic field that describe (a) the leading order term for a small inhomogeneous conducting permeable object and (b) the response in the case of multiple small conducting permeable objects, thus, extending the rank 2 MPT description of each of the objects to these cases. Some properties of the MPT are described in Ledger and Lionheart, 13 and the availability of the explicit formula for the isolated single object case has been communicated to the engineering community.…”

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confidence: 99%

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The spectral properties of the magnetic polarizability tensor for metallic object characterisation

Ledger

Lionheart

2019

Math Methods in App Sciences

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113

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The measurement of time-harmonic perturbed field data, at a range of frequencies, is beneficial for practical metal detection, where the goal is to locate and identify hidden targets. In particular, these benefits are realised when frequency-dependent magnetic polarizability tensors (MPTs) are used to provide an economical characterisation of conducting permeable objects, and a dictionary-based classifier is employed. However, despite the advantages shown in dictionary-based classifiers, the behaviour of the MPT coefficients with frequency is not properly understood. In this paper, we rigorously analyse, for the first time, the spectral properties of the coefficients of the MPT. This analysis has the potential to improve existing algorithms and design new approaches for object location and identification in metal detection. Our analysis also enables the response transient response from a conducting permeable object to be predicted for more general forms of excitation. KEYWORDSasymptotic analysis, eddy current, inverse problems, magnetic polarizability tensor, metal detection, spectral problems MSC CLASSIFICATION 35R30; 35B30 INTRODUCTIONIn metal detection, there is considerable interest in being able to locate and identify conducting permeable objects from the measurements of mutual inductance between a transmitting and a measurement coil. Applications include security screening, archaeology excavations, ensuring food safety as well as the search for land mines, and unexploded ordnance. There are also closely related topics such as magnetic induction tomography for medical imaging and eddy current testing for monitoring the corrosion of steel reinforcement in concrete structures.Within the metal detection community, magnetic polarizability tensors (MPTs) have attracted considerable interest to assist with the identification of objects when the transmitting coil is excited by a sinusoidal signal, eg, 1-7 Engineers believe that a rank 2 MPT provides an economical characterisation of a conducting permeable object that is invariant of position. An asymptotic formula providing the leading order term for the perturbed magnetic field due to the presence of a small conducting permeable object has been obtained by Ammari, Chen, Chen, Garnier, and Volkov, 8 which characterises the object in terms of a rank 4 tensor. We have shown that this simplifies for orthonormal coordinates and allows an object to be characterised by a complex symmetric rank 2 MPT, with an explicit formula for its coefficients, thus, justifying the This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Section: The Following Symmetric Bilinear Forms On Real Vectorsmentioning

confidence: 85%

mentioning

confidence: 99%

The spectral properties of the magnetic polarizability tensor for metallic object characterisation

Ledger

Lionheart

2019

Math Methods in App Sciences

Self Cite

113

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“…A generalization of (11) has recently been derived [23], which extends the leading order term to a complete asymptotic expansion of the perturbed field. The higher order terms are expressed in terms of a new class of (higher rank) generalized MPTs (GMPTs) and higher order derivatives of G(x, z) and H 0 (z).…”

Section: Asymptotic Expansionmentioning

confidence: 99%

“…However, this is incorrect since, despite the substitution of the Taylor series expressions in (15), the integrands in R d (x) still depend on A , which itself is a function of α, and consequently, we cannot say that the remainder is of the form 4 with C independent of α. A different approach is required to achieve this rigorously, leading to the asymptotic expansion (11) [4], [23].…”

Section: A Validity Of (4)mentioning

confidence: 99%

An Explicit Formula for the Magnetic Polarizability Tensor for Object Characterization

Ledger

Lionheart

2018

IEEE Trans. Geosci. Remote Sensing

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The magnetic polarizability tensor (MPT) has attracted considerable interest due to the possibility it offers for characterizing conducting objects and assisting with the identification and location of hidden targets in metal detection. An explicit formula for its calculation for arbitrary-shaped objects is missing in the electrical engineering literature. Furthermore, the circumstances for the validity of the magnetic dipole approximation of the perturbed field, induced by the presence of the object, are not fully understood. On the other hand, in the applied mathematics community, an asymptotic expansion of the perturbed magnetic field has been derived for small objects and a rigorous formula for the calculation of the MPT has been obtained. The purpose of this paper is to relate the results of the two communities, to provide a rigorous justification for the MPT, and to explain the situations in which the approximation is valid.

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“…In applied mathematics and analysis, previous studies by [1,14,15,16,17,18,19] have shown that the perturbation due to the presence of the conducting objects can be represented by asymptotic formulas and PT is actually the dominant term in the formula. The asymptotic formula and the corresponding PT are generally not the same for different systems.…”

Section: Introductionmentioning

confidence: 99%

Classification of materials for conducting spheroids based on the first order polarization tensor

Khairuddin

Yunos

Aziz

et al. 2017

J. Phys.: Conf. Ser.

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Abstract. Polarization tensor is an old terminology in mathematics and physics with many recent industrial applications including medical imaging, nondestructive testing and metal detection. In these applications, it is theoretically formulated based on the mathematical modelling either in electrics, electromagnetics or both. Generally, polarization tensor represents the perturbation in the electric or electromagnetic fields due to the presence of conducting objects and hence, it also desribes the objects. Understanding the properties of the polarization tensor is necessary and important in order to apply it. Therefore, in this study, when the conducting object is a spheroid, we show that the polarization tensor is positive-definite if and only if the conductivity of the object is greater than one. In contrast, we also prove that the polarization tensor is negative-definite if and only if the conductivity of the object is between zero and one. These features categorize the conductivity of the spheroid based on in its polarization tensor and can then help to classify the material of the spheroid.

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Generalised magnetic polarizability tensors

Cited by 17 publications

References 16 publications

The spectral properties of the magnetic polarizability tensor for metallic object characterisation

The spectral properties of the magnetic polarizability tensor for metallic object characterisation

An Explicit Formula for the Magnetic Polarizability Tensor for Object Characterization

Classification of materials for conducting spheroids based on the first order polarization tensor

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