Instrumentation & Measurement Magazine 23-3 - 38

magnetic or non-magnetic.
On the other hand, nonuniformly shaped objects,
i.e., objects having one
or two dominant dimensions along their principal
axes, respond distinctively
different, depending on
material type.
In case of a magnetic object, i.e., an object where
magnetization effects are
dominant with respect to
eddy current effects, the response is strongest when
the incident field is parallel to the principal axis
that relates to the longest
object's dimension. This
means that the eigenvalues corresponding to those
direction(s) would have
higher magnitudes with
respect to the others. For
a magnetic rod oriented
Fig. 2. Using a scanning metal detector to magnetically illuminate the target from different directions [5] (© 2020 IEEE).
along the z-axis whose
Feature Interpretation Level
lengths in the x- and y-diThe theory behind the magnetic polarizability tensor is now- rection are negligibly small, only λ 33 would be observed.
adays considered as well-established, and there is a common Similarly, in case of a very thin magnetic disc or a quaperception in the engineering community that the target's in- dratic plate placed in the x-y plane, the magnetic field would
trinsic features embedded within the tensor could provide be equally concentrated in x- and y-directions only, and
good basis for discrimination between different classes of hence λ11 = λ22 = λ while λ33 ≈ 0 (Fig. 3).
For conducting and non-magnetic objects, the EMI remetallic targets, for a range of applications [8]. A simplified
relationship between the tensor eigenvalues (observed at a sin- sponse is strongest when the incident field is in such direction
gle frequency) and the target's general shape and material type so that eddy currents circulate along their longest possible
is given in Fig. 3 (eigenvectors are assumed to point towards path. If we recall a simple right-hand rule relating magnetic
x, y and z-axis). (These eigenvalues are obtained by arranging field and a circular current loop, it follows that the stronthe elements of v into a symmetric 3x3 matrix and perform- gest response would be induced when the incident field is
ing standard eigenvalue decomposition.)
perpendicular to the principal axis that corresponds to the
An object having equal length along all of its three princi- longest object's dimension. In case of a thin non-magnetic
pal axes, such as sphere or a cube, responds equally in the x-, disc, eddy currents circulate in the x-y plane only and hence
y- and z-direction, so λ11 = λ22 = λzz = λ, regardless if the target is λ33 = λ and λ11 = λ22 ≈ 0, while for a non-magnetic rod the eddy

Fig. 3. Simplified interpretation of the magnetic polarizability tensor in terms of target's shape and material type.
38	

IEEE Instrumentation & Measurement Magazine	

May 2020



Instrumentation & Measurement Magazine 23-3

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