This paper considers a dipole solution to the low-frequency electromagnetic responses of a typical in-line metal detector to metal contaminants. This solution is determined by the characteristics of metal targets and incident magnetic fields, which are treated separately as two independent factors. For the metal targets, the responses of sphere and wire samples are determined. The electromagnetic polarizability matrix of a metal sphere is directly computed from a spherical response function. The electromagnetic polarizability tensor of metal wire is derived from a measured eigenvalue matrix and a rotation matrix. The approximated responses of sphere and wire samples from the proposed solutions agree well with the measured responses from in-line metal detectors. In theory, the approximation method on metal wire samples is also applicable to the metal contaminants of other shapes.

On the Low-Frequency Electromagnetic Responses of In-Line Metal Detectors to Metal Contaminants

A general model to compute the response of an electromagnetic induction sensor to a magnetic soil, in both time and frequency domains, is developed. The model requires modest computational resources and can be applied to arbitrary soil inhomogeneities and relief, and to arbitrary sensor coil shapes, orientations, and positions. Central to the model is the concept of a head sensitivity map, which can be used to characterize the sensor head as a function of the shape, size, and position of the sensor coils. Two further concepts related to the head sensitivity are presented, which are the zero equisensitivity surface and the volume of influence. We demonstrate that these concepts aid the understanding of the detector behavior. The general model is based on the Born approximation, which is valid if the soil magnetic susceptibility is sufficiently small. A simpler model, which is only valid for homogeneous half-space soils but does not require the Born approximation, is also developed. The responses predicted by both models are shown to be in good agreement with each other and also with available analytic solutions. Comparing the two models also enabled an expression for the error incurred when using the Born approximation to be established. We shown that, for most soils of relevance to mine clearance, the corresponding error is negligible.

Modeling the Response of Electromagnetic Induction Sensors to Inhomogeneous Magnetic Soils With Arbitrary Relief

We derive the electromagnetic induction (EMI) response to conducting anomalies of spheroidal shape embedded in a weakly conducting host medium. As one application, prolate and oblate spheroids are convenient shapes for modeling buried unexploded ordnance, landmines, and naval mines. Under the assumptions of a perfectly conducting or nonconducting target and the assumption of a uniformly incident field, simple analytical solutions are obtained. Both the eddy-current and the current channeling responses are derived for prolate and oblate spheroids. For example, in a marine environment the current-channeling contribution can be quite large. As expected, these responses differ depending on the direction of the incident field relative to the spheroidal symmetry axis. The problem is solved separately for axial and transverse incidence, with the general case being a superposition of the two. These solutions could be used for fitting a spheroidal model to EMI data in which a small number of parameters, such as the location, size, shape, and orientation of the object, are to be determined.

Eddy-current and current-channeling response to spheroidal anomalies

The magnetic dipole polarizability tensor of a metallic object gives unique information about the size, shape and electromagnetic properties of the object. In this paper, we present a novel method of coin characterization based on the spectroscopic response of the absolute tensor. The experimental measurements are validated using a combination of tests with a small set of bespoke coin surrogates and simulated data. The method is applied to an uncirculated set of US coins. Measured and simulated spectroscopic tensor responses of the coins show significant differences between different coin denominations. The presented results are encouraging as they strongly demonstrate the ability to characterize coins using an absolute tensor approach.

/pdf/on-the-magnetic-polarizability-tensor-of-us-coinage-3es8kiqzqj.pdf

On the magnetic polarizability tensor of US coinage

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.

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

Eddy-current or permeability-contrast based metal detectors may be characterized by static sensitivity maps, a new graphic representation that maps detector response to a standardized infinitesimal object in a static field. A sphere is shown to be a suitable standard object because its behavior describes, to within multiplicative constants, objects of arbitrary conductivity and permeability. Static sensitivity maps take full account of both the excitation and detection coil shapes. They are compact, easy to understand, closely related to industrial testing procedures, and likely to prove a useful design tool. Their usefulness is illustrated by examples based on a metal detector for which published data exist.

Sensitivity maps for metal detector design

The sensitivity of magnetic metal detectors to prolate or oblate spheroidal targets depends both on the semiaxis ratio and on the orientation of the spheroid polar axis relative to the local magnetic field. A spherical target produces null response only if the generator and detector coil magnetic fields are orthogonal, but the spheroid possesses a null direction for a large range of magnetic field orientations. A spheroid can therefore be made undetectable by rotating it into a particular orientation. The existence of such blind-position angles is investigated theoretically in detail and families of curves are given to illustrate them in a particular case.

P.P. Silvester

Papers

Sensitivity maps for metal detector design

Sensitivity of metal detectors to spheroidal targets