Magnetic Polarizability Tensor Research Articles

Discrimination of Disposable Vapes from Batteries Using the Magnetic Polarizability Tensor

Discrimination of Disposable Vapes from Batteries Using the Magnetic Polarizability Tensor

Measuring the Magnetic Polarizability Tensor of Nonsymmetrical Metallic Objects

Measuring the Magnetic Polarizability Tensor of Nonsymmetrical Metallic Objects

Computations and measurements of the magnetic polarizability tensor characterisation of highly conducting and magnetic objects

PurposeThe ability to characterise highly conducting objects, that may also be highly magnetic, by the complex symmetric rank–2 magnetic polarizability tensor (MPT) is important for metal detection applications including discriminating between threat and non-threat objects in security screening, identifying unexploded anti-personnel landmines and ordnance and identifying metals of high commercial value in scrap sorting. Many everyday non-threat items have both a large electrical conductivity and a magnetic behaviour, which, for sufficiently weak fields and the frequencies of interest, can be modelled by a high relative magnetic permeability. This paper aims to discuss the aforementioned idea.Design/methodology/approachThe numerical simulation of the MPT for everyday non-threat highly conducting magnetic objects over a broad range of frequencies is challenging due to the resulting thin skin depths. The authors address this by employing higher order edge finite element discretisations based on unstructured meshes of tetrahedral elements with the addition of thin layers of prismatic elements. Furthermore, computer aided design (CAD) geometrical models of the non-threat and threat object are often not available and, instead, the authors extract the geometrical features of an object from an imaging procedure.FindingsThe authors obtain accurate numerical MPT characterisations that are in close agreement with experimental measurements for realistic physical objects. The assessment of uncertainty shows the impact of geometrical and material parameter uncertainties on the computational results.Originality/valueThe authors present novel computations and measurements of MPT characterisations of realistic objects made of magnetic materials. A novel assessment of uncertainty in the numerical predictions of MPT characterisations for uncertain geometry and material parameters is included.

Reduced order model approaches for predicting the magnetic polarizability tensor for multiple parameters of interest

The magnetic polarizability tensor (MPT) is an economical characterisation of a conducting magnetic object, which can assist with identifying hidden targets in metal detection. The MPT’s coefficients depend on multiple parameters of interest including the object shape, size, electrical conductivity, magnetic permeability, and the frequency of excitation. The computation of the coefficients follow from post-processing an eddy current transmission problem solved numerically using high-order finite elements. To reduce the computational cost of constructing these characterisations for multiple different parameters, we compare three methods by which the MPT can be efficiently calculated for two-dimensional parameter sets, with different levels of code invasiveness. We compare, with numerical examples, a neural network regression of MPT eigenvalues with a projection-based reduced order model (ROM) and a neural network enhanced ROM (POD–NN) for predicting MPT coefficients.

Lower Bounds to the Q Factor of Electrically Small Resonators Through Quasistatic Modal Expansion

The problem of finding the optimal current distribution supported by small radiators yielding the minimum quality (Q) factor is a fundamental problem in electromagnetism. Q factor bounds constrain the maximum operational bandwidth of devices including antennas, metamaterials, and nanoresonators, and have been featured in seminal papers in the past decades. Here, we determine the lower bounds of Q factors of small-size plasmonic and high-permittivity dielectric resonators, which are characterized by quasi-electrostatic and quasi-magnetostatic natural modes, respectively. We expand the induced current density field in the resonator in terms of these modes, leading to closed-form analytical expressions for the electric and magnetic polarizability tensors, whose largest eigenvalue is directly linked to the minimum Q factor. Our results allow also to determine in closed form the corresponding optimal current density field. In particular, when the resonator exhibits two orthogonal reflection symmetries the minimum Q factor can be simply obtained from the Q factors of the single current modes with non-vanishing dipole moments aligned along the major axis of the resonator. Overall, our results open exciting opportunities in the context of nano-optics and metamaterials, facilitating the analysis and design of optimally shaped resonators for enhanced and tailored light-matter interactions.

Classification of Threat and Nonthreat Objects Using the Magnetic Polarizability Tensor and a Large-Scale Multicoil Array

This article describes the development of a large-scale multicoil arrangement capable of characterizing the magnetic polarizability tensor (MPT) of large threat objects such as firearms. The system has been applied to the measurement of a comprehensive range of weapons made available by the National Firearms Centre of the U.K. For comparison, a number of nonthreat items such as metallic belt buckles, keys, and coins have also been characterized. Clear differences in the magnitude and spectroscopic response of the MPT data for different firearm types and nonthreat items are presented. The application of unsupervised machine-learning (ML) algorithms to MPT data of threat and nonthreat objects enables a better understanding of target object classification. The presented results are encouraging as they demonstrate the ability of the MPT used in combination with the adopted classification algorithms to robustly discriminate between threat and nonthreat objects.

Inversion-Based Magnetic Polarizability Tensor Measurement From Time-Domain EMI Data

Inversion-Based Magnetic Polarizability Tensor Measurement From Time-Domain EMI Data

Properties of generalized magnetic polarizability tensors

We present new alternative complete asymptotic expansions for the time harmonic low‐frequency magnetic field perturbation caused by the presence of a conducting permeable object as its size tends to zero for the eddy current approximation of the Maxwell system. Our new alternative formulations enable a natural extension of the well‐known rank 2 magnetic polarizability tensor (MPT) object characterization to higher order tensor descriptions by introducing generalized MPTs (GMPTs) using multi‐indices. In particular, we identify the magnetostatic contribution, provide new results on the symmetries of GMPTs, derive explicit formulae for the real and imaginary parts of GMPT coefficients and also describe the spectral behavior of GMPT coefficients. We also introduce the concept of harmonic GMPTs (HGMPTs) that have fewer coefficients than other GMPT descriptions of the same order. We describe the scaling, translation and rotational properties of HGMPTs and describe an approach for obtaining those HGMPT coefficients that are invariant under the action of a symmetry group. Such an approach is one candidate for selecting features in object classification for hidden object identification using HGMPTs.

Identification of metallic objects using spectral magnetic polarizability tensor signatures: Object classification

AbstractThe early detection of terrorist threat objects, such as guns and knives, through improved metal detection, has the potential to reduce the number of attacks and improve public safety and security. To achieve this, there is considerable potential to use the fields applied and measured by a metal detector to discriminate between different shapes and different metals since, hidden within the field perturbation, is object characterization information. The magnetic polarizability tensor (MPT) offers an economical characterization of metallic objects and its spectral signature provides additional object characterization information. The MPT spectral signature can be determined from measurements of the induced voltage over a range of frequencies in a metal signature for a hidden object. With classification in mind, it can also be computed in advance for different threat and non‐threat objects. In this article, we evaluate the performance of probabilistic and non‐probabilistic machine learning algorithms, trained using a dictionary of computed MPT spectral signatures, to classify objects for metal detection. We discuss the importance of using appropriate features and selecting an appropriate algorithm depending on the classification problem being solved, and we present numerical results for a range of practically motivated metal detection classification problems.

Measurement of GMPT Coefficients for Improved Object Characterisation in Metal Detection

Magnetic polarizability tensors (MPTs) have become popular for characterising conducting permeable objects and assisting with the identification of hidden objects in metal detection for applications in security screening, humanitarian demining and scrap sorting. A rigorous mathematical justification of the complex symmetric rank 2 MPT object characterisation has been established based on the leading order term in an asymptotic expansion of the perturbed field for small objects. However, the accuracy of an MPT object characterisation is limited by the tensor’s small number of independent coefficients. By considering higher order terms in the asymptotic expansion, generalised magnetic polarizabilty tensors (GMPTs) have been introduced and the purpose of this work is to show that GMPT coefficients can, for the first time, be measured in practice. GMPTs offer the possibility to better discriminate between objects and, hence, the potential for better classification and identification, overcoming the limitations of a rank 2 MPT object characterisation. In a metal detector, the low-frequency background fields generated by a set of coils is almost always non-uniform and using GMPTs allow us to make a virtue of this. In this work we include both measurements and simulations to demonstrate the advantages that using GMPTs offer over using an MPT characterisation alone.

Measuring the Magnetic Polarizability Tensor Using an Axial Multi-Coil Geometry

The Magnetic Polarizability Tensor (MPT) is a representative property of an electrically conducting or magnetic object that includes information about the object’s characteristics such as, shape, size and material. The MPT is especially relevant to metal detection (MD) and can be used to improve MD performance by helping to distinguish between objects. This paper describes an instrument intended to measure the MPT of objects such as anti-personnel landmines and metallic clutter, up to 130 mm in diameter. The instrument uses a novel multi-coil geometry to generate a uniform electromagnetic field over the volume containing the test object to accurately determine the MPT. Performance tests of the system shows peak variance in the MPT is approximately 15 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> . Typical experimental repeatability is better than one percent for tests involving copper disks. Additionally, simulated data as well as previously published simulated and experimental data are used as a validation method of the experimental results. Good agreement between these and the measured MPTs of example targets are seen, proving the system’s capability of characterizing metallic objects.

Electronic Currents Induced by Optical Fields and Rotatory Power Density in Chiral Molecules.

The electric dipole–magnetic dipole polarizability tensor , introduced to interpret the optical activity of chiral molecules, has been expressed in terms of a series of density functions , which can be integrated all over the three-dimensional space to evaluate components and trace . A computational approach to , based on frequency-dependent electronic current densities induced by monochromatic light shining on a probe molecule, has been developed. The dependence of on the origin of the coordinate system has been investigated in connection with the corresponding change of . It is shown that only the trace of the density function defined via dynamic current density evaluated using the continuous translation of the origin of the coordinate system is invariant of the origin. Accordingly, this function is recommended as a tool that is quite useful for determining the molecular domains that determine optical activity to a major extent. A series of computations on the hydrogen peroxide molecule, for a number of different HO–OH dihedral angles, is shown to provide a pictorial documentation of the proposed method.

Identification of metallic objects using spectral magnetic polarizability tensor signatures: Object characterisation and invariants

AbstractThe early detection of terrorist threat objects, such as guns and knives, through improved metal detection, has the potential to reduce the number of attacks and improve public safety and security. To achieve this, there is considerable potential to use the fields applied and measured by a metal detector to discriminate between different shapes and different metals since, hidden within the field perturbation, is object characterisation information. The magnetic polarizability tensor (MPT) offers an economical characterisation of metallic objects that can be computed for different threat and non‐threat objects and has an established theoretical background, which shows that the induced voltage is a function of the hidden object's MPT coefficients. In this article, we describe the additional characterisation information that measurements of the induced voltage over a range of frequencies offer compared with measurements at a single frequency. We call such object characterisations its MPT spectral signature. Then, we present a series of alternative rotational invariants for the purpose of classifying hidden objects using MPT spectral signatures. Finally, we include examples of computed MPT spectral signature characterisations of realistic threat and non‐threat objects that can be used to train machine learning algorithms for classification purposes.

Efficient computation of the magnetic polarizabiltiy tensor spectral signature using proper orthogonal decomposition

AbstractThe identification of hidden conducting permeable objects from measurements of the perturbed magnetic field taken over a range of low frequencies is important in metal detection. Applications include identifying threat items in security screening at transport hubs, location of unexploded ordnance, and antipersonnel landmines in areas of former conflict, searching for items of archeological significance and recycling of valuable metals. The solution of the inverse problem, or more generally locating and classifying objects, has attracted considerable attention recently using polarizability tensors. The magnetic polarizability tensor (MPT) provides a characterization of a conducting permeable object using a small number of coefficients, has an explicit formula for the calculation of their coefficients, and a well understood frequency behavior, which we call its spectral signature. However, to compute such signatures, and build a library of them for object classification, requires the repeated solution of a transmission problem, which is typically accomplished approximately using a finite element discretization. To reduce the computational cost, we propose an efficient reduced order model (ROM) that further reduces the problem using a proper orthogonal decomposition for the rapid computation of MPT spectral signatures. Our ROM benefits from a posteriori error estimates of the accuracy of the predicted MPT coefficients with respect to those obtained with finite element solutions. These estimates can be computed cheaply during the online stage of the ROM allowing the ROM prediction to be certified. To further increase the efficiency of the computation of the MPT spectral signature, we provide scaling results, which enable an immediate calculation of the signature under changes in the object size or conductivity. We illustrate our approach by application to a range of homogenous and inhomogeneous conducting permeable objects.

Comparative Study of Planar Coil EMI Sensors for Inversion-Based Detection of Buried Objects

In a context of buried objects detection using electromagnetic induction (EMI), dipole inversion refers to the estimation of object's location and magnetic polarizability tensor from EMI and sensor's positional data. In case of planar coil sensors, dipole inversion may become a surprisingly difficult and potentially ill-posed problem due to non-uniform distribution of directional sensitivities, nonlinear nature of target localization, as well as strong correlations between tensor elements and target's depth. In this paper, we evaluate inversion performances of two categories of planar coil sensors; single-receiver sensors used in conventional metal detection (MD), and multi-receiver sensors aimed at metal characterization (MC). We use three different inversion methods; nonlinear least squares (NLS), HAP method featuring novel auxiliary source model for improved object localization, and differential evolution (DE). Comparative study is performed using synthetic EMI and sensor's positional data under realistic scenarios involving different targets, depths and signal-to-noise ratios (SNRs). Our results suggest that relatively simple planar MC sensors clearly outperform conventional MD sensors, especially at greater depths. On average, DE method notably improves the invertibility of MD sensors, while a denser scan pattern may help to tackle lower SNR at greater depths.

Wideband Models for the Electromagnetic Induction Signatures of Thin Conducting Shells

Wideband electromagnetic induction sensors have been shown to be more effective than traditional metal detectors at identifying metallic targets of interest when buried near abundant metallic clutter. A promising strategy for performing target identification using wideband data relies on characterizing the target response using a magnetic polarizability tensor (MPT) that is a function of frequency. In this paper, a surface integral method is presented for deriving the MPT in singularity expansion form using a modal decomposition. The method is verified by comparing the singularity expansion for a spherical shell to a derived analytical solution. The expansion coefficients for cylindrical tubes, of various aspect ratios, are compared to experimental results, showing good agreement. Finally, expansion coefficients are given for a disk and are compared to other numerical results.

An Initial Value Estimation Method for the Kalman and Extended Kalman Filters in Underground Metal Detection

As an underground metal detection technology, the electromagnetic induction (EMI) method is widely used in many cases. Therefore, the EMI detection algorithms with excellent performance are worth studying. One of the EMI detection methods in the underground metal detection is the filter method, which first obtains the secondary magnetic field data and then uses the Kalman filter (KF) and the extended Kalman filter (EKF) to estimate the parameters of metal targets. However, the traditional KF methods used in the underground metal detection have an unsatisfactory performance of the convergence as the algorithms are given a random or a fixed initial value. Here, an initial state estimation algorithm for the underground metal detection is proposed. The initial state of the target’s horizontal position is estimated by the first order central moments of the secondary field strength map. In addition, the initial state of the target’s depth is estimated by the full width at half maximum (FWHM) method. In addition, the initial state of the magnetic polarizability tensor is estimated by the least squares method. Then, these initial states are used as the initial values for KF and EKF. Finally, the position, posture and polarizability of the target are recursively calculated. A simulation platform for the underground metal detection is built in this paper. The simulation results show that the initial value estimation method proposed for the filtering algorithm has an excellent performance in the underground metal detection.

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

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.

Electric Quadrupole Moment and the Tensor Magnetic Polarizability of Twisted Electrons and a Potential for their Measurements.

For a twisted (vortex) Dirac particle in nonuniform electric and magnetic fields, the relativistic Foldy-Wouthuysen Hamiltonian is derived including high order terms describing new effects. The result obtained shows for the first time that a twisted spin-1/2 particle possesses a tensor magnetic polarizability and a measurable (spectroscopic) electric quadrupole moment. We have calculated the former parameter and have evaluated the latter one for a twisted electron. The tensor magnetic polarizability of the twisted electron can be measured in a magnetic storage ring because a beam with an initial orbital tensor polarization acquires a horizontal orbital vector polarization. The electric quadrupole moment is rather large and strongly influences the dynamics of the intrinsic orbital angular momentum (OAM). Three different methods of its measurements, freezing the intrinsic orbital angular momentum and two resonance methods, are proposed. The existence of the quadrupole moment of twisted electrons can lead to practical applications.

An Explicit Formula for the Magnetic Polarizability Tensor for Object Characterization

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.