Note: Descriptions are shown in the official language in which they were submitted.
CA 02443248 2003-10-10
MAGNETOMETER OF INCREASED SENSITIVITY
SELECTIVITY AND DYNAMIC RANGE
This application is a divisional of Canadian patent application No.
2,125,138, tiled on November 3(>, 1902 which claims the benefit of priority
of US patent application serial No. 803,504, fled Dccembcr 6, l~)~)1, now
L.)S patent No. 5,453,680, issued on September 26, 1995.
Background of the Invention
The technical field of this invention is
magnetometry and, in particular, the nondestructive
electromagnetic interrogation of materials of
interest to deduce their physical properties and to
measure kinematic properties such as proximity. The
disclosed invention applies to both conducting and
magnetic media.
Conventional application of magnetometers,
specifically eddy current sensors, involves the
excitation of a conducting winding, the primary,
with an electric current source of prescribed
temporal frequency. This produces a time-varying
magnetic field at the same frequency. The primary
winding is located in close proximity to the
material under test (MUT), but not in direct contact
with the MUT. This type of nondestructive electro-
magnetic interrogation is sometimes-called near
field measurement. The excitation fields and the
relevant spatial and temporal variations of those
fields are quasistatic. The magnitude and phase (or
the real and imaginary parts) of the impedance
measured at the terminals of the primary winding
(i.e., the measured voltage at the primary winding
terminals divided by the imposed current) or the
transimpedance (i.e., the voltage measured at a
secondary winding terminals divided by the imposed
CA 02443248 2003-10-10
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current in the primary winding) is used to estimate
the MUT properties of interest.
The time-varying magnetic field produced by the
primary winding induces currents in the MUT that
produce their own magnetic fields. These induced
fields have a magnetic flux in the opposite
direction to the fields produced by the primary.
The net result is that conducting MUTs will tend to
exclude the magnetic flux produced by the primary
windings. The measured impedance and transimpedance
at the terminals of the sensor windings is affected
by the following: the proximity to the MUT, the
physical properties (e.g., permeability and
conductivity) of the MUT and the spatial
distribution of those properties; the geometric
construct of the MUT; other kinematic properties
(e.g., velocity) of the MUT; and the existence of
defects (e. g., cracks, corrosion, impurities).
The distribution of the currents induced within
conducting MUTs and the associated distribution of
the magnetic fields in the MUT, in the vicinity of
the MUT, and within the conducting primary and
secondary windings are governed by the basic laws of
physics. Specifically, Ampere's and Faraday's laws
combined with ohm's law and the relevant boundary
and continuity conditions result in a mathematical
representation of magnetic diffusion in conducting
media and the Laplacian decay of magnetic fields.
Magnetic diffusion i_s a phenomena that relates the
distribution of induced currents in conducting
CA 02443248 2003-10-10
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materials to the distribution of the imposed and induced magnetic fields.
Laplacian decay
describes the manner in which a magnetic field decays along a path directed
away from the
original field source.
Magnetometers, such as eddy current sensors, exploit the sensitivity of the
impedance or trans-
impedance (measured at the sensor winding terminals) to the physical and
geometric properties
of the MUT. This is sometimes accomplished by using multiple temporal
excitation frequencies.
As the primary winding excitation frequency is increased, the currents in a
conducting MUT
exclude more and more flux until all the induced currents in the MUT are
confined to a thin layer
near the surface of the MUT. At frequencies for which the induced currents are
all at the surface
of the MUT, the MUT can be represented theoretically as a perfect conductor.
In other words, at
high enough frequency variations, the conductivity of the MU'T will no longer
affect the
impedance or transimpedance measured at the sensor windings.
This effect has been used in proximity measurement relative to a conducting
media.
Measurement of proximity to a metal surface is possible at a single excitation
frequency, if that
frequency is high enough that the MUT can be treated as a perfect conductor.
For proximity
measurement at lower frequencies, it is necessary to account for the effects
of the conductivity of
the MUT on the measured impedance, either by physical modeling or by
calibration.
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In applications requiring the measurement of
conductivity, it is necessary to operate at
frequencies low enough that the measurements at the
terminals of the conducting windings are sensitive
to the MUT conductivity. Such applications include
the monitoring of aging in conducting media, as well
as the direct measurement of conductivity for
quality monitoring in metal processing and
manufacturing process control. For example, the
accurate measurement of the case depth (e.g., the
thickness of a heat-affected zone at the surface of
a metal after heat treatment) requires a sensor
winding geometry and excitation conditions (e. g.,
frequency, proximity to the MUT) that produce the
required sensitivity to the conductivity and
thickness of the heat-affected zone.
Two methods are available for determining the
desired conditions: (1) experimentation and
calibration, and (2) physical modeling and response
prediction from basic principals. In practice, each
of these techniques has met with some success. The
principal limitations of experimentation and
calibration are the need for fabrication of
expensive calibration test pieces (standards) for
each new application, the relatively small dynamic
range (i.e., the small range of permissible MUT
property variations over which the measurement
specifications can be met), and the inaccuracies
produced by variation in uncontrolled conditions
such as temperature and lift-off errors.
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The principal limitations of the physical
modeling approach are the inaccuracies introduced by
modeling approximations and the existence of
unmodeled effects. These limitations are most
severe for sensor winding constructs that are not
specifically designed to minimize unmodeled affects.
In spite of these limitations, the successful
use of conducting windings driven by a current
source, as in eddy current sensors, to measure
physical and kinematic properties has been widely
demonstrated.
For example, eddy current sensors have been
used to measure the thickness of conducting strips
of known conductivity, as disclosed in Soviet
Patents 578,609 and 502,205. Eddy current sensors
have also been used for flaw detection, as disclosed
in U.S. Patent 3,939,404. Other eddy current sensor
applications include measurement of the
conductivity-thickness product for thin conducting
layers, measurement of the conductivity of
conducting plates using calibration standards, and
measurement of proximity to conducting layers. Such
sensors are also used in proximity measurement for
control of machines and devices.
The ability to resolve distributions of
parameters and properties of different layers in
multi-layered materials has been addressed in U.S.
Patent 5,015,951. The referenced patent introduced
the concept of multiple wavenumber magnetic
interrogations of the material of interest, by
imposing several different spatial magnetic field
CA 02443248 2003-10-10
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excitations, using multiple preselected sensor
winding constructs, each with a different wave-
length.
There is a substantial need for enhancements to
the measurement performance capabilities of magneto-
meters. This includes the ability to measure (1)
the conductivity and thickness of thin metallic
layers independently to improve quality control in
deposition and heat treatment processes (in
practice, only the product of conductivity and
thickness can be measured for thin layers for which
the conductivity-thickness product is below a
certain threshold); (2) more than one property
independently with reliable and predictable
performance over a wide dynamic range to provide a
more accurate characterization of the MUT; (3)
geometric or physical properties over a wide dynamic
range without calibration to reduce cost and
measurement setup time; (4) material properties such
as permeability and conductivity of ferrous metallic
layers or conductivity of deposited metallic layers,
for quality control and property monitoring after
processing (e. g., in situ monitoring of permeabiltiy
for sheets of transformer core alloy, or
conductivity measurement for thin metallic layers of
different conductivity that form on metallic
surfaces during heat treatment); (5) the thickness
of conducting layers or heat affected zones on
conducting substrates that do not have
conductivities which are significantly different
from that of the surface layer, to control heat
CA 02443248 2003-10-10
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treatment and monitor MUT properties; (6) the
independent measurement of both the conductivity and
height (i.e., the distance between the sensor
windings and the MUT) of a conducting layer, to
accurately account for lift-off affects in
applications such as crack detecting (i.e., air gaps
between the sensor windings and the MUT surface);
and (7) measurement of kinematic properties such as
proximity and relative velocity to conducting and
magnetic media for actuator and process control.
Furthermore, there is a need for measurement
methods that provide estimates of the actual
physical properties of the MUT. Current techniques
often measure "effective" properties that are only
indirectly related to the actual physical properties
(e. g., permeability and conductivity at a specified
excitation frequency). These "effective property
measurements often provide insufficient character-
ization of the MUT. For example, multiple temporal
excitation frequencies are often used to obtain
estimates of conductivity or permeability. This is
not acceptable if these physical properties vary
with temporal excitation frequency. In applications
such as monitoring of aging and fatigue in ferrous
and nonferrous metal alloys, it may be necessary to
completely characterize the dispersive properties of
the MUT, including the variations of conductivity
and permeability with temporal excitation frequency.
Thus, a technique is required that provides accurate
estimates of actual physical and geometric
properties of the :UT from measurements at a single
temporal. excitation frequency.
CA 02443248 2003-10-10
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Summary of the Invention
To overcome the aforementioned limitations in
current practice, magnetometers must provide
increased sensitivity, selectivity and dynamic range
as well as the capability to measure actual MUT
properties without calibration when required. Note
that sensitivity is defined herein as the
incremental change in the transimpedance measured at
the sensor terminals in response to an incremental
change in the geometric or physical MUT property of
interest. Selectivity is defined herein as a
measure of the ability to independently estimate two
distinct properties (e. g. conductivity and thickness
of a thin conducting layer). Dynamic range is
defined herein as the range of MUT properties over
which sufficient sensitivity and selectivity can be
achieved.
In accordance with the present invention,
apparatus and methods are disclosed which provide
increased sensitivity, selectivity and dynamic range
for non-contact measurement of actual physical
and/or kinematic properties of conducting and
magnetic materials. The disclosed invention is
based upon various methods for increasing
sensitivity, selectivity and dynamic range through
proper construction of the magnetometer sensor and
proper selection of operating point parameters for
the application under consideration.
In one embodiment, a measurement apparatus f_or
measuring one or more MUT properties includes an
electromagnetic winding structure which, when driven
CA 02443248 2003-10-10
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by an electric signal, imposes a magnetic field in
the MUT and senses an electromagnetic response. An
analyzer is provided for applying the electric
signal to the winding structure. A property
estimator is coupled to the winding structure and
translates sensed electromagnetic responses into
estimates of one or more preselected properties of
the material. In accordance with the present
invention, the temporal excitation frequency of the
electric signal applied to the winding structure
might be proximal to a transverse diffusion.effect
(TDE) characteristic frequency of the winding
structure.
The TDE characteristic frequency is defined as
the temporal excitation frequency at which the
currents within a primary winding of the winding
structure transition from a nearly uniform
distribution throughout the primary winding cross-
section to a distribution in which the currents are
confined to a thin layer near the surface of the
primary winding. In many applications, the
sensitivity of response measurements to specific MUT
properties of interest, or the selectivity for two
MUT properties of interest, is increased when the
frequency of the electric signal is near the TDE
characteristic frequency. As such, the TDE-based
apparatus is intentionally constructed to amplify
the effects of the TDE. To that end, the winding
structure comprises an optional permeable substrate
and an optional conducting backplane for tuning
(i.e., intentionally altering) the TDE
characteristic frequency of the winding structure.
CA 02443248 2003-10-10
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The electromagnetic winding structure in the
preferred embodiments comprises a plurality of
electromagnetic windings forming a meandering
pattern. The meandering winding structure is a
significant feature of the invention in that its
geometry provides physical behavior which may be
accurately modeled. As such, the magnetometer is
capable of accurately estimating preselected
material properties based on sensed responses
obtained by the meandering winding structure.
A TDE-based apparatus may further comprise a
model which is successively implemented by the
property estimator for generating a property
estimation grid which translates sensed electro-
magnetic responses into estimates of preselected MUT
properties. The model provides for each implement-
ation a prediction of electromagnetic response for
the preselected properties based on a set of
properties characterizing the winding structure and
the MUT. The model is described in more detail
below in accordance with a method for generating a
property estimation grid.
A TDE-based magnetometer may be manipulated to
obtain multiple responses for various operating
conditions. For example, sensed responses may be
obtained by the winding structure at multiple
proximities to the MUT and converted to material
property estimates. In another example, sensed
responses may be obtained b~~ the winding structure
for a plurality of positions along a surface of the
MUT. Further, for each position relative to the MUT
the winding structure may be adjusted to obtain
CA 02443248 2003-10-10
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sensed responses for various proximities and
orientations relative to the MUT. In yet another
example, the magnetometer winding structure may be
capable of being adapted to conform to a curved
surface of the MUT for obtaining sensed responses
and providing estimates of MUT properties. In
another example, the frequency of the electric
signal may be varied for obtaining a plurality of
frequency related sensed responses with the winding
structure.
A TDE-based magnetometer may be employed in a
plurality of specific applications to provide
substantially independent estimates of specified
properties of interest. To that end, a TDE-based
magnetometer is capable of providing independent
estimates of each of a pair of properties at a
single temporal excitation frequency from a single
sensed response. This enables the TDS-based magnet-
ometer to obtain estimates of dispersive properties
of single and multiple layered MUTs. Potential
paixs of MUT properties include (1) conductivity and
thickness, (2) conductivity and proximity, (3)
conductivity and permeability, (4) thickness and
permeability, (5) permeability and proximity and (7)
the real and imaginary parts of the complex perme-
ability. The MUT property estimates may then be
processed to estimate other MUT properties such as
aging/fatigue, bulk and surface crack location and
heat affected zone properties.
In other preferred embodiments, it is desirable
to shift the TDE characteristic frequency away from
the characteristic transition frequency associated
with magnetic diffusion in the MUT in order to
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measure preselected MUT properties with required
levels of sensitivity, selectivity and dynamic
range. This is accomplished by changing the
physical and geometric properties of the
magnetometer.
In one embodiment in which the TDE character-
istic frequency may or may not be significant, a
magnetometer has a winding structure comprising a
primary winding capable of imposing a magnetic field
in the MUT when driven by an electric signal. The
winding structure also includes one or more
secondary windings for sensing electromagnetic
responses. In this winding structure, the primary
winding has a width which is substantially greater
than the width of the gap between the primary and
secondary windings. Further, the width of the
primary winding may also be substantially larger
than the thickness of the primary. The winding
structure of this embodiment preferably forms a
meandering pattern. An analyzer is provided for
applying an electric signal to the primary for
imposing the magnetic field in the MUT, and a
property estimator translates sensed responses into
estimates of preselected MUT properties.
Preferably, the magnetometer employs a model which
is implemented by the property estimator for
generating a response prediction table which
translates sensed electromagnetic responses into
estimates of the preselected MUT properties.
As in the other embodiments, the magnetometer
may be used to obtain multiple responses for a
plurality of operating conditions. To that end, in
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one example the magnetometer winding structure may
be capable of being adapted to conform to a curved
surface of the MUT for obtaining sensed responses
and providing estimates of MUT properties. In
another example, the winding structure may be
adjusted to obtain sensed responses at multiple
proximities to the MUT. In yet another example, a
magnetometer with a winding structure comprising a
single primary and single secondary may be employed
for estimating dispersive properties of an MUT with
responses obtained at a single temporal excitation
frequency and for single or multiple proximities to
the MUT. In yet another example, the winding
structure may be adjusted to obtain sensed responses
for a plurality of positions along a surface of the
MUT. Further, for each position the winding
structure may be adjusted to obtain sensed responses
for multiple proximities and orientations relative
to the MUT. In another example, the frequency of
the electric signal applied to the winding structure
may be varied for each sensed response.
Devices which are constructed to incorporate
both magnetoquasistatic (MQS) inductive coupling
terms and electroquasistatic (EQS) capacitive
coupling terms are referred to as MQS/EQS devices.
These dwices have applications for materials having
properties of interest which are out of the dynamic
range cf existing MQS magnetometers and EQS dielect-
rometers. The introduction of capaciti.ve coupling
corrections permits the extension of the dynamic
range for MUT properties of interest by allowing
responses to be obtained at temporal excitation
CA 02443248 2003-10-10
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frequencies at which capacitive coupling is
significant in order to increase sensitivity to the
MUT properties of interest.
Accordingly, in another embodiment of the
invention, an MQS/EQS device provides estimates of
distributed properties of a layered MUT. The
MQS/EQS device includes an electromagnetic winding
structure capable of imposing a magnetic field and
an electric field in the MUT when driven by an
electric signal and sensing electromagnetic and
electric responses. The winding structure comprises
a primary winding, a plurality of coplanar first
secondary windings and an optional second secondary
winding positioned in a different plane. An
analyzer provides electric signals to the winding
structure and a property estimator translates sensed
responses into estimates of preselected properties
of the MUT.
Depending on the application, the MQS/EQS
device may be operated in an MQS mode and/or an
MQS/EQS mode and/or an EQS mode. Accordingly, when
the input current temporal excitation frequency is
within the MQS range for the device, the input
current is applied to the primary winding for
imposing a magnetic field in the MUT. Sensed
electromagnetic responses are obtained at the first
secondary windings for each layer of. the MUT. When
the input current temporal excitation frequency is
within the MQS range and an input voltage temporal
excitation frequency is within an EQS range, the
input current is applied to the primary to impose a
magnetic field and the input voltage is applied to
CA 02443248 2003-10-10
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the first secondary windings in a push-pull sense to
impose an electric field in the MUT. Sensed
electromagnetic responses are obtained at the second
secondary winding for each layer of the MUT. When
the input current temporal excitation frequency is
within the EQS range, the input voltage is applied
to the first secondary windings to impose an
electric field in the material. Sensed electric
responses are obtained at the primary winding for
each layer of the MUT. The property analyzer is
employed for translating the sensed responses into
estimates of preselected distributed properties of
each layer of the layered MUT.
The present invention also comprises a method
for generating property estimates of one or more
preselected properties of an MUT. Accordingly, an
electromagnetic structure, an analyzer and a
property estimator are provided. The first step in
the method requires defining dynamic range and
property estimate tolerance requirements for the
preselected properties of the material. Next, a
winding geometry and configuration is selected for
the electromagnetic structure. A continuum model is
used for generating property estimation grids for
the preselected material properties as well as
operating point response curves for preselected
operating point parameters_
The grids and curves are subsequently analyzed
to define a measurement strategy. Next, operating
point parameters and a winding geometry and
configuration are determined to meet the dynamic
range and tolerance requirements. To accomplish
this:, property estimati on gr id~~ and operati nq point_
CA 02443248 2003-10-10
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response curves are generated and analyzed for
various operating points. Next, sensed electro-
magnetic responses are obtained at each operating
point and converted by the property estimator into
estimates of the preselected material properties.
Property estimate tolerances are then estimated as a
function of values of the estimated preselected
properties over the defined dynamic range using the
property estimation grids and operating point
response curves. If the property estimate tolerance
requirements are not achieved, the process is
repeated for different operating point parameters
and winding dimensions.
As stated previously, the property estimator
implements a model for generating a property
estimation grid which translates sensed responses
into preselected material property estimates.
Accordingly, the present invention includes a method
for generating a property estimation grid for use
with a magnetometer for estimating preselected
properties of a MUT. The first step in generating a
grid is defining physical and geometric properties
for a MUT including the preselected properties of
the MUT. Next, operating point parameters and a
winding geometry and winding configuration for the
magnetometer are defined.
The MUT properties, the operating point
parameters and the magnetometer winding geometry and
configuration are input into a model to compute an
input/output terminal relation value. Preferably,
the input/output terminal relation is a value of
transimpedanc~ magnitude and phase. The terminal
CA 02443248 2003-10-10
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relation value is then recorded and the process is
repeated after incrementing the preselected
properties of the MUT. After a number of
iterations, the terminal relation values are plotted
to form a property estimation grid.
The present invention also includes a method of
selection of a magnetometer winding structure and
operating point for measuring one or more
preselected properties of an MUT which achieves
specified property estimate requirements. The first
step includes defining physical and geometric
properties for the MUT including preselected
properties of the MUT. Next, the
magnetometer operating point parameters, winding
geometry and winding configuration are defined.
The MUT properties and the magnometer operating
point parameters, winding geometry and configuration
are then input into a model for computing an input/
output terminal relation value. The preselected
properties of the material are then adjusted to
compute another terminal relation value. Using the
terminal relation values, Jacobian elements are
computed. Note each Jacobian element is a measure
of the variation in a terminal relation value due
to the variation in a preselected material property.
Next, a singular value decomposition is applied
to the Jacobian to obtain singular values, singular
vectors and the condition number of said Jacobian.
An evaluation is then made of the sensitivity,
selectivity and dynamic range of the magnetometer
winding structure and operating point parameters
using the singular values, singular vectors and
CA 02443248 2003-10-10
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condition number. If the material property estimate requirements are not met,
the process is
repeated with adjusted magnetometer operating point parameters, arid winding
geometry and
configuration until the material property estimate requirements are achieved.
Brief Descr~tion of the Drawings
Figure 1 is an overall schematic diagram of an apparatus for measuring the
physical and
kinematic properties of a material under test according to the present
invention.
Figures 2(a-c) are schematic cross-sectional views of a sensor winding
construct showing an
embodiment of the invention which has a primary width larger than the gap
between the primary
and the secondary winding, and showing the distribution of the current
density, J, in the span-
wise (transverse) direction at two different temporal excitation frequencies.
Figure 3 is a generalized procedure flow diagram for the estimation of MUT
properties and
measurement tolerances according to the present invention.
Figure 4 is a top view of the winding geometry for an example of a single
wavelength sensor
construct designed to provide increased transverse diffusion effect
sensitivity (TDES).
Figure 5 is a top view of the winding geometry for an example of a single
wavelength sensor
construct with two secondaries to provide a differential measurement designed
to provide
increased TDES.
CA 02443248 2003-10-10
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Figure 6 is a top view of the winding geometry
for another example of a single wavelength sensor
construct designed to provide increased TDES.
Figure 7 is a top view of an example winding
geometry for a single turn winding construct with a
primary and a secondary designed to provide
increased TDES.
Figure 8 is a cross-sectional view of an
example single wavelength winding geometry and
sensor construct with the primary and secondary
confined to two planes (levels) and the current in
the primary circulating in a direction perpendicular
to the winding planes and designed to provide
increased TDES.
Figure 9 is a cross-sectional view of an
example single wavelength winding geometry and
sensor construct with the primary and secondary
confined to two planes (levels) and the current in
the primary circulating in a direction perpendicular
to the winding planes and designed to provide
increased TDES.
Figure 10 is a top view of a mask for an
embodiment of the invention called the Inter-Meander
Magnetometer, an example of a meandering array that
applies a magnetic potential to the MUT with several
cycles of the same spatial wavelength.
Figure l1 is an (a) cross-sectional view and
(b) top view of a sensor winding geometry and
construct that has the primary and secondary
confined to two planes and applies a magnetic
potential to the MUT with several cycles of the same
spatial wavelength.
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Figures 12 (a-c) are cross-sectional views of three winding geometries for
measurement of
physical and geometric properties of curved parts.
Figure 13 is a cross-sectional view of a III-V compound crystal growth process
with a melt-
condition-probe, a liquid-solid interface-condition-probe and a crystal-
condition-probe.
Figure 14 is a cross-sectional view of a sensor winding construct that has its
relative position
to the material under test defined by the coordinates (xs, ys,a)
Figure 15 is (a) a cross-sectional view and (b) a top view of a sensor winding
construct that
uses the Inter-Meander Magnetometer winding geometry at the drive plane to
induce
orthogonal electric and magnetic potentials, and has an optional secondary on
a second level.
Figure 16 is a cross-sectional view for a multiple layered material under test
with a
conductivity which transitions from the conductivity of the metal substrate to
the conductivity
of air.
Figures 17(a-d) are a series of cross-sectional views of the property
estimation steps for
monitoring and control of the manufacturing of a multi-layer MUT.
Figure 18 is a flow diagram of the generation of a property estimation grid
using a continuum
model according to the invention.
Figure 19 is a flow diagram of the evaluation and selection of a sensor design
and operating
point parameter set, using singular value decomposition of a Jacobian relating
variations in
the design or operating point parameters to variations in the
CA 02443248 2003-10-10
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winding terminal measurements according to the invention.
Figure 20 is a schematic top view of another example of a winding construct
for a meandering
array that applies a magnetic potential to the MUT with several cycles of the
same spatial
wavelength.
Figure 21 is a table of two example winding dimensions and physical properties
for the Inter-
Meander Magnetometer which produce significant 'fDES near the TDECF.
Figure 22 is a flow diagram of the continuum model for the Inter-Meander
Magnetometer.
Figure 23 is a side-view of a material under test with Y layers above the
sensor winding plane.
Figure 24 is a cross-sectional view of one half wavelength of the Inter-
Meander Magnetometer
(a) and a schematic representation (b) of the collocation surface current
density approach used in
the continuum model.
Figures 25 is a set of plots of the surface current density distribution, o,
and the magnetic vector
potential distribution, D, over the first quarter wavelength of an lnter-
Meander Magnetometer
with the original construct, as predicted by the continuum model, at three
different temporal
excitation frequencies for the collocation on K approach in (d) through (f)
and for the collocation
on A approach in (a) trough (c).
Figure 26 is a plot of the current distribution in the primary winding for an
Inter-Meander
Magnetometer with the construct as predicted by the continuum model, compared
with the
1 /(r. ~ iz)
CA 02443248 2003-10-10
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distribution predicted with an analytical model for a perfectly conducting
fin.
Figures 27(a-c) are representations of a "Generalized Sensitivity Ellipse" for
a singular value
decomposition representation of a 2x2 Jacobian that relates variations in the
MUT properties, 0,
and 82, to variations in the measurements, r, at the sensor terminals.
Figures 2$(a-b) are plots of the transinductance magnitude and phase predicted
by the continuum
model for several different foil thicknesses and conductivities.
Figure 29 is a transinductance magnitude versus phase plot with a two-
dimensional property
estimation grid constructed from lines of constant foil conductivity and lines
of constant foil
thickness.
Figures 30(a-6) are plots illustrating the effect of foil thickness on the
transinductance magnitude
and phase.
Figures 31 (a-b) are plots showing experimental data measured with the Inter-
Meander
Magnetometer prototype sensor for two different foil thicknesses indicated
with squares and
crosses, and the predicted response simulated with the continuum model
indicated with the
curved lines.
Figures 32(a-b) are expanded views of the region near the TDECF of figures 31
to demonstrate
the behavior produced by the transverse diffusion effect.
Figures 33(a-6) are plots of the condition number, singular values, and
singular vectors of the
Jacobian for measurement of conductivity and
CA 02443248 2003-10-10
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thickness for a material layer with conductivity of 3.72E7 mhos/m (similar to
that of aluminum).
Figures 34(a-b) are plots of the condition number, singular values, and
singular vectors of the
Jacobian for measurement of conductivity and thickness for a material layer
with conductivity of
5.8E7 mhos/m (similar to that of copper).
Figure 35 is an example of a two-dimensional property estimation grid for
conductivity and
thickness measurement on a metal foil.
Figure 36 is another example of a two-dimensional property estimation grid for
conductivity and
thickness measurement on a metal foil.
Figures 37(a-b) are plots of the transinductance magnitude and phase measured
with the Inter-
Meander Magnetometer prototype and predicted by the continuum model for three
different
copper foil thicknesses.
Figures 38(a-b) are plots of the transinductance magnitude and phase measured
with the Inter-
Meander Magnetometer prototype and predicted by the continuum model for three
different
aluminum foil thicknesses.
Figures 39(a-b) are plots of the transinductance magnitude and phase measured
with the Inter-
Meander Magnetometer prototype and predicted by the continuum model for a
brass plate at
several different heights above the winding plane.
Figure 40 is a plot of the condition number for the Jacobian for measurement
of conductivity and
height for a metal plate above the winding plane, as
CA 02443248 2003-10-10
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predicted with the continuum model for the Inter-Meander Magnetometer as a
function of the
height and log (conductivity).
Figures 41 (a-b) are plots of the condition number, singular values, and
singular vectors of the
Jacobian for measurement of conductivity and height of a metal plate above the
winding plane as
a function of the plate height.
Figures 42(a-b) are plots of the condition number, singular values, and
singular vectors of the
Jacobian for measurement of conductivity and height of a metal plate above the
winding plane as
a function of log (conductivity) for the plate.
Figure 43 is a two-dimensional parameter estimation grid for measurement of
conductivity and
air-gap height for very thick conducting layers.
Figure 44 is a plot of the maximum and minimum singular values and right
singular vectors of
the Jacobian for measurement of permeability and height of a high permeability
layer.
Figures 45(a-b) are plots of the transinductance magnitude variation with the
height of a high
permeability layer above the Inter-Meander Magnetometer simulated with the
continuum model,
(a) with no back-plane, and (b) with a back-plane at 0.5 mm below the winding
plane.
Figures 46(a-b) are plots of the transinductance variation with temporal
excitation frequency
with a high permeability layer at various heights above the winding plane,
with a back-plane at
0.5 mm below the winding plane.
Figures 47(a-b) are plots of the surface current density distribution, o, and
the magnetic vector
CA 02443248 2003-10-10
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potential distribution, D, over the first quarter wavelength of an Inter-
Meander Magnetometer
with the original construct, as predicted by the continuum model, with a high
permeability layer
immediately above the winding plane.
Figures 48(a-b) are plots of the surface current density distribution, o, and
the magnetic vector
potential distribution. 0, over the f rst quarter wavelength of an Inter-
Meander Magnetometer
with the original construct, as predicted by the continuum model, with a high
permeability layer
0.1 mm above the winding plane.
Figures 49(a-b) are plots of the surface current density distribution, o, and
the magnetic vector
potential distribution, ~, over the first quarter wavelength of an Inter-
Meander Magnetometer
with the original construct, as predicted by the continuum model, with a high
permeability layer
1 mm above the winding plane.
Figure 50 is a universal transinductance plot for a diamagnetic infinite half
space used as a two-
dimensional property estimation grid for the complex magnetic susceptibility.
Figure 51 (a) is a table of experimental data using the Inter-Meander
Magnetometer prototype
with the original geometry for measurements on a granular aluminum layer at 0
and 0.8 mm
above the winding plane, and (b) the first guess and estimated values of the
complex magnetic
susceptibility estimated using the experimental data for the layer immediately
above the winding
plane.
CA 02443248 2003-10-10
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Figures 52(a-b) are plots of the experimental (crosses) and predicted (curved
line) responses of
the transinductance magnitude and phase as a function of the temporal
excitation frequency.
Figures 53(a-b) are plots of the predicted and analytically determined complex
magnetic
susceptibility for the granular aluminum layer.
Figure 54 is a plot of a two-dimensional property estimation grid for
conductivity and
permeability for the Inter-Meander Magnetometer, with no back-plane, at 1 KHz.
Figure 55 is a plot of a two-dimensional property estimation grid for
conductivity and
permeability for the Inter-Meander Magnetometer, with no hack-plane, at 10
MHz.
Figures 56(a-b) are side views of the magnetic field lines induced by two
Inter-Meander
Magnetometers located on opposite sides of a material under test layer,
operated in the odd and
even modes.
Detailed Description of Preferred Embodiments
Apparatus, devices, methods, and techniques are disclosed for non-contact
measurement of
physical and kinematic properties of a Material Under Test (MUT). The
disclosed measurement
apparatus is depicted in Figure 1. The measurement apparatus includes an
electromagnetic
element 2 comprised of a primary winding 4, secondary winding 6, an insulating
substrate 8, an
optional highly permeable substrate 9, and an optional conducting backplane
10. The primary
winding 4 (also called the driven
CA 02443248 2003-10-10
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winding) is driven by an input current or voltage
source at a temporal excitation frequency, f,
measured in cycles per second where f=~/2n and ~ is
the angular frequency of the input electric signal,
measured in radians per second. The voltage induced
at the terminals of the secondary winding 6 (also
called the sensing winding) divided by the current
applied to the primary winding 4 is called the
transimpedance (or transfer impedance). The trans-
impedance is measured by an impedance analyzer 14.
The magnitude 22 and phase 24 of the transimpedance
are inputs to a property estimator 16 which~uses a
measurement grid 18 to estimate pre-selected
properties of a single or multiple layered MUT 12.
The measurement grid can be generated either with a
continuum model 20 or through experimental measure-
ments on calibration test pieces. The model,
measurement grid(s), and property analyzer are part
of a property estimator 26 that converts
measurements at the sensor terminals for single or
multiple operating points (e. g., multiple temporal
excitation frequencies) to estimates of pre-selected
MUT properties of interest.
The disclosed invention is founded upon the
ability to increase sensitivity, selectivity, and
dynamic range through proper design of the electro-
magnetic element 2 and methods for proper selection
of operating points) parameters. In many cases,
the disclosed invention is the enabling component of
measurement systems for MUT properties of interest
that are not measurable with alternative winding
designs (e. g., independent non-invasive measurement
CA 02443248 2003-10-10
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of conductivity and thickness for thin conducting
films on conducting or insulating substrates).
The Transverse Diffusion Effect Sensitivity (TDES)
A principal feature of the disclosed invention
is a phenomenon hereinafter referred to as the
Transverse Diffusion Effect Sensitivity (TDES). The
key factors in the design of TDES-based sensors are
(1) the distribution of the currents within the
conducting windings of the sensor construct (i.e.,
the spatial variation of the current density, ,7,
within the conducting windings in the direction
transverse, perpendicular, to the direction of the
imposed current flow; this distribution is also
called the primary winding transverse-current
distribution), (2) the sensitivity of this
distribution to the properties of the MUT, (3) the
selectivity (i.e., the ability to independently
measure two or more MUT properties of interest), and
(4) the dynamic range for the pre-selected MUT
properties of interest, over which high sensitivity
and selectivity can be achieved.
Design methods for conventional eddy current
sensors assume the current density within the sensor
windings is either uniformly distributed, or
confined to a thin layer along the winding surface,
and that variations in the transverse-current-
distribution has no significant effect on the
measurements at the terminals of the sensor
windings. A TDES-based sensor is intentionally
designed to amplify the effects of the transverse-
current-distribution on the measurements at the
terminals of thc~ primary and .recondarv ~.:indinc~~;.
CA 02443248 2003-10-10
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This is accomplished by introducing cross-
sectional shape to the primary and secondary
windings. The dependence of the transverse-current-
distribution in the primary on the MUT properties of
interest provides increased sensitivity,
selectivity, and dynamic range for property
estimation in many applications of interest.
However, measurements at the terminals of the
primary and secondary windings will not be sensitive
to the primary winding transverse-current-
distribution, unless the windings are properly
designed to provide increasing inductive coupling to
the secondary as the currents crowd-out closer and
closer to the primary winding surface in the
direction transverse to the direction of the imposed
current flow (i.e., as the current density
distribution transitions from a uniform distribution
at low temporal excitation frequencies to a
distribution with the currents confined to a thin
layer at the surface of the conducting windings at
high temporal excitation frequencies).
Increased sensitivity, selectivity, and dynamic
range can be achieved for many common applications
of conventional eddy current sensors and other
magnetometers by amplifying these effects arid by
increasing the sensitivity of the transverse-
current-distribution within the windings to the MUT
properties of interest.
One specific embodiment is shown in Figure 2c.
In this winding construct, the winding geometry is
designed so that the width c of the primary 4, is
larger than the gap g between the primary 4 and the
CA 02443248 2003-10-10
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secondary 6. In the embodiment of Figure 2, the
thickness, o, of the deposited conducting winding
material 28 is small compared to the widths, c and
d, of the primary and secondary conducting windings
respectively. Other winding constructs could
exhibit significant TDES without having the major
axis of the winding cross-section (c, in this
embodiment) much larger than the minor axis (o, in
this case).
The transverse diffusion effect characteristic
frequency (TDECF) is defined as the temporal
excitation frequency of the input electric signal at
which the currents within the primary windings
transition from a nearly uniform distribution
throughout the primary cross-section, as shown in
Figure 2a, to a distribution for which the currents
are confined to a thin layer near the surface of the
conducting windings.
The TDECF occurs at fTD=lrrm, where rm=~a12.
In this relationship, ~ and o are an effective
permeability and conductivity, respectively. The
effective conductivity, o; that is, the effective
conductivity which influences the diffusion of
magnetic fields within the conducting sensor
windings is not only influenced by the conductivity
of the winding material 28, but also it is
influenced by the conductivity, proximity, and shape
of the neighboring media 12. The characteristic
length, 1, for diffusion of magnetic fields within
the sensing windings derives from the geometry and
dimensions of the windings themselves.
CA 02443248 2003-10-10
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It is important not to mistake the TDECF for
the common characteristic frequencies which produce
the dominant phase shift in conventional eddy
current sensors. In conventional eddy current
sensors, the characteristic magnetic diffusion
transitions within the MUT dominate the frequency
response of the sensor. This characteristic
frequency is related to the time constant of
magnetic diffusion, rm, within the MUT, where
rm=~a12; but, now ~, o and 1 are the effective
properties within the MUT.
The designer has the ability to vary the TDECF
by changing the characteristic lengths for the
winding construct, altering the electric properties
and cross-section shape of the windings themselves,
or by adding a conducting back-plane with specified
properties or a magnetic substrate of known complex
permeability with or without a controlled bias
ffield.
There are advantages to the winding geometry
illustrated in Figure 2 with c>d»0. These
advantages are explained in the following few
paragraphs.
At input excitation frequencies well below the
TDECF, the current density, J, within the primary
winding is essentially uniform throughout the
winding cross-section. As the excitation frequency
is raised, the currents begin to "crowd out" towards
the surface of the conducting windings. This
effect is referred to as transverse or span-wise
diffusion of currents within the conducting
windings. This is often referred to as the skin
CA 02443248 2003-10-10
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effect, because at high enough frequencies, the
currents within conducting media are confined to a
thin layer, "skin", near the surface of the
conductor. The approximate thickness of this layer
is commonly referred to as the skin depth, and is
given by a=SQRT[2/(c~~o)]. At frequencies well above
the TDECF, the surfaces of the conducting windings
become equipotentials and the windings act as
perfect conductors.
One such winding construct which may be
accurately modeled is the Inter-Meander Magnetometer
construct. The mask for this winding construct is
shown in Figure 10. The primary winding 4 meanders
through several wavelengths, a, and has terminal
measurements (vl,il). Two secondary windings 6
meander on opposite sides of the primary. As
described in the Magnetometer Windings section,
these terminals can be connected in-several
different ways to achieve different measurement
objectives. In the principal usage, the secondaries
are connected in parallel, and the secondaries links
flux over the same area. This winding design is
discussed further in the Inter-Meander Magnetometer
Design Section. A complete continuum model for this
magnetometer is presented in later sections.
Examples of parameter estimation grid; and
measurement optimization techniques are also
included for specific applications.
For the Inter-Meander Magnetometer construct
shown in Figure 10, with a>c>d>g and c »t~, the
ability to accurately predict the response at the
terminals of the sensor winding results in the
,ZCCUratc~ e~timat.ion of ab~:>c:~lut.Ee m~at:er:ia.~l ~,:~ropor'~ie~;,
CA 02443248 2003-10-10
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without the need for calibration or measurements on
calibration test pieces. The measurement of actual,
absolute physical properties is possible under many
conditions without the use of calibration test
pieces. This results in significant cost savinc
potential for a wide range of applications, as w~
as a substantial increase in the usefulness of such
property measurements for quality monitoring and
control, process control.
Other winding geometries, that do not include
multiple wavelengths, such as those in Figures 4
through 9, must be modeled in a different manner.
Continuum models for these geometries could use
modal analysis with Fourier Transforms, or 2- and
3-dimensional finite element techniques. A variety
of different winding geometries are possible, as
shown in Figures 4 through 11. These are describes
in some detail in the Magnetometer ~lindings and
Sensor Construct section.
Generalized Material Under Test Property Estimation
Fr ~ rrw.t~rlr
The methods and techniques of the disclosed
invention comprise a general property estimation
framework. A typical measurement procedure flow
would include the following steps (also shown in the
procedure flow diagram in Figure 3):
Step 1 Define MUT property measurement
requirements - define the dynamic range
and measurement tolerance requirements for
the MUT properties of interest.
CA 02443248 2003-10-10
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Step 2 Select sensor winding geometry and
configuration - select a sensor winding
geometry and configuration (i.e.,
referring to Figure 1, the structure,
shape and design of the primary 4 and
secondary 6 windings, and the back-plane
10 and substrate 8 and 9 characteristics,
with c>g). Selection is based on test and
evaluation of property estimation
sensitivity, dynamic range, and
selectivity, using the predicted responses
and measurement grids 18 generated by the
continuum model 20 or through experimental
measurements on calibration test pieces
over the required range of properties for
a variety of winding geometries,
dimensions and configurations.
Step 3 Analyze the property estimation grids and
operating point responses to define the
measurement strategy - the measurement
strategy includes the number of
measurements required at different
operating points and with different sensor
geometries, dimensions and configura-
tions. A continuum model 20 or set of
experiments is used to generate property
estimation grid_~ 1S and a set of response
curves which are functions of operating
point parameter variations. Operating
point response curves include (1) the
standard temporal frequency response, and
CA 02443248 2003-10-10
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responses to (2) variations in the defined
spatial wavelength of the sensor winding
construct (the defined spatial wavelength
a, is the wavelength of the dominant
eigenfunction, or Fourier component, in
the magnetic potential distribution
imposed along the surface of the MUT; the
def_~_ed spatial wavelength can be adjusted
in actual measurements by including
several similar winding constructs, each
with a different defined spatial
wavelength, as described in U.S. Patent
5,015,951), (3) the relative position of
the winding construct to the MUT
(including the height above or below the
MUT surface, xs, the position along the
surface, ys, and the orientation relative
to the surface, a, as shown in Figure 14),
and (4) adjusting the geometry of the
winding construct (including the distance
between the primary 4 and secondary 6, g;
the relationship between the primary
width, c, and the defined spatial
wavelength, a; the relative position of
the back-plane 10 to the winding plane;
and in the case of magnetic media the
magnitude, direction, and spatial or
temporal variation of an applied DC or AC
bias field.
Step 4 Determine optimal operating points) and
winding dimensions - a set of operating
point parameters, for one opera:.ing point,
CA 02443248 2003-10-10
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includes the proximity to the MUT, h, the
temporal excitation frequency, f, and all
other adjustable parameters described in
step 3. Singular value decomposition on
the Jacobian, relating variations in the
transimpedance magnitude and phase to
variations in the MUT properties of
interest, is used when an accurate
continuum model is available to determine
the relative performance potention at
different operating points (if such a
model is not available, a set of carefully
designed calibration experiments can be
used, along with models of related winding
and MUT geometries to provide additional
insight). Relative performance potential
includes sensitivity to variations in the
MUT properties of interest, selectivity
for pairs of properties of interest, and
dynamic range for each property of
interest. Then parameter estimation grids
18 are generated at optimal/selected
operating points along with operating
point response curves for use in property
estimation, Step 6.
Step ~~ Measure transim-pedance for MUT at each
berating point - measure the trans-
impedance at each prescribed operating
point defined in the measurement strategy,
using the impedance analyzer 14.
CA 02443248 2003-10-10
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Step 6 Estimate the preselected MUT properties -
estimate the MUT properties of interest,
using root-searching techniques, trial and
error, table look-up and interpolation; or
graphical interpolation from measurement
grids 18 generated with the continuum
model 20 (or calibration experiments).
This is accomplished in the property
estimator 26.
Step 7 Estimate the property estimation
tolerances -
using measurement grids 18 and operating
point response curves generated with the
continuum model 20 (or calibration
experiments) and the measurement tolerance
specifications of the impedance analyzer
14, estimate the measurement tolerances
and tolerance variations over the dynamic
range of interest for each pre-selected
MUT property of interest.. If the
property estimation measurement
requirements are not achieved, repeat
steps 2 through 7.
For any application, calibration experiments can be
used to tune the model parameters and improve MUT
property estimation accuracy. Such calibration,
although not always required, should always be used
when available.
CA 02443248 2003-10-10
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Magnetometer Windings and Sensor Construct
As shown in Figures 4 through 11, there are many winding geometries and
constructs that can
provide the required relationship, c > g, for the sensor winding dimensions.
In each of these
winding constructs, the deposited windings are confined to one surface as in
Figures 4 through 7
or two surface as in Figures 8, 9 and 11. These surfaces can be planes in
Cartesian coordinates
(as in Figures 4 through 1 l, cylinders or arcs in cylindrical coordinates, as
in Figures 12a and
12b, or spiral surfaces (each layer approximately cylindrical, as in Figure
12c) when it is
desirable to wrap the winding construct around a circular cylinder for
measurements on surfaces
with other complex shapes.
Examples of cylindrical 54, wrapped 56, and curved 48 winding constructs are
shown in Figures
12. If the local radius of curvature is much larger than 5 times the defined
spatial wavelength of~
the winding construct for the Inter-Meander Magnetometer, then the Cartesian
continuum model,
presented for the Inter-Meander Magnetometer, can be used to obtain accurate
MUT property
estimates without calibration. For small cylindrical parts, it is also
possible to wrap the winding
construct around the part as shown in Figure 12c (this is accomplished by
depositing the winding
onto a flexible substrate material). The windings can also be wrapped around a
cylindrical
insulating, conducting or magnetic core (i.e., as opposed to wrapping the
flexible sensor around a
cylindrical MUT 52) to make measurements on curved or flat
CA 02443248 2003-10-10
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surfaces 50, which are in close proximity to the cylindrical core.
One application which could use a wrapped Inter-Meander Magnetometer winding
construct
with multiple turns around a magnetic or insulating cylindrical core is the
control of III-V crystal
growth processes, such as for gallium arsenide or indium phosphide. An
illustration of this
application is shown in Figure 13.
The instantaneous position of the liquid-solid interface, solidification
front, may be measured for
other MUT geometries as well. For the example in Figure 14, the MUT material
in the horizontal
layer closest to the sensor might be divided, as shown, into two regions. On
the left 72, the
material might be solid, and the material on the right 74 of the vertical
interface (e.g.,
solidification front) might be liquid.
Furthermore, the winding constructs can incorporate multiple defined spatial
wavelengths, as
shown in Figures 10, 11 and 12, or single spatial wavelengths as shown in
Figures 4 through 9.
Also, it is possible to design a TDES-based sensor with only a primary winding
4 (i.e., no
secondary 6) and measure only the impedance at the terminals of the primary
winding. However,
with only a primary winding, the effects of variations in the contact
resistance must be carefully
accounted for.
The input electrical signal and the measurements at the terminals may vary
with application. In
the principal embodiment, the primary winding 4 is excited by a controlled
current
CA 02443248 2003-10-10
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source, i1, with a prescribed temporal excitation
frequency, f, by an impedance analyzer 14. The
output is the transinductance, r=v2/(jc~il), where v?
is the voltage measured at the terminals of the
secondary winding 6 by the impedance analyzer 14.
The transinductance is simply the derivative with
respect to time of the transimpedance (i.e., the
transimpedance divided by j~ where j=SQRT(-1)).
It is also possible to conceive TDES-based
winding constructs that have the secondary 6 and
primary windings 4 confined to different parallel
surface levels, as shown in Figure 15, or in
perpendicular planes. Figure 8 provides a variation
on the latter case, where the currents in the
primary circulate in the plane perpendicular to the
secondary winding surface, but the primary winding 4
has a cross-section in the plane of the secondary
winding 6, with its major axis along that plane.
When the primary and secondary windings are not
confined to single or multiple parallel planes, then
a second defined spatial wavelength, a', is
introduced for completeness, as shown in Figures 8,
9 and 11.
Figure 14 illustrates the concept described
earlier for scanning the relative position and
orientation of the sensor to the MUT surface in
order to provide additional parameter estimation
information. The position (x~,yc,a), of the sensor
relative to the MUT surface at the instant the
measurement is made is considered part of the
operating point specifications. The estimation of
more than two properties requires sensor terminal
measurements at morn than one o~:~ert:3tinc~ point.
CA 02443248 2003-10-10
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An example of a multiple height, h=xs,
measurement to produce an operating point parameter
response, with all other operating point parameters
constant and with a=90° is described later for
measurement of the conductivity of a metal plate
(using the Inter-Meander Magnetometer construct).
The ability to independently measure the
conductivity and air-gap height of the thick metal
layer is also demonstrated.
This independent conductivity and height
measurement provides an enabling component of
measurement systems designed to monitor aging/
fatigue and detect cracks in metal parts. These
systems would be far less costly if the lift-off
error did not effect the accuracy of the MUT
property measurements. One key capability is the
ability to accurately measure dispersive (frequency
dependent) conductivity, which would be
significantly altered by the presence of macro- and
micro-cracks at the surface and in the bulk of the
MUT. Further, the variations caused by the presence
of different sized cracks would vary with temporal
excitation frequency, as well as with variations in
other operating point parameters such as the defined
spatial wavelength, a. This supports the potential
to estimate the depth below the surface, the size ofd
~.arge cracks, and the density of microcracks, by
investigating the variation of the measured
dispersive conductivity with the input current
temporal excitation frequency. This is not possible
with conventional techniques.
One additional variation on the apparatus
i llustrateu iro H'ic~u.~~- 1 ~_. th<- inclusion of a
CA 02443248 2003-10-10
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magnetic coupling media which increases the coupling
of the magnetic flux to the MUT in a manner similar
to the common practice of introducing a coupling
media for ultrasonic matching for ultrasonic
measurement probes.
In many measurements, the special design of the
Inter-Meander Magnetometer and the accuracy of the
continuum model 20 provide the enabling features
without requiring operation near the TDECF. For
example, the accurate measurement of conductivity-
thickness product can be achieved, as demonstrated
in Figures 37 and 38, for thin conducting layers by
obtaining a single frequency response.
Another variation on TDES-based sensors, is the
use of a driven electroquasistatic electrode, or
electrode pair, to alter the distribution of
currents within the primary sensor winding 4. As
illustrated in Figure 15, a sensing winding 86 could
then be located on a parallel plane-at a different
level. One embodiment, shown in Figure 15, includes .
the application of an imposed electric potential 82
that is 90° out-of-phase with the imposed magnetic
potential 80. The key feature is the capacitive
coupling between the wide primary 4, which is driven
by a current source, and the two secondaries 6,
which are driven by voltage sources, v2a and v?b, in
a "push-pull" manner. Variations on this design
permit some active control of the di.stri.bution of
currents within the conducting wi_nding~>, and may
allow increased sensitivity, selectivity, and
dynamic range for speci.fi.c applications.
CA 02443248 2003-10-10
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One method for parameter estimation, using the
Inter-Meander Magnetometer construct involves the
addition of a correction for the capacitive coupling
between the primary and secondary windings. The
terminal current, i, and voltage, v, are then
related by
i~
t = ]c.rCt~ -~ ( 1 )
j c.~ L
resulting in a transimpedance with a clear frequency
dependent capacitive coupling.
j~L ~ ~~,L~1 +~'LC~ (2)
_ v
1 - c.~= L C,
This is consistent with the behavior observed
in experiments with the Inter-Meander Magnetometer
at high temporal excitation frequencies, when the
capacitive coupling term becomes significant. This
could also be modeled in a continuum sense by adding
higher order terms in the electric field
representation.
Sensors intentionally designed to incorporate
both magnetoquasistatic (MQS), inductive coupling
terms and electroquasistatic (EQS), capacitive
coupling terms are referred to here as hybrid
MQS/EQS sensors. These sensors may have
applications for materials such as biological media,
or ceramics which have properties that arc out of
CA 02443248 2003-10-10
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the dynamic range of existing MQS magnetometers and
EQS dielectrometers.
One application of interest which involves the
use of the Inter-Meander Magnetometer in several
different modes is illustrated in Figures 16 and 17.
For example, consider a multi-layered media designed
not to reflect electromagnetic energy in specific
wavelengths. Such a multi-layered media might be
conceived with the conductivity varying from the
conductivity of a conducting substrate (e. g., metal)
at the bottom of the first layer, to that of air at
the top of the last layer, along the direction, x,
perpendicular to the surface of the metal substrate
(as shown in Figure 16).
For this example, the manufacturing and quality
control procedure might follow the following steps
(the quality control step> 3, 5, 7 and 9 are shown
in Figure 17):
Manufacturing Steps Property Estimation
Steps for Quality Control
step 1 Estimate the complex
permeability and
conductivity of the
metal plate (including
any heat affected zone
propert.i.e~ near the
metal surface ) , using
CA 02443248 2003-10-10
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the Inter-Meander
Magnetometer in MQS
mode.
step 2 Apply layer 1
(thickness Dl)
to metal plate.
step 3 Estimate the complex
permeability and
conductivity of layer 1,
using the Inter-Meander
Magnetometer in MQS
mode.
step 4 Apply layer 2
(thickness o2)
on top of
layer 1.
step 5 Estimate the complex
permeability and
conductivity of layer 2,
using the Inter-Meander
Magnetometer in MQS
mode, with an EQS
capac~tmc~ correction
CA 02443248 2003-10-10
-4 6-
(i.e., a hybrid MQS/EQS
mode ) .
step 6 Apply layer 3
(thickness ~3)
on top of layer 2.
step 7 Estimate the complex
permeability, complex
permittivity, and
conductivity of layer 3,
using the Inter-Meander
Magnetometer in EQS _
mode, with an MQS
capacitive correction
(i.e., a different
hybrid MQS/EQS mode than
used in step 5), or with
the addition of a "push-
pull" capacitive
coupling drive as shown
in Figure 15 (i.e., a
third hybrid MQS/EQS
mode).
step 8 Apply Layer 4
(thickness o ~ )
on top of layer 3.
CA 02443248 2003-10-10
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step 9 Estimate the complex
permittivity of layer 4,
using the Inter-Meander
Magnetometer in EQS
mode.
The Inter-Meander Magnetometer is operated in
EQS mode by applying a controlled voltage to the two
secondaries 6, shown in Figure 15, which are now
called the driven electrodes, and using the primary
4 as the sensing electrode. The voltage on.the
sensing electrode (formerly the primary winding)
divided by the voltage applied to the driven
electrodes (formerly the secondary windings) is now
the gain of the sensor. The gain response is then
used to estimate the complex dielectric properties,
as in a standard interdigital-electrode-
dielectrometer construct (M. C. Zaretsky, et al.,
Continuum_Properties from Interdigifal Electrode
Dielectrometry, IEEE Transaction on Electrical
Insulation, Volume 23, No. 6, Dec. 1985).
The MUT 12 shown in Figure 1 has two
homogeneous layers of thickness of and o2,
conductivity v1 and a2, and permeability ~1 and u2.
The height of the material of interest above the
sensor windings is h.
In the preferred embodiments, pairs of
properties can be estimated from a single
transinductance measurement at the terminals of the
sensor windings. The measurement apparatus in
Figure 1 is capable of providing near-real time
estimation of pairs of properties including: (1) a
1
CA 02443248 2003-10-10
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& ~1~ (2) al & h~ (3) °1 & ~'1~ (4) ~1 ~ ~11~ (5) dl &
a2, (6) Ell & h, and (7) ~c 1 =Eel + j~l~~ = complex
permeability. These property estimates could then
be used to estimate other properties such as
aging/fatigue in aluminum plates (e. g., conductivity
measurement with lift-off compensation), or heat
affected zone (HAZ) thickness, hardness and
electrical properties.
Example measurement grids are provided later
for al & al, al & h, and ~l & ul~~. Also, an example
of a single property measurement of the proximity to
a highly permeable media is provided, and an example
of conductivity-thickness product measurement on
thin conducting layers.
Property Estimation Grid and Operating Point
Response Curve Generation
Each parameter estimation application will
require a set of property estimation grids 18 and
operating point response curves. The number of
grids and response curves required will depend on
the application. The grids and response curves have
several different uses throughout the parameter
estimation process. These uses include the
following:
1) Develop a measurement strateqy and select the
measurement operating paints by evaluating the
MUT property estimation grids and operating
point response curves, at a variety of
different operating points over the required
CA 02443248 2003-10-10
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dynamic range for. the MUT properties of
interest (step 3: of the generalized MUT
property estimation procedure in Figure 3).
Evaluating a property estimation grid includes
investigating the sensitivity, selectivity and
dynamic range for the MUT properties of
interest. This is first accomplished by
visually inspecting the grids. For example, a
grid which provides a large variation in the
magnitude and phase of the transinductance in
response to relatively small variation .in the
MUT properties of interest would provide a good
property estimation performance.
2) Graphical estimation of the MUT properties of
interest (step 6: of the generalized MUT
property estimation procedure in Figure 3).
3) Determination of the estimate tolerances, as a
function of the estimated values for the MUT
properties of interest (step 7: of the
generalized MUT property estimation procedure
in Figure 3). The tolerances at a given grid
point are estimated by averaging the variation
in transinductance magnitude and phase between
that grid point and its neighboring grid points
and dividing both the averagE :-hange in
magnitude and the average change in phase ir~-~
the corresponding change in the ML1T property c:f
s.nterest.
Property estimation problems requiring three or
more' 1'~IT'I' T~T'O~F'ry' E'~t1.T11c3tE-~ 'v,'111 eil~n'e:'.'.'~ rE?qllir<?_
T1:OY-(
CA 02443248 2003-10-10
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than one estimation grid or at least one additional
operating point response curve, (e. g., in the case
of three properties, at least one grid and one
additional response curve is required).
Figure 18 provides a flow diagram describing
the generation of a property estimation grid 18,
using a continuum model 20. The same concepts
described in this figure apply to the generation of
operating point response curves. The only
difference is that for property estimation grids the
main loop is repeated for different MUT property
pairs (e.g., conductivity & thickness, or
conductivity & proximity), while for the generation
of operating point response curves one operating
point parameter is varied over a range of interest.
To generate a property estimation grid, first
input at 96 the winding specifications and
configuration, including the winding geometry,
conductivity, back-plane conductivity and proximity,
and substrate permeability. Also, input at 98 the
operating point parameter set (i.e., h, ~, a, Q, xs,
y ). A continuum model 20 is then used to compute
s
the terminal relations at 106 for the first MUT
property pair. The continuum model for the Inter-
Meander Magnetometer is described in detail later.
The terminal relations are translated into trans-
inductance at 107 . To generate the complete
property estimation grid for two MUT properties of
interest (e.g. conductivity & thickness of a
conducting layer), these properties are varied over
the dynamic range of interest at 10~. The continuum
model is then used to comnut.c~ the terminal. relation
CA 02443248 2003-10-10
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for each new MUT property pair, and each new grid
point is plotted at 108, until the property
estimation grid 18 is complete for the dynamic range
of interest.
A similar approach could be used to generate a
property estimation grid when an accurate continuum
model is not available. This would require the use
of calibration test pieces with a variety of
different property pairs covering the MUT property
range of interest.
Sensor Design and Operating Point Selection/
Optimization
Singular value decomposition can be used for
many aspects of sensor design and operating point
selection/optimization. The distinction between
selection and optimization is made here.
Identification and selection of operating points and
sensor designs which provide the desired performance
does not require optimization.
Singular value decomposition is described in
detail in later sections for specific examples
including (1) the independent measurement of
conductivity and thickness for metal foils, (2) the
independent measurement of conductivity and air-gap
height for metal plates, and (3) the measurement of
air-gap height relative to a highly permeable media.
Figure 19 provide; a basic flow diagram for
optimization of sensitivity, selectivity and dynamic
range using singular value decomposition on the
Jacobian relating perturbations in the MUT
properties of interest t.o clnanger~ in the value of
CA 02443248 2003-10-10
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the terminal relation measurements at the sensor
windings.
Inter-Meander Magnetometer Design
The Inter-Meander Magnetometer sensor construct
was intentionally configured to provide the symmetry
necessary to permit accurate response prediction.
The proposed sensor is fabricated with
"meandering" conductors confined to a single
surface. The resulting periodic structure forms a
transformer in the plane x = 0, as shown in~Figures
l0 and 20. The primary of the sensor has the
terminals (il,vl) and could be driven by an input
current or voltage source. The secondary consists
of a pair of conductors that meander to either side
of the primary. The terminals of this pair of
windings are connected in parallel so that their
voltage, v2, will reflect the flux produced by the
driven winding. The.return paths for the pair of
secondary conductors are arranged, in Figure 10, so
that each conductor will link flux over areas of the
same size. The open circuit voltage or the current
through a prescribed load at the secondary terminals
could be the sensor
output. This structure is represented in cross
section in Figure 24(a), where what are shown as
"wires" in Figure 20 are now shown to have widths c
and d for the primary and secondary conductors,
respectively. There are m wavelengths, a, to the
structure and the length, 1, is large enough
compared to ,~ so that the fi<~ld;.~ can be regarded a=
two dimensional.
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Optimization of Measurement Performance
A quantitative technique that permits the
identification of regions of optimal measurement
performance within the parameter space of interest
is required. The measurement performance can be
characterized by the following performance
specifications:
(i) Performance bandwidth - range of
frequencies over which accurate,
uncalibrated, absolute measurement is
possible with available
instrumentation
(ii) Dynamic range - range of properties
over which accurate parameter
estimates can be obtained.
(iii) sensitivity - variation in output
signal produced by a variation in the
measured property
(iv) Robustness - a measure of the ability
to obtain accurate measurements at
the limits of the sensor bandwidth
and dynamic range.
(v) Selectivity - a measure of the
ability to differentiate between (1)
the effects of two or more physical
or geometric properties of interest
(thi. s definition is used throughout
this document) (2) the effects of the
estimated parameter and other modeled
effects, (3) the desired signal and
disturbances of other frequencies or
phase, ( >) th~-~ deri.red signal and
CA 02443248 2003-10-10
noise (signal-to-noise ratio), (5)
the desired signal and the effects of
unmodeled dynamics.
(vi) Threshold level-the minimum output
signal level required for accurate
measurement of output magnitude and
phase.
A typical measurement optimization procedure
would follow the general procedure described below:
(1) Use the continuum model to numerically compute
elements of the Jacobian relating differential
variations in the vector of unknown quantities
(e. g., conductivity and thickness of a metal
foil) to the vector of measured quantities
(e. g., the Inter-Meander Magnetometer Trans-
impedance, v2/il, magnitude and phase)
(2) Determine the singular values and associated
right singular vectors using Singular Value
Decomposition for the Jacobian.formulated in
(1)
(3) Select the optimal frequency for the primary
excitation and determine the performance
bandwidth for an operating point at the center
of the bounded parameter space for the
application under consideration
(4) Determine the dynamic range by establishing the
minimum acceptable selectivity, which relates
to the condition number (= minimum singular
value/maximum singular value), and the minimum
sensitivity determined by the magnitude of the
minimum relevant singular value
CA 02443248 2003-10-10
-~J~-
(5) Evaluate robustness by comparing the dynamic
range to the application parameter space of
interest, and by evaluating the relative
observability for specific modes associated
with the right singular vectors
(6) Confirm performance potential through proof of
concept measurements and tune sensor geometry
and geometric construct parameters if required.
Continuum Modeling
In the continuum models, two -.-egimes of
behavior are considered. In the first regime, the
frequency ranges from low frequencies (currents are
uniform with respect to the x and y directions
throughout the conductors) to frequencies beyond the
TDECF. In this range, span-wise diffusion is
accounted for in the conducting windings, along the
y direction, up until the currents in the conductors
can no longer be assumed uniform with respect to the
x direction. In the second regime, the frequency is
assumed high enough that the magnetic vector
potential can be approximated as constant, with
respect to y, along the surface of the conducting
windings.
The media above and below the windings are
represented by surface inductance densities, Ln,
which relate the Fourier amplitudes of the magnetic
vector potential, An, to the Fourier amplitudes of
magnetic field intensity, I~yn, in tho planes just
above (a) and below (b) the windings.
The preliminary objective is to predict the
response of any particular circuit. connected to thc~
CA 02443248 2003-10-10
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secondary for any excitation on the primary, with
various neighboring media. This requires a detailed
description of the windings that can be used with
subroutines describing any particular neighboring
media. A schematic representation of the response
prediction algorithms is provided in Figure 22.
The neighboring media is represented as a
multi-layered structure of P homogeneous layers
above and/or below the winding plane, as shown in
Figure 23. Representation of distributed properties
can be achieved by introducing a large number of
thin layers.
This approach permits a complete analytical
solution for the field distributions in the
direction perpendicular to the winding plane. A
numerical solution using the subdomain method of
weighted residuals (B.A. Finlayson, "The Method of
Weighted Residuals and Variational Principles",
Academic Press, NY, (1972)) is then.introduced to
incorporate the winding geometry, other relevant
dynamics, and boundary conditions in the winding
plane.
First, the specification of the meandering
array 126 and the specifications of the MUT 128 are
input to the continuum model 20. Then the
collocation current densities, Kn, and vector
potentials, An, are computed 130. The modeling
effort is carried out in the following steps: (1)
Fourier amplitudes are determined in terms of
collocation current densities or vector potentials,
(2) flux continuity and Ampere's continuity
condition are introduced, (3) Faraday's law is
CA 02443248 2003-10-10
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evaluated to obtain the collocation conditions and subdomain integrals, and
(4) eduivalent circuit
admittances are derived.
The result is a complete set of admittances 132 (Y", Y,2, YZi, Y22), as shown
in Figure 22. These
admittances are functions of the magnetometer geometry 126, the neighboring
media properties,
the primary excitation, and the secondary load. Predictions of the
magnetometer responses are
then obtained directly from the admittances using the standard two-port
transfer relations 132.
Surface Inductance Density
The media above and below the windings are described by surface inductance
densities, L",
defined as the Fourier amplitudes of the normal flux density responses to
single Fourier
amplitudes of magnetic potential in the planes,just above (a) and below (b)
the windings. In the
following, the magnetic field is assumed to be independent of z and is
represented by the z
component of the vector potential.
A = AZ (x, y)i. (3)
aA - aA, - (4)
B= zi~= iv
ay ax
CA 02443248 2003-10-10
Hence, with the Fourier series written in the form:
+~
2n'
A T, y) = Fce ~ ~n(2~e~'k""f'"' , ~n = (5)
n-_a,
the surface inductance densities are given by
La - ICnAn . Lb _ - ICnlln
n ' $a ~ n
Y~ Y~
The first objective is to predict the response of
any particular circuit connected to the secondary to
any excitation on the primary for various
neighboring media. This requires a detailed
description of the windings that can be used with
subroutines describing any particular linear
neighboring media.
The neighboring media is accounted for by
introducing the concept of a surface inductance
density. Derivation of the appropriate surface
inductance densities is required for each
application considered. A generic representation
suitable for many of these applications is developed
in this section. This representation is then
incorporated as a subroutine in the response
prediction and parameter e,rti.mat.ion algorithms.
CA 02443248 2003-10-10
-59-
Many applications can be represented using a
media with multiple homogeneous layers. The
required surface inductance densities can be
conveniently obtained using transfer relations (J. R.
Melcher, Continuum Electromechanics, Cambridge, MA,
MIT Press (1981)). A medium with P layers (each of
uniform conductivity, a, and permeability, ~~) is
represented in Fig. 23
Layer j has the properties ~j,aj and the
thickness hj. The upper surface of the jth~layer is
designated by j. The transfer relation representing
the solution of Laplace's equation for the magnetic
vector potential in region j is given by
~l~ Q(O a(;) (~)~
-, m i _ X v"
Ac~+i~ Q2i) ac;~ H(~m)
where
aZZ~ - -aii~ = ~' coth~~h~
W
Q(~) = -a(~) __ fy .
1: 1 -~~ 51 R ~1 '~' j h J
71 - , ~r, + ~F~'~C''~
~1
and F ~~ ) and F (> > represent the compley
amplitude o~ the nth Fourier component of a field
auantity just above the 7 o~.~e~r and -ju~;t bE~~ ~oG~ the
~h
upr».r ~ uteri acc.: of t.hc~ wj l a~yc~r , Iw~ ;pie cv ~ vFe ~ y' .
CA 02443248 2003-10-10
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At the jth surface, the boundary conditions are
n
Surface current densities could also be considered
at the interfaces but are not included in this
example.
The surface inductance density above the jth
interface is given by
k=,4W
= n n
n H(7) (10)
Y"
The surface inductance density at x=0 is given by
Lna - Lna(P+1). Lna is obtained by progressing from
the j=1 surface to the j=P+1 surface using the
relation
La(J+i) = yQ(~) . ai~)a(;)k4 (11)
n n 2- ~ ~0~7) +'~z~(7)
L n n
The j-1 surface i; generally at infinity so that
I, a~' )_~:' a ~l~ .
n n 2a
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An identical relation is obtained for the
surface inductance density below the magnetometer
interface, with Lnb defined as in Eq. 6. (The
details of the model are contained in "Uncalibrated,
Absolute Property Estimation and Measurement
Optimization for Conducting and Magnetic Media Using
Imposed c~-k Magnetometry", by Neil Jay Goldfine, MIT
Ph.D. Thesis, September 1990.)
Current and Vector Potential Distributions
Conduction in the windings at low frequencies
is quasi-steady and the distribution of surface
current density is uniform in both the x and y
directions. The vector potential at low frequencies
should exhibit a relatively smooth distribution
since the presence of the conducting windings will
not deflect the lines of magnetic flux at low
frequencies. The symmetry of the Inter-Meander
Magnetometer construct permits a qualitative
prediction of the vector potential distribution. A
sample distribution is shown in Fig. 25, where the
surface current density and vector potential at a
particular collocation point are designated by a
circle or triangle, respectively. At the quarter
wavelength point, the vector potential is zero due
to symmetry assumptions. Consider the flux linked
through a surface bounded by a line in the z
direction at position y', between y=0 and y=a/~, and
a line at y=a/4. Assuming the current in the
primary is in the +z direction, as y' moves away
from a/4 toward the primary in the -y direction,
more and more flu}; is linked until a maximum vector
potential is reached at the center of the primary.
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As the frequency is raised, the conductors tend
to exclude the normal flux density, and the current
redistributes over the widths of the conducting
windings in the x and y directions. However, with
the thickness of the conductors in the x direction,
o, much less than the widths c and d of the primary
and secondary i.n the y direction, there will be a
range of frequencies over which the current
distribution remains essentially uniform in the x
direction, but not in the y direction. The current
begins to crowd out until it reaches a distribution
with a 1/SQRT(r) dependence. The current density at
the edge of the conducting windings goes to infinity
and the vector potential distribution becomes
uniform across the conducting intervals.
The simulated responses of the collocation on A
and collocation on K approaches (described in
"Uncalibrated, Absolute Property Estimation and
Measurement Optimi2ation for Conducting and Magnetic
Media Using Imposed ~-k Magnetometry", by Neil Jay
Goldfine, MIT Ph.D. Thesis, September 1990) are
shown side by side in Fig. 25 for the parameters in
the original construct of Figure 21. The (a)
construct in Figure 21 provides increased TDES for
some specific applications.
The collocation on A approach remains
numerically well behaved until. about 100 MHz for the
original geometry in Figure 21. The collocation on
K approach runs into numerical trouble at about 1
MHa., even with large numbers of collocation points.
The current distribution in the primary for the
(a) construct of Figure 21 at 10 MHz using
collocation on A is compared with the predicted
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1/SQRT(r) distribution in Fig. 26. As the frequency
is raised from 0.l MHz to l0 MHz, the current
distribution approaches the predicted 1/SQRT(r)
distribution.
Measurement Optimization, Using Singular Value
Decomposition (S~7D)
The wide range of applications and the complex
nonlinear parameter space common in nondestructive
electromagnetic measurement applications
necessitates the introduction of a generic tool for
evaluating measurement performance. Properties such
as sensitivity, selectivity, robustness, dynamic
range and bandwidth must be quantified in order to
provide a useful tool for optimization and
comparison of sensor design and measurement
performance.
A useful visualization which relates to the
sensitivity of the measurement vector to
perturbations in the unknown properties is provided
by the "Generalized Sensitivity Ellipse"
representation in Fig. 27. Such ellipsoids have
been used to provide visual tools for design of
mechanical linkages (H. Asada and K. Youcef-Toumi,
Direct Drive Robots: Theory and Practice, MIT
Press, 1387) . The major a~:is of the ellipse is
assigned the magnitude of the maximum singular
value, ~ ,, and the direction of its associated
m a ~.
right singular vector, as shown. Similarly, the
minor a5:is of the ellipse is assigned the magnitude
of the minimum ~.ingular value and a~>~ociated right
CA 02443248 2005-10-24
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singular vector. The left singular vectors can
also be used to map perturbations of the unknown
vector into the measured quantity space.
The ability to estimate two properties
independently is called the selectivity. In the
following sections, it is shown that the condition
number, Q mint Q maxi provides an excellent measure
of selectivity for a two-property measurement
application. For this definition of the condition
number, a value of 1.0 provides the highest degree
of selectivity, while a condition number 0.0, a
singularity point, implies that it is possible to
perturb the unknown property vector in a manner
that would be unobservable from the measured
quantities. Each of these cases is demonstrated
for actual measurement applications in the
following sections.
Conductivity and Thickness Measurement for Thin
Foils
Conventional methods for interpreting eddy
current measurements using ghaser diagrams often
draw on first order approximations. For example,
it is common to introduce similarity conditions
such as Q f (the conductivity-thickness product).
For many conventional eddy current sensor
measurements, maintaining either of these products
constant implies similitude (Nondestructive
Testing Handbook, 2d Edition, Vol. 4,
Electromagnetic Testing, ASNT, 1986).
A limit frequency, fg, can. be defined. Below
fg assumptions such as uniform current in the
driven
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and sensing coils are accurate. It is quite
reasonable under this condition to expect a degree
of similitude associated with the of product. This
condition is derived from the skin depth or depth of
penetration, which is defined by 6 - SQRT(2/wuo).
Unfortunately, for the applications considered here
it is of particular interest to go beyond this limit
frequency.
One might also be tempted to normalize the
frequency axis by the limit frequency. This is
commonly called the frequency ratio (Nondestructive
Testing Handbook, 2d Edition, Vol. 4, Electromagne-
tic Testing, ASNT, 1986). This may be a useful
scaling but should not generally be used as a
similarity criterion. The limitation of such a
similitude assumption is apparent from a closer look
at the parameter 7 in the magnetic diffusion
transfer relations presented in the surface
inductance density section.
The excitation of higher order Fourier
components (n > 1) would effect the relevant
magnetic diffusion time, rm = X012. Of course in a
continuum representation there are an infinite
number of relevant magnetic diffusion times - one
associated with each Fourier component in the
infinite series of Eq. 14. The Inter-Meander
Magnetometer was originally designed to impose a
prescribed magnetic potential at a fixed wavelength.
However, the excitation oi: shorter wavelength
Fourier components is increased when span-wise
diffusion in the conducting windings is significant,
which of: ten occurs when ttnc:e neighboring material i.~;
CA 02443248 2003-10-10
located a small fraction of the imposed wavelength
above the sensor.
Fortunately, this additional complexity
provides additional leverage and, consequently,
improved selectivity, sensitivity, and dynamic range
for many applications. In this section it is used
to enable measurement of conductivity and thickness
at a single temporal frequency_
In general, eddy current sensors provide only
a measure of surface conductivity, as=ao. This
section demonstrates that the excitation of~a wide
range of Fourier components including short
wavelengths enables the independent measurement of
conductivity and thickness at a single temporal
frequency.
Improved measurement performance results from
the excitation of shorter spatial wavelength
excitations.
First, a plot of the nonlinear~parameter space
for a wide range of conductivity and thickness is
displayed. Second, the frequency responses over a
range of foil conductivity and foil thickness are
discussed and experimental validation of the
span-wise diffusion continuum model is provided.
Then SVD is performed to determine the optimal
measurement range for two different metal foils.
Finally, the actual measurement of conductivity and
thickness is demonstrated for the two metal foils.
It is assumed in the remainder of this section
that the height of the condor ct.ing foil is measurable
by some other means as discussed in the nest
paragraph. It may be possible to measure the
CA 02443248 2005-10-24
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conductivity, height and thickness of a conducting
layer at a single temporal frequency, but this is
not attempted here.
One method for independent measurement of the
foil height above sensor is to use a temporal
frequency at which the skin depth is smaller than
the thickness of the conducting windings for the
Inter-Meander Magnetometer used in the experiments
is 25 ~,m. At 1.58MHz the skin depth in copper (Q =
5.8E7 mhos/m) is about 50~,m. The foils selected
for the two examples must therefore be thicker
than about 100 ~.m to permit independent
measurement of the foil height at 1.58 MHz without
knowledge of the foil thickness or conductivity.
To demonstrate that this measurement can also be
performed without knowledge of the foil
conductivity, a plot of transinductance magnitude
and phase is provided in Fig. 28.
From this figure it is clear that a gross
estimate of the foil conductivity provides
sufficient knowledge for independent measurement
of the foil height. It is also clear that the foil
thickness 0, has only a small effect on the
transinductance magnitude. As a result, the
transinductance magnitude at 1.58 MHz will be used
to adjust the height in the experimental setup.
Note also that a good measure of the foil
conductivity could be obtained from the phase
measurement. Thus, the independent measurement of
the conductivity and height is possible at
frequencies meeting the prescribed limitations
with regard to skin depth.
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The nonlinear parameter space for the
transinductance magnitude and phase is plotted in
Fig. 29. Lines of constant conductivity are plotted
for foil conductivity, o, ranging from 3.2 x 107
mhos/m to 6.0 x 107 mhos/m in increments of 2.0 x
106 mhos/m. Lines of constant foil thickness are
plotted for foil thickness, o, ranging from 0.1 mm
to 0.6 mm in increments of 0.0125 mm.
Several observations can be made from this
plot. First, and most interesting, there is a wide
range of thickness and conductivity values f.or which
a small increase in thickness at a constant
conductivity actually results in a larger trans-
inductance magnitude.
An experimental demonstration is provided in
Fig. 31 and Fig. 32. The experimental measurements
are indicated by crosses and squares for the two
different copper foils. The micrometer measured
thickness, n, is indicated for each~foil; and a
conductivity of 5.49E7 mhos/m was used in the
simulations that are indicated by solid lines. This
value of conductivity is the actual value measured
for the thinner foil - a demonstration of this
measurement will follow. Excellent agreement is
demonstrated for frequencies above the impedance
analyzer 14 threshold frequency at about 100 KI-~z.
Magnitude measurements are possible below this
frequency, but accuracy is limited for
transinductance magnitudes below 0.05 ti. Figure 32
shows the unanticipated behavior. Better agreement
for the thic~:er foil would be possible if its
conductivity were also estimated and used in the
simulations.
CA 02443248 2003-10-10
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The last observation from the plot of the nonlinear parameter space in Figure
29 relates to the top
of the curve, where increasing the thickness actually causes a reversal in the
phase.
Now, SVD is performed on the Jacobian for foils at a prescribed height of 0.4
mm, a drive
frequency of 1.58 kHz, and for an Inter-Meander Magnetometer wavelength,
~,=12.7 mm.
As stated earlier, the condition number, c, provides a measure of the
selectivity for a two-
parameter estimation application. It also indicates the relative sensitivity
of the two orthogonal
modes associated with the singular vectors. For very thin layers (below 0.1
mm), the conditional
number approaches zero for both copper and aluminum foils. This implies that
an unobservable
mode exists. This mode is associated with the minimum singular value, 6~,;",
and has the
associated right singular vector [0.7-0.7]~~. This is exactly what physical
intuition would have
predicted. For foils that are very thin compared to the imposed wavelength, a
perturbation in the
unknown vector along the indicated right singular vector would produce no
change in the surface
conductivity, as = a4. of the foil. The next section provides a demonstration
of surface
conductivity estimation using a multiple frequency nonlinear least squares
algorithm.
It is important to note, however, that the largest sensitivity to measurement
of either foil
conductivity or thickness, when the other property
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is given, occurs at n=0.12 mm, where omax reaches a
maximum - for aluminum foils with conductivity near
3.72E7 mhos/m, and at n=0.07 mm - for copper foils
with conductivity near 5.8E7 mhos/m.
For thick layers, o above 0.6 mm, the singular
vectors indicate that the thickness of the foil is
essentially unobservable. However, excellent
sensitivity to foil conductivity is sustained
indefinitely, as the thickness increases. This is
consistent with the observation that when the upper
surface of the foil is farther and farther away from
the sensor, the measured transinductance should
become insensitive to thickness variations.
The transition between singular modes indicated
by the right singular vectors is gradual between
[0.7 -0.7]T and [1 0]T, and between [0.7 0.7]T and
[0 1]T_ The crossing of the two singular modes
associated with constant conductivity-thickness
product, (0.7 -0.7]T, and maximum sensitivity of the
conductivity-thickness product [0.7 0.7]T is also
associated with a shifting in dominant behavior from
the imposed wavelength to the shorter wavelength
excitations.
The singularity points at 0.39 mm for aluminum
and 0.32 mm for copper are coincident with the
reversal in the variation of the Transinductance
phase indicated in Fig. 2.9.
Two actual measurements are now demonstrated
for copper and aluminum foils G;ith thicknesses near
the peak in the condition number. An expansion of
the parameter space about a preliminary estimate of
th~~ operating point is provided for the two
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measurements in Fig. 35 and Fig. 36. The estimated
foil conductivity and thickness are indicated. As a
rough check of the foil thickness measurement, a
micrometer measurement is provided for comparison.
The error in the micrometer measurement is about 15
um. The estimated values for foil thickness are in
excellent agreement with the micrometer measured
values in both cases. The conductivity estimates
are also reasonable for copper and aluminum.
Note that effective thickness of a diffusion
layer near the surface of a material can also be
estimated using this approach. For example; a
conductivity and effective thickness grid could be
generated to detect and characterize titanium a-case
properties or carburized steel case properties.
Multiple Frequency Measurement of Conductivity-
Thickness Product
A demonstration of the measurement of the
surface conductivity and height of a thin-metal foil
above the sensor is provided for several foils using
a multiple frequency nonlinear least squares
parameter estimation algorithm. This demonstration
addresses applications for which b »4 and the
selectivity ( condition number) for conductivity and
thickness is much less than one 1. No attempt is
made to optimize this multiple frequency
measurement.
The parameter estimation programs incorporate a:3
pac3~;age developed by Argonne National Laboratory,
Minpacl~: Project in 1980. This package uses a
modified Levenberg-Marquardt method (also called
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Marquardt method) in which the steepest descent
method is used far from the minimum and then smooth
transition to the inverse Hessian method occurs as
the minimum is approached (L. Ljung, System
Identification: Theory for the User, Prentice-Hall
NH (1987); W.H. Press et al., Numerical Recipes, The
Art of Scientific Computing, Cambridge U. Press
(1986)).
The results for six different foils are
presented in Fig. 37 and Fig. 38. For the thicker
foils, the condition number has increased
sufficiently to require a more robust estimation
approach. In other words, for the thicker foils, it
is necessary to adjust a and a independently to
achieve better agreement between the simulated and
experimental response.
At this point it is important to emphasize that
all measurements described here are both
uncalibrated and absolute. The consistent agreement
between simulated and experimental data provides
further support for this claim. The capability to
measure absolute physical and geometric properties
without calibrations will provide significant cost
and performance benefits to many applications.
Conductivity and Height Measurement far Thicl~:
Conducting Plates
The independent measurement of conductivity and
height is a common requirement in eddy current
sensors application . However, the extremely high
sensitivity of measurements to the height of a MtIT
often prevents accurate conductivity measurements.
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This is especially the case when calibration must be
used and accurate location of the sensor is
difficult.
In this section, the SVD-based measurement
optimization techniques presented earlier are used
to provide accurate independent measurement of the
conductivity and height (lift-off) for relatively
thick metal plates.
First, a comparison of simulated and
experimental data is provided in Fig. 39 for a brass
plate at various heights above the sensor. In this
case, the conductivity was adjusted in the
simulations to obtain visual agreement with the
experimentally measured phase.
SVD is now performed on the new Jacobian.
Plots of the condition number and associated
singular values and singular vectors as a function
of height and conductivity are provided in Figs. 40,
41 and 42. For good conductors, such as brass,
aluminum and copper, the measurement shows excellent
dynamic range and would permit sorting of a wide
range of conducting materials located for this ex-
ample at an unknown height between 0.03 mm and
0.5mm.
Finally, the independent measurement of height
and conductivity is demonstrated in Figure 43 for an
aluminum and brass plate with no calibration. The
experimental data points for each plate trace out a
line of constant conductivity. This provides strong
support for the claims of absolute uncalibrated
measurement of conductivity.
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It is important to note that the multiple
height measurement provides a single frequency
multiple measurement approach. This will enable
accurate measurement of conductivity in applications
for which the conductivity is dispersive (i.e.,a
varies with frequency). This should have direct
application in crack detection and aging/fatigue
monitoring in metal plates, foils and pipes. This
provides a simple alternative to the multiple
wavelength approach (J. R. Melcher, US patent number
5,015,951) to property estimation and can also be
applied to magnetic media.
Height Measurement for Hiah Permeability Layer
In this section, a brief evaluation of
measurement performance and design issues is
provided for the measurement of height for a high
permeability layer.
SVD results are provided in Fig. 44 for a
highly permeable layer at various heights above the
sensor. In this example, the condition number
is always zero. This is consistent with the fact
that the phase is zero with no ground plane and zero
bulk conductivity, so that only the magnitude
provides useful measurement information. With a
back-plane it may be possible to estimate both the
height and the permeability. The optimal sensor
position for measurement of small variations in
layer height is approximately 0.2 mm for this
example.
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A wide range of potential sensor design
variations is possible to enhance the sensitivity to
height measurement. For demonstration purposes, a
conducting back-plane (ground-plane) is introduced
at 0.5 mm below the sensor. The proximity of this
back-plane to the winding plane could be optimized
using the SVD-based methods described earlier. This
optimization is not provided here. The variation in
the magnitude of the Transinductance with and
without this ground plane for different heights of
the highly permeable layer is demonstrated in Fig.
45a and 45b.
The measurement of transimpedance, v2/j~il, is
demonstrated at 1 MHz for an infinite half space of
a highly permeable material (xm = 1E3, o - 0.1
mhos - for example, a sintered powder) at the
heig? ~a(2) above the magnetometer surface. A
significant increase in sensitivity-f or close
proximity height measurement is apparent when the
ground plane is present. Measurements are possible
with the HP LF 4192 Impedance Analyzer at 1 MHz;
however, with the back-plane, these measurements
could not easily be made below 100 KHz. Without the
back-plane, measurements can typically be made
as low as 20 KHz with the available instrumentation
for the original winding construct from Figure 21.
It is always a good idea to check the
performance of the computer simulations by plotting
the spatial variations of current and vector
potential. These plots are provided in Fig. 47,
Fig. 48 and Fig. 49. Variations in the distribution
of the currents in the secondary, and more subtl}v in
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the primary, are shown in these three figures. The
current at each collocation point is denoted in
these figures by o, and the vector potential by D.
Single Frequency Estimation of Complex Permeability
The estimation of complex magnetic
susceptibility is demonstrated in this section for
dispersive media with no significant bulk
conductivity. The span-wise diffusion continuum
model provides predictions of the response for any
layered media with completely specified properties.
The media selected for this demonstration is a thick
layer of granular aluminum (= 1 mm particle radius)
placed at two different heights above the sensor
windings. This measurement is ideal for parameter
estimation, since with no ground plane and no
significant bulk conductivity, the universal
transinductance plot in Fig. 50 can be used to
graphically estimate the complex magnetic
susceptibility for the granular aluminum layer. The
universal plot and the fact that the transimpedance
is an analytic function of the complex magnetic
susceptibility permit graphical estimation at any
frequency from a single "universal" plot.
In this plot, the magnetometer response,
v?/jmil, is plotted for a grid of complex
permeability values (Xn = X' -jx ")- The lines of
constant X~ and ~" are always orthogonal because
v?/j~i_1 is an analytic function oi: Xm. This
orthogonality is exhibited in the figure by
consistently scaling the magnitude and phase axis in
accordance with the logarithm of the complex
transimpedance (M. C. Zarets~~}~, cat al. Continuum
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properties from Interdigital Electrode
Diolectrometry, IEEE Transactions on Electrical
Insulation, Vol. 23, No. 6, Pp. 899-917, Dec. 1988).
The parameter estimation methodology is
initiated with a first guess obtained visually from
the universal transinductance plot_ The secant
method is then used in a root searching procedure to
minimize the error, a (e ), between the
experimentally measured transimpedance, v2/j~il, and
the predicted transimpedance (M. C. Zaretsky, et al.
Continuum properties from Interdigital Electrode
Diolectrometry, IEEE Transactions on Electrical
Insulation, Vol. 23, No. 6, Pp. 899-917, Dec. 1988;
L. Lyung, System Identification: Theory of the Use,
Prentice Hall, Inc., NH, 1987). The parameters,
B*i, are updated by 0e i by forming a secant using
the most recent two guesses. The fact that the
transimpedance is an analytic function of the
complex magnetic susceptibility permits the direct
use of the secant method with parameter updates
determined from (M. C. Zaretsky, et al. Continuum
properties from Interdigital Electrode
Diolectrometry, IEEE Transactions on Electrical
Insulation, Vol. 23, No. 6, Pp. 899-917, Dec. 1988).
~B.' _ a ~P~ )
(12)
_,
Parameter estimation of dispersive complex
permeability is now demonstrated for the diamagnetic
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granular aluminum layer. The initial estimate of the derivative is obtained by
simulating a
second guess with a 2% variation in the real and imaginary parts of X", The
magnitude and
phase of the trans-impedance, v2/jwi,, is obtained experimentally using the HP
LF 4192
Impedance Analyzer. In order to demonstrate absolute measurement for layered
media, a 2
cm layer of granular aluminum is measured for two different heights, ha (3)=0
and ha (3)=0.8
mm, above the magnetometer windings. Figure 51 a provides the experimental
measurement
of trans-impedance magnitude and phase at each frequency and height (note: the
precision oi'
the phase measurement with the HP Ll~ 4192 Impedance Analyzer increases
incrementally
with the magnitude of the trans-impedance). The input to the parameter
estimation is the first
guess for the real and imaginary parts of Xm at each frequency. The program
then provides
updated predictions for the Xm detern~ined from Eq. 12. The first guess and
resulting
estimates for this example are provided in Figure S 1 b.
The estimated Xm in Figure 51 b are now used to predict the response of the
sensor with the
granular aluminum layer at 0.8 mm above the sensor (note: the estimated
aggregate setup
error is about 10% for the height above the sensor and possible variations in
coverage of the
active sensor region with a consistent layer of granular aluminum). Figure 52
shows the
experimental and predicted responses for the two cases (ha (3)=0 and h$
(3)=0.8 mm) using
the estimated values of Xm from Figure 51 b. Of course, the predicted and
measured
responses are identical for ha (3)=0 since the parameter estimation routines
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were run for this MUT height. For ha(3)=0.8 mm, the
predicted response is well within the estimated 10%
setup error. This result provides solid
verification of the algorithms and parameter
estimation methodology.
Further verification is obtained by comparison
with an analytical model of conducting spheres built
up from a magnetic dipole representation. If the
effects of contact between the spheres is neglected,
a model derived by Inkpen and Melcher (S. L. Inkoen
and J. R. Melcher, Smoothing the Electromagnetic
Heating Pattern In Polymers," Mid-April 1985, Vol.
25, No. 5, Pp. 289-294) applies directly. This
model also neglects the effect of the fields induced
in one sphere on the fields induced in neighboring
spheres. Thus, some disagreement between this model
and the actual measurements is expected.
The examples discussed in this section
demonstrate the capability of the Inter-Meander
Magnetometer and associated parameter estimation
algorithms to estimate complex magnetic
susceptibility for diamagnetic materials. This
methodology can be applied directly to applications
involving layered ferrous media. Care must be taken
in that case to ensure the universality of the
transimpedance plots. If universal plots are not
obtainable the only adjustment in the methodology is
the required use of frequency dependent trans-
impedance plots to obtain a first guess at each
frequency.
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Conductivity and Permeability Estimation for
Homogeneous Infinite Half Space
The bulk conductivity introduces shape variance
into the magnitude-phase plots as a function of
drive frequency. Although it is possible that
universal plots may exist for a properly normalized
transimpedance in specific examples, obtaining a
general universal plot is unlikely. Furthermore,
unlike the real and imaginary parts of the complex
permeability, the transimpedance can not be
represented over the entire relevant parameter space
as an analytic function of a complex parameter
incorporating both the permeability and the
conductivity (e.g., for electroquasistatics such a
parameter is E - e' - je " - E - j°
However, there are regions of practical importance
over which the transimpedance exhibits some of the
same properties of an analytic function. This
implies that all derivatives exist and are
continuous at all points in the region; satisfaction
of the Cauchy-Riemann equations is also a necessary
condition for analyticity (R. V.Churchill, and G. W.
Brown, "Complex Variables and Applications", McGraw-
Hill, NY, 1984; F. B. Hildebrand, "Advanced Calculus
for Applications", Prentice-Hall, N5, 1976). The
graphical analog states that in regions of
analyticity with respect to a complex parameter
space the magnitude vs. phase plot will always
exhibit orthogonality between lines of constant real
part and lines of constant imaginary part. In the
case discussed here, the magnitude vs. phase plot
for conductivity and permeability does approach this;
property for certain parameter space regions.
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This is demonstrated in Figures 54 and 55 for
1 KHz and to MHz. Clearly, even by scaling these
plots in accordance with Eq. 51 the desired
orthogonal characteristic is not exhibited over the
entire relevant parameter space. The double-valued
nature of the magnitude vs. phase plot at 10 MHz and
the saturation of the magnitude for large values of
u,o are related to magnetic diffusion in the MUT.
Two characteristics are most apparent. First, as
the permeability, u, increases, the transimpedance
magnitude generally increases at a given
conductivity, o. This is the result of an increased
inductive coupling between the primary arid secondary
windings. Second, as the conductivity increases for
a given permeability, the transimpedance magnitude
decreases. This is the result of a reduction in
inductive coupling to the secondary due to increased
shielding associated with decreasing magnetic skin
depth in the measured media. In the double valued
region, the skin depth, decreases significantly with
E~ at 10 MHz resulting in increased shielding. The
result is a region over which different combinations
of permeability and conductivity result in the same
transimpedance magnitude and phase. The independent
estimation of E~ and o could also be optimized using
the SVD-based method described earlier. This is not
shown here.
Increased Selectivity
The region of high selectivity (i.e. the region
where the grid lines are nearly orthogonal) can be
expanded by using a meanderincr (f.igure 10 or 11.) or-
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single turn (figure 4, 5, 6 or 7) winding with a
spatial wavelength, a, that is on the same order or
smaller than the skin depth~at the selected
operating frequency. This is apparent from Eg. 8,
Where the parameter, 7, indicates the tradeoff
between the wavenumber, k, and the term ~o~ which
can be rewritten as 2/b2, where b is the skin depth.
This permits the independent measurement of
conductivity and permeability for homogeneous plates
and the measurement of conductivity and permeability
distributions near the surface of heat treated or
carburized steel parts. A near real-time
measurement of the conductivity and permeability
distribution near the surface of a carburized steel
part would provide significant economic savings and
quality enhancement potential for many applications,
such as bearing manufacturing, which currently use
destructive means to measure properties such as
percent carbon content near the surface of
carburized parts.
As in the prior Melcher Patent, U.S. Patent No.
5,015,951, May 14, 1991, with any of the above
applications we can use multiple primaries.
Double-Sided Measurement
Two new configurations are now proposed for
measurement of geometric and physical properties of
a layer. of conducting or magnetic media. The
proposed apparatus might incorporate a winding
construct similar to the previously discussed
Inter-Meander Magnetometer structure shown in Fig.
10.
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The measurement of complex permeability, for
example, might be accomplished with a new construct
that incorporates a set of two identical
Inter-Meander Magnetometer structures located above
and below the layer of magnetic media. The inherent
symmetry of the resulting apparatus provides for two
modes of operation. Schematics of these two
operating modes are provided in Fig. 56. The odd
mode is generated by applying the excitation
currents or voltages a half wavelength out of phase,
as shown in the figure. In this mode, the magnetic
flux normal to the center line (in the x direction)
of the thin layer is exactly zero for all y. In the
even mode, the excitation is in phase, as shown, and
the magnetic field intensity in the y direction at
the center line of the layer is exactly zero for all
Y.
Information obtained from measurements in each
of these modes is then combined to obtain estimates
of the property of interest. The variation of these
properties as a function of an external bias field
could also be considered, since the measurement is
based on a perturbation of the excitation fields.
Equivalents
While the invention has been particularly shown
and described with reference to preferred
embodiments thereof, it wi.7_1 be understood to those
s?~:illed in the art that various changes in form and
details may be made therein without departing from
the spirit and scope of the invention a~ defined by
the appended claims.
