Low-Cost Multi-Frequency Eddy Current Coating Thickness Measurement System

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Low-Cost Multi-Frequency Eddy Current Coating
Thickness Measurement System
Ana C. Santos
Mechatronics Department
Universidade de Évora
Évora, Portugal
André Barrancos
Instituto de Telecomunicações,
Lisboa, Portugal
andre.barrancos@tecnico.ulisboa.pt
Fernando M. Janeiro
Instituto de Telecomunicações,
Mechatronics Department
Universidade de Évora
Évora, Portugal
fmtj@uevora.pt
Luís S. Rosado
Instituto de Telecomunicações,
Dept. of Elec. and Comp. Engineering
Instituto Superior Técnico
Lisboa, Portugal
luis.rosado@tecnico.ulisboa.pt
Abstract— A low-cost coating thickness gauge based on Eddy
Current Testing (ECT) is reported in this paper. This
measurement system employs a Direct Digital Synthesizer
(DDS) to generate pure sinusoidal stimulus applied to a
measurement coil whose impedance varies with the measured
coating thickness. The coil current and voltage are digitally
acquired using an ARM Cortex M4F microcontroller where
sine-fitting digital signal processing algorithms are applied to
estimate the coil inductance and resistivity at different operation
frequencies. Post-processing implements a simple
multi-frequency estimate algorithm providing accuracy
improvements around 10% when compared with the use of a
single frequency.
Keywords—Eddy Current Testing, Coating Thickness,
Multi-Frequency, Sine-Fitting Algorithms.
I. INTRODUCTION
The measurement of the protective coating thickness of
metal parts is an important step of their final quality control.
Using the correct amount of coating is essential to improve
wear resistance, thermal isolation, corrosion resistance and
therefore, increase the parts life span [1].
Non-Destructive Testing (NDT) approaches have been
employed in measuring the coating thicknesses while
preserving the metallic part serviceability. From the vast NDT
options, Ultrasonic Testing (UT), X-Ray Spectrometry, and
Eddy Current Testing (ECT) have been here applied.
However, UT is unsuitable for sound-absorbing coatings and
X-Ray Spectrometry is substantially expensive and requires
personnel protection from high-intensity radioactive
sources [2]. On the other hand, ECT is one of the most used
techniques for measuring the protective coating thickness of
both ferrous and non-ferrous metal parts.
ECT relies on electromagnetic sensors, e.g., a coil that
generates a time-varying magnetic field, which induces an
electromotive force on the metallic material under testing,
leading to the creation of Eddy Currents (EC). In turn, these
EC will generate a secondary magnetic field which can be
measured with the original coil or some other sensing element,
e.g., another coil or a magnetoresistive sensor [3] [4]. Besides
other characteristics of the metallic part, the EC secondary
magnetic field reflects the distance between the coil and the
part surface therefore allowing the assessment of the coating
thickness.
Testing frequency plays an important role on ECT as it
determines the EC density along the depth of the metallic part.
High frequencies lead to concentrate EC in surface while
lower frequencies allow for deeper penetration in the metallic
part. While measuring coating thickness it is important to
select a frequency high enough to reduce the influence of the
metallic part geometrical variations (e.g., the metal sheet
thickness) in the EC signal.
Beside the use of a single frequency, different EC
excitations have been tried for coating measurement thickness
as Swept-frequency Eddy Current (SEC), Pulsed Eddy
Current (PEC), and Multi-frequency Eddy Current (MEC) [5].
In the SEC technique, frequency is swept within a range [6],
where different implementations revealed the ability to
perform measurements between 168 μm to 1.35 mm [7], and
50 μm to 250 μm [8]. An impedance analyzer is needed for
this implementation while thickness estimates are provided
while dealing with potentially complex analytical solutions
[9].
PEC have been increasingly used for diversified testing
purposes because of their rich information and deep
penetration. PEC signals have been demonstrated measuring
the coating thickness when both the coating and metallic part
are magnetic [7]. The literature reports coating thickness
measurements between 150 μm and 350 μm
(non-ferromagnetic coatings and ferromagnetic substrate) [1],
and 25 μm to 400 μm (ferromagnetic coatings and
ferromagnetic substrate) [10]. However, this technique
requires advanced signal processing [6] to retrieve useful
information from the pulsed signals.
The analysis of MEC signals is predominantly realized in
the frequency-domain. The technique has been reported on the
detection of cracks or defects located at different depths in the
test material [11] [12] [13]. For thickness measurements as in
[14], the MEC signals were used to measure non-magnetic
plates' thickness, as small as 1 mm. However, this type of
methods requires multi-frequency impedance analyzers,
which are complex and expensive [6]. Therefore, this paper
presents the development of a measuring system to measure
the metals' protective coating thickness using a low-cost
system based on ECT using MEC signals.

II. T
HICKNESS
M
EASUREMENT
S
YSTEM
A. Measurement Hardware
The proposed system relies on the combination of a Direct
Digital Synthesis (DDS) excitation signal generator and an
advanced microcontroller for digital signal acquisition and
processing. Beside those two main components, analog signal
conditioning circuitry is needed to create the signals of the
measurement coil voltage and current. The system high-level
block diagram is shown in Fig. 1.
A fully integrated AD9833 DDS generates the signal
waveform for the impedance measurement. An SPI bus
between the AD9833 and the selected microcontroller is used
to program the internal state machine registers and configure
the output frequency and phase. The employed
microcontroller is an Arm Cortex-M4F TM4C1233H6PM
based microcontroller. It features an 80 MHz maximum
clock, 256kB of FLASH and 32kB of SRAM memories. It
also includes a 12-bit Successive Approximation Register
ADC capable of generating 1 MSamples/s maximum. To
facilitate the developments, the microcontroller was used in a
Stellaris Launchpad LM4F120XL provided by Texas
Instruments.
For convenience, all the operational amplifiers used for
signal conditioning use the same integrated circuit model, the
INA121P. This instrumentation amplifier is first used as a
current buffer to drive the measured circuit branch which
includes the coil and a resistor to sense the current. Two
additional amplifiers generate voltages proportional to the coil
voltage and current, Fig. 2.
B. ECT Sensor
An improvised ECT sensor was implemented using a
conventional discrete through-hole 22 mH radial inductor,
Fig. 3. This inductor comprises a ferrite core, around which
the windings remain. After some preliminary experiments to
validate the sensor proper operation, this option was adopted
to avoid the effort of winding a dedicated coil.
C. Signal Processing Algorithms
The AD9833 is used to generate a sinewave, therefore the
signals at the terminals of the reference resistance and the
measurement coil are also sinewaves. These two sinewaves
are simultaneously acquired by the internal ADCs of the
microcontroller and then a sine-fitting algorithm is applied to
the samples of each channel to estimate the amplitude and
phase of each waveform. Since the excitation frequency f is
known, the noniterative 3-parameter sine-fitting can be
applied [15].
Assuming that the samples
i
y
are acquired at timestamps
i
t
, then they should fit the model
( ) ( )
cos 2
cos(2 ) sin(2 )
= π + φ +
= π + π +
y t D ft C
A ft B ft C
(1)
where
( )
2 2
, = atan2 ,= + φ −D A B B A
. (2)
The sine-fitting algorithm finds the value of
[ ]
ˆ
, ,
=
T
A B C
x
by
minimizing
( ) ( )
( )
2
1
cos 2 sin 2
=
 
− π + π +
 

N
n n n
n
y A ft B ft C (3)
which, since it is linear, can be obtained non-iteratively
through
( ) ( )
1
ˆ
−
=
T T
x D D D y
(4)
corresponding to a least-squares minimization process where
[ ]
1 2
, ,...,=
T
N
y y yy (5)
( ) ( )
( ) ( )
( ) ( )
1 1
2 2
2
cos 2 sin 2 1
cos 2 sin 2 1
cos 2 sin 2 1
π π 
 
π π
 
= 
 
π π
 
 
M M M
N
ft ft
ft ft
ft ft
D
. (6)
Fig. 1 Measurement system block diagram.
Fig. 2 Analog conditioning circuit. Includes the DDS AD9833 for signal
generation, Instrumentation Amplifier INA121, the 1 kΩ reference
resistance and the coil being measured, Z. The 2 output amplifiers
convert bipolar into unipolar signals as required by the micorcontroller
ADC.
Fig. 3 Conventional radial inductor used as ECT sensor.
Face towards
the metal part

Due to the memory limitations of embedded measurement
systems, it is possible to avoid the construction of matrix (6)
by directly computing
T
D D
and
T
D y
as [16]
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( )
2
1 1 1
2
1 1 1
1 1
cos cos sin cos
cos sin sin sin
cos sin
= = =
= = =
= =
 
2π 2π 2π 2π
 
 
 
= 2π 2π 2π 2π
 
 
 
2π 2π
 
 
  
  
 
N N N
i i i i
i i i
N N N
T
i i i i
i i i
N N
i i
i i
ft ft ft ft
ft ft ft ft
ft ft N
D D
, (7)
( ) ( )
1 1 1
cos sin
= = =
 
= 2π 2π
 
 
  
T
N N N
T
i i i i i
i i i
y ft y ft yD y
. (8)
These matrices can be sequentially computed as each new
sample arrives avoiding the need to store the acquired samples
saving even more memory.
Application of the sine-fitting algorithm to the voltage
across the reference resistance results in its estimated
amplitude
1
D
and phase
1
φ
. Similarly,
2
D
and
2
φ
are
obtained from the voltage across the measurement coil. The
impedance of the measurement coil
co il
Z
can then be
obtained from
2
1
=
coil r
D
Z R
D
and
2 1
φ = φ − φ
coil
. (9)
D.
Graphical User Interface
A simple Graphical User Interface (GUI) was implemented
exploring the LCD addon BOOSTXL-K350QVG-S1 from
Texas Instruments, Fig. 4. The main goal for the interface was
to allow a prompt display of the impedance resistivity and
inductance values while varying the measurement conditions.
III.
C
OIL
M
EASUREMENT
R
ESULTS
After having sorted all the system implementation tasks, it
was used to perform diversified measurements. The system
was operated while the coil was positioned over an aluminum
plate including multiple plastic sheets between the probe and
the metal. The probe resistance and inductance were registered
at frequency 1 kHz, 5 kHz and 10 kHz for emulated coating
thickness 0 mm, 0.11 mm, 0.22 mm, 0.33 mm, 0.44 mm. The
results are shown in Fig. 5 and Fig. 6.
As verified, both the resistance and inductance exhibit the
effect of the varying coating thickness. Simultaneously,
frequency also affects the registered values therefore allowing
additional measurements potentially improving the final target
estimates. Modelling the two impedance components,
resistance and inductance, would allow reaching highest
accuracies for coating thickness estimates. Nevertheless, this
option would require the inversion in
R
2
and its inherent
complexity. The option was to select between the resistance
or the inductance bearing in mind observed metrological
characteristics as sensitivity and precision.
Measurements for the different frequencies were gathered.
For illustration purposes, the results for 1 kHz and 10 kHz are
shown in Fig. 7 to Fig. 10. As shown, coating thickness has a
greater effect over the coil inductance than on its resistivity.
At the same time, the relative standard deviation for the
resistivity curves is much higher than for the inductance.
Therefore, the decision was to only the inductance
information for the coating thickness estimates.
Fig. 4 Developed Graphical User Interface.
Fig. 5 Average measured probe coil resitivity as a function of frequency
for multiple coating thickness. Error bars represent the standard
deviation of the processed 200 measurements.
R [Ohm]
Fig. 6 Average measured probe coil inductance as a function of
frequency for multiple coating thickness. Error bars represent the
standard deviation of the processed 200 measurements.
0246810
Frequency [kHz]
17
17.5
18
18.5
19
19.5
d = 0 mm
d = 0.11 mm
d = 0.22 mm
d = 0.33 mm

IV. THICKNESS ESTIMATION ALGORITHM
To obtain an algorithm that provides thickness estimates
from the acquired signals, the inductance was firstly displayed
for the tested frequencies and coating thickness variations as
shown in Fig. 11.
A simple algorithm was designed for the inversion of the
coil measurements into thickness estimates. The option was to
fit a template for the inductance curve for each tested
frequency. The final estimate was provided through a
weighted averaging applied to the estimates achieved on each
frequency. The main goal was to develop an algorithm simple
enough for implementation in the available measurement
system resources.
The selected template for the inductance curve was a
second order polynomial whose coefficients for each
frequency were
2
1 kH z
ˆ
1.5 862 6 0.0 7 8 568.93,
t L L= × − × + (10)
2
5 kH z
ˆ
0.2248 7.4318 61.261,
t L L= × − × + (11)
2
10 k Hz
ˆ
0.2138 7.0241 57.585
t L L= × − × + , (12)
where L is the measured inductance expressed in mH.
Fig. 7 Average measured inductance as a function of distance, for
f = 1 kHz. Error bars represent the standard deviation of 200
measurements.
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Thickness [mm]
49.5
50
50.5
51
51.5
52
52.5
53
53.5
Fig. 8 Average measured inductance as a function of distance, for
f = 1 kHz. Error bars represent the standard deviation of 200
measurements.
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Thickness [mm]
19.05
19.1
19.15
19.2
19.25
19.3
19.35
19.4
19.45
19.5
Fig. 9 Average measured resistance as a function of distance, for
f = 10 kHz. Error bars represent the standard deviation of 200
measurements.
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Thickness [mm]
84
86
88
90
92
94
96
98
100
102
Fig. 10 Average measured inductance as a function of distance, for
f = 10 kHz. Error bars represent the standard deviation of 200
measurements.
L [mH]
Fig. 11 Coil inductance plane for the tested frequencies and measured
thicknessess. Each point represents the average of 200 measurements.
L [mH]

The final estimate is computed by averaging the coating
thickness estimates provided with each frequency. The
weights assigned to each estimate bear in mind the precision
observed on each of them. The standard deviation of 200
observations for the different coating thickness estimates at
different frequencies were computed and displayed in
TABLE I.
TABLE I. STANDARD DEVIATION FOR THE THICKNESS ESTIMATES
USING EACH SINGLE FREQUENCY AND THE MULTI-FREQUENCY ALGORITHM
1 kHz
5 kHz
10 kHz
Multi-frequency
0.11 mm
19.1 µm
10.9 µm
5.50 µm
5.10 µm
0.22 mm
26.3 µm
9.50 µm
9.00 µm
6.10 µm
0.33 mm
34.5 µm
15.0 µm
3.50 µm
6.60 µm
0.44 mm
35.0 µm
7.60 µm
10.5 µm
7.60 µm
Mean
28.7 µm
10.7 µm
7.10 µm
6.30 µm
Weight
0.1298
0.3468
0.5233
The weight assigned to the estimates provided by each
frequency is also shown in TABLE I. This weight was
computed bearing in mind the ratio between the average
standard deviations observed for the different frequencies.
Finally, the coating thickness estimates are computed as
1 kHz 5 kH z 10 k Hz
ˆ ˆ ˆ ˆ
0.1 298 0.3468 0.5 2 3 3 .
t t t t= × + × + × (13)
CONCLUSIONS
A low-cost ECT coating thickness gauge was designed
and successfully validated. A simple architecture relying on
digital signal generation and processing allowed reducing the
analog circuitry necessary with particular impact on the
needed demodulation analog electronics. The used sine-fitting
algorithm revealed to be a suitable option given the low
throughput needed in the application and the limited resources
available in a microcontroller. A simple weighted averaging
algorithm was employed to combine estimates of the
inductance at different ECT operation frequencies. This
combination allowed an improvement of around 10% in the
thickness measurement precision.
As future work, it would be interesting to experiment the
developed system to measure coatings of different metals,
e.g., stainless steel and copper. Another improvement would
rely on implementing the thickness estimation algorithms in
the system available microcontroller, allowing the prompt
results display.
ACKNOWLEDGMENT
This work was supported in part by the Portuguese
Foundation for Science and Technology - FCT-MCTES under
grant EXPL/EEI-EEE/0394/2021.
This work is funded by FCT/MCTES through national
funds and when applicable co-funded EU funds under the
project UIDB/50008/2020.
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