Computer Graphics and Image Processing by Field Theory
Yoshifuru SAITO1,
1 Graduate School of Hosei University. Tokyo 184-8584, Japan

Field theory in physics is the most important counterpart establishing the modern physics. Startingwith the Newton mechanics, any of the field problems, such as the theory of sound, light,
electromagnetism reduce into solving for their field governing equations. Classical field theory had
exploited the vector and variational calculus, and led to the modern quantum mechanics.
Mathematically, the orthogonal functions representing the solution of field equations have led asystematical formulation of the Hilbert space theory [1].
On the other side, modern computer graphics has been started with the developments of modern
high-speed digital computers. At the beginning of computer graphics, the simple primitivegeometrical methodologies were widely used to construct a graphical object. The extensive spreadingof the digital computers with higher performance has stimulated the expectation of the computer
graphics versatilities, because the computer graphics is capable to communicate a large amount of
information. In order to respond and realize, such an expectation and requirement to the computer
graphics, it is not simple geometry any more, and more advanced geometry, such as the projective,
topological, homotopic geometries and cellar spatial theory, must be applicable [2].
The problems of modern computer graphics to be breakthrough may be focused on the two majordifficulties, one is the data quantity and the other is how to unite with the simulation technology ofexistent engineering as well as physics. The field theory of computer graphics described in this paper
is one of the systematic approaches to remove these difficulties.
The image processing, compressing, visualizing, identifying and animating are efficiently carriedout by means of the field theory. The field theory of computer graphics regards an each of the pixels as
one of the potentials in vector fields. As is well known, gradient operation to the scalar potentials
yields the image vector fields. A norm distribution of the field vectors generates a sketch like image.
Also, an inner product between the unit directional and image vectors generates a three-dimensional
shadowed image. Further spatial differential operation, i.e., divergence operation, changes the image
vector into a scalar quantity called an image field source density. In electromagnetic fields, this source
density corresponds to an electric charge density, while the image scalar potential corresponds to anelectric scalar potential called a voltage. Such an electromagnetic fields, the voltage can be exactly
evaluated by solving a partial differential (Poisson’s) equation having the electric charge density as an
input electric field source [3,4]. This is true in the image source density. Namely, an exact original
image can be recovered from the image source density. Since the image source density can beobtained by the twice-partial differentiations, i.e., Laplacian operation, the constant and first
derivative terms are essentially not included in the source density. This means that the original image
is compressed in terms of the image source density while the singular point information of the original
image is extracted by the Laplacian operation in homotopic sense. Even though, an efficiency of thedata compression depends on each of the distinct images, data compression is always possible notloosing any original image information.
References[1] P.M.Morse and H. Feshbach, “Methods of Theoretical Physics,” McGraw-Hill, New York (1953).
[2] J.H.C.Whitehead, "Combinational Homotopy 1," Bulletin of American Mathematical Society, Vol.55, pp.213-245 19
49[3] P.P.Silvester “Modern Electromagnetic Fields”, Prentice-Hall, Inc., 1968.
[4] P.P.Silvester and R.L.Ferrari, “Finite elements for electrical engineers”, Cambridge University Press (1983).

Development of a New High Sensitive Eddy Current Sensor
Hiroki KIKUCHIHARA1, a, Iliana MARINOVA2,b , Yoshifuru SAITO3,cManabu OHUCHI3, d, Hideo MOGI3,b and Yoshiro OIKAWA3,e1

Graduate School of Hosei University, Tokyo 184-8584, Japan
2
3

Technical University of Sofia, Sofia 1756, Bulgaria

Denshijiki Industry Co., Ltd, Tokyo 115-0051, Japanahiroki.kikuchihara.6e@stu.hosei.ac.jp, biliana@tu-sofia.bg, cysaito@hosei.ac.jpdet.factory@emic-jp.com, foikawa@emic-jp.com

Keywords: Eddy current, Nondestructive testing

Abstract. Eddy current testing (ECT) is one of the most representative nondestructive testing
methods for metallic materials, parts, structures and so on. Operating principle of ECT is based on
two major properties of the magnetic field. One is that alternating magnetic field induces eddy current
in conducting materials. Thereby, an input impedance of the magnetic field source, i.e., electric source,
depends on the eddy current path. Second is that the magnetic field distribution depends not only on
the exciting but also on the reactive magnetic fields caused by the eddy currents in targets. Former andlatter are the impedance sensing and magnetic flux sensing types, respectively.
This paper concerns with an optimization of a new magnetic flux sensing type sensor named“∞ coil”. Exciting and sensing coils are composed of ∞ shape coil and a finite length solenoid coilwound on ferrite bar, respectively. Development of this ∞ coil fully depends on the 2D and 3D finite
elements method modeling. According to the simulation results, we have worked out two types of ∞coils. Practical experiments reflect the validity of both simulation and design aims, quite well. Thus,
we have succeeded in developing ∞ coil having a higher sensibility compared with that ofconventional one.
Introduction
Modern engineering products such as air-plane, automobile, smart building, high speed train andso on are essentially composed of metallic materials for forming the shape of product, suspending themechanical stress and constructing the structural frames. In particular, the mass transportation
vehicles, e.g. large air plane, high-speed train, express highway bus and so on, carrying a large numberof people are required ultimately high safety as well as reliability.
To keep the safety, nondestructive testing to the metallic materials is one of the most important
technologies because most of the structure materials are composed of the metallic materials.
Various nondestructive testing methods, such as eddy current testing (ECT), electric potential
method, ultrasonic imaging and x-ray tomography, are currently used. Among these methods, ECT
needs not complex electronic circuits and direct contact to target. Furthermore, a target whose major
frame parts are composed of conductive metallic materials can be selectively inspected by ECT [1,3].
In this paper, a new ECT sensor coil named “∞ coil” is proposed. Development of this ∞ coil fully
depends on the 2D and 3D finite elements method modeling and also optimizes the eddy current
testing methodology.
The most important key idea of the ∞ coil is in setting the sensor coil in the lowest magnetic fieldspace caused by the exciting coils, because this sensor coil is capable of catch only the magnetic fields
caused by the detour eddy currents flowing around a defect. This paramount important key idea has
been yielded by carrying out the intensive 2D finite elements simulations. After that 3D finite
elements simulation has been carried out to check up the validity of this key idea.

Thus, we have succeeded in innovating and optimizing a new high sensibility eddy current sensor“∞ coil” by means of the 2D and 3D finite elements simulations [2,3].
New ECT Sensor CoilOperating principle of the separately installed sensing coil type is fundamentally based on that thesensing coil catches the magnetic field intensity variation caused by the detour eddy currents flowing
around a defect in the target metallic materials.
To realize this, three methodologies could be considered. The first detects the variation of entire
magnetic fields caused by both exciting and eddy currents. In this case, the sensing coil detects themagnetic fields distribution caused by the detour eddy currents around defects among the entire
magnetic fields. The second is that the sensing coil surface is installed in a perpendicular direction toan exciting coil surface. This means that the sensing coil never induce an electric voltage caused by
the exciting fields because the surface of sensing coil always parallels to the exciting magnetic fields,
so that this sensing coil is capable of selectively catching the magnetic fields caused by the detour
eddy currents around a defect. This type of sensor has high liftoff characteristics compared with thoseof the first one. The final third one is that the sensing coil is set on the zero exciting magnetic fields
space in addition to the second one coil layout. This final one is capable of catching only the magnetic
fields caused by the detour eddy currents around a defect, and has been innovated in this paper by aseries of the intensive finite elements simulations.
At the beginning of our new sensor project, to concentrate the magnetic fields, the two exciting
coils whose magneto-motive forces becomes in additive were employed, as shown in Fig.1.
To decide a location of sensing coil whose
surface is orthogonal to the exciting magnetic
fields, we have carried out a lot of 2D finite
elements simulations. As a result, it is foundthat there is nearly zero exciting field space
between the two exciting coils. This leads toour ∞ coil. Since the zero exciting magnetic
fields condition in addition to the orthogonal
Fig. 1 Two exciting coils
coil surface layout to the exciting magnetic
fields enhances the sensibility of ∞ coil in an ultimately. Fig 2(a) shows an exciting magnetic field
intensity distribution. In this figure, it is possible to find the zero magnetic fields space between thetwo parallel exciting coils. According to this simulation result, we put on a ferrite bar at the bottom
surface of the two exciting coils in order to enhance the sensibility of sensor coil. As shown in
Fig.2(b), setting the ferrite bar hardly disturb the exciting magnetic fields intensity distribution. Thus,
winding around the sensor coil around the ferrite core leads to an ultimately optimized high sensibility
ECT sensor, i.e., ∞ coil.

(a) Without ferrite bar(b) With ferrite bar
Fig. 2 Magnetic fields intensity

Table 1 Various constants used in the 3D simulation.
Exciting coil
Coil outer diameter
Coil inner diameter
Coil length
Number of turnInput current(peak)
Frequency

22.4mm
20mm
10mm
75
250mA
256kHzSensing coilFig. 3 3D simulation model of the ∞ coil

Coil outer diameter
1.4mm×2.4mm
Coil inner diameter
1mm×2mm
Coil length
6mm
Number of turn100
Axis core
JFEferrite_MB1H _23°C

To evaluate the validity of our ∞ coil performance, we employed a 3D simulation model shown in
Fig.3.Table 1 lists various constants used in the 3D simulation. The eddy currents in a plane target
located under the two exciting coil surfaces are shown in Fig. 4, where the two adjacent exciting coilsside to the no-defect, 0 degree, 90 degree and 45 degree line defects are shown in Figs. 4(a),4(b),4(c)and 4(d), respectively.

(a) No defect(b) 0 degree defect(c) 90 degree defect(d) 45 degree defectFig. 4 Eddy currents in a plane metallic target.

(a) No defect(b) 0 degree defect(c) 90 degree defect(d) 45 degree defectFig. 5 Magnetic flux density vector distributions in the ferrite bar

Fig. 6 Induced voltages in the sensor coilFig. 5 shows the magnetic flux density vector
distribution corresponding to that of eddy
currents in Fig. 4. Observe the magnetic flux
density vector distributions in Fig. 5 reveals
that the sensing coil wound around the ferrite
bar could be induced the electric voltages not
the cases (a), (b), (c) and (d). The induced
voltages of the sensor coil under the conditions(a)-(d) in Figs. 4 and 5 are shown in Fig. 6.
Observing the induced voltages in Fig.6
reveals that the case (d) yields the highest
voltage.

Experiment
We employed two coppers plate having 1mm thickness as target metal plates. One has no defectand the other has a line defect having 2mm width. Also, we worked out a prototype of the ∞ coil.
Table 2 lists various constants of the prototype ∞ coil. We used two exciting coils and one sensing coilhaving ferrite core. Fig. 7 shows a picture of the prototype ∞ coil. The physical dimensions of thisprototype ∞ coil are corresponding to the 3D simulation model shown in Fig.3.
Table 2 Various constants of the prototype ∞ coil.
Exciting coil

Sensing coilFig.7 Picture of the prototype ∞ coil.

Conductor length
4.7m
Diameter of conductor
0.4mm
Coil outer diameter
23mm
Coil inner diameter
20mm
Coil length
10mm
Number of turn75
Number of coil layers
3
Number of coils
2
Conductor length
60cm
Diameter of conductor
0.1mm
Axis core
Ferrite bar (MnZn)
Coil outer diameter
1.4mm×2.4mm
Coil inner diameter
1mm×2mm
Coil length
6mm
Number of turn100
Number of coil layers
2

Fig.8 Measured voltages of the practicalsensing coil.
①②

Fig. 8 shows the measured voltages
corresponding to that of cases in Figs. 4 and 5.
Even though the peak measured voltage issomewhat smaller than those of Fig.6, sensing
characteristics of the prototype ∞ coil wellcorrespond to that of Fig. 6. Thus, we havesucceeded in innovating new type eddy current
sensor "∞ coil" by means of the 2D and 3D
finite elements simulations.

③Fig. 9 Target piece with three defects.

Fig. 10 ET-5002 produced by Denshijiki
Industry Co., Ltd.

To compare ∞ coil with conventional ECT sensors, we measured liftoff characteristics of three
type sensors. Fig. 9 shows a target piece which is composed of SS400 steel. The target piece has threedefects which are 20 mm length, 0.2 mm width and 0.2, 0.3, 0.4 mm depth on the surface. The defectwas made by the electrical discharge machining. We moved the tested three ECT sensors with
50mm/s speed and measured the signal of defect by means of the commercial based signal processing
device "ET-5002", shown in Fig. 10. Operating principle of the ET-5002 is that the equilibriumbalanced condition of the bridge circuit picks up only the discontinuity of signals when the sensor
runs over the defect. We employed 256 kHz operating frequency. Liftoff was changed every 1mmfrom 1mm to 10mm. The gain in dB, high pass filter in Hz, low pass filter in Hz and the liftoff
distances were set up to the ET-5002.
Table 3 lists specifications of ∞ coil,
Table 3 Specification of the tested three sensors
Magnetic flux sensing type sensor and∞ coilSensing coil
Exciting coil
Impedance sensing type sensor. The size ofDiameter of conductor:
0.1mm Diameter of conductor: 0.12mm
sensing coil and exciting coils of the ∞ coil were
Axis core:
Ferrite bar (MnZn) Axis core:No
Coil inner diameter: 0.5mm×2mm Coil inner diameter:
6mm
constructed by means of the optimization based
Coil length:
4mm Coil length:
6mm
on the 3D finite elements simulations.
Number of turn:
100 Number of turn:100
Number of coil layers
3 Number of coil layers
3
Magnetic flux sensing and Self-induction
Number of coils:
1 Number of coils:
2
type sensors are the commercial based products
Magnetic flux sensing type sensor
of Denshijiki Industry Co., Ltd.
Sensing coil
Exciting coil
Diameter of conductor:
0.1mm Diameter of conductor: 0.12mm
Both of the sensors are based on the
Axis core:
Ferrite bar (MnZn) Axis core:No
differential
property of 8 shape coil. The
Coil inner diameter: 1mm×2mm Coil inner diameter:
4mm
Coil length:
10mm Coil length:
12mm
difference between them is that the magnetic
Number of turn:
50 Number of turn:100
flux sensing type employs an independent
Number of coil layers
2 Number of coil layers
1
Number of coils:
2 Number of coils:
1
exciting coil surrounds 8 shape coil. On the
Impedance sensing type sensor
other side, the exciting magnetic fields of
Sensing coil
Exciting coilself-induction type are produced by the currents
Diameter of conductor:
0.1mm
Axis core:
Ferrite bar (MnZn)
flowing through the 8 shape coil.
Coil inner diameter: 0.5mm×2mm
Thus, both two commercial based sensors are
Coil length:
10mm
Number of turn:100
capable of detecting the defects in the target
Number of coil layers
3materials with high sensibility.
Number of coils:
2Fig. 11 shows induced voltages of the three typesensors when passing close to and get away from atarget piece having a line defect.
Observe the signal makes it possible to find the 5
distinct peaks in each of the sensor signals. Among
5 peaks, the first and last ones are occurred when
the sensors are getting close and away from thetarget. Thereby, let us focus on the 3 peaks causedby the three defects excepting the first and lastpeaks.
Magnitudes of these 3 peaks depend on each of
Fig. 11 Induced voltage (liftoff = 2mm)
the defect depths while every sensor is used.
Among the signals in Fig. 11, the signal obtained
by ∞ coil is the most sensitive compared with that of the others. To evaluate a more detailed
characteristic, we focus on the signal caused by defect whose depth is 0.2mm.
Fig. 12 shows the peak induced voltages when changing the liftoff distances from 1mm to 10mm. It
is found that the ∞ coil is superior in most of liftoff cases. However, we confront to intensive
difficulty when obtaining the highly noisy signals. To overcome this difficulty, it is required toevaluate the signal to noise (S/N) ratio. In the present paper, the S/N ratio is defined by the ratio
between the peak defect and no defect signals.
Fig. 13 shows results for the S/N ratios. As shown in Fig. 13, the S/N ratio is inversely proportional
to the magnitude of liftoff. Comparison of the results in Figs. 12 and 13 suggests that our ∞ coil issuperior S/N ratio to the others. Thus, we have succeeded in developing ∞ coil having a higher
sensibility compared with those of conventional one.

Fig. 12 Peak signal magnitude vs. liftoff

Fig. 13 S/N Ratio vs. liftoff

Conclusion
As shown above, we have succeeded in innovating and optimizing a new high sensibility eddy
current sensor "∞ coil".
All of the 2D and 3D finite elements simulations were carried out by the finite element package"Femtet" produced by Murata Software Co. Ltd.
References[1] I.Marinova, S.Hayano and Y.Saito, Ployphase eddy current testing, Journal of Applied Physics,
Vol. 75, No.10, pp. 5904-5906, 1994.
[2] N.Burais and A.Nicolas, Electromagnetic field analysis in remote field eddy current testing
systems, IEEE Transactions on Magnetics, Vol.25, No.4, pp.3010-3012, 1989.
[3] S.McFee and J.P.Webb, Automatic mesh generation for h-p adaption, IEEE Transactions on
Magnetics, Vol.29, No.2, pp.1894-1897, 1993.

Enhance the Sensibility of the Eddy Current Testing
Kouki MARUYAMA1, a, Illiana MARINOVA2,b
and
Yoshifuru SAITO1,c
1 Graduate School of Hosei University, Tokyo 184-8584, Japan
2 Technical University of Sofia, Sofia 1756, Bulgaria
a kouki.maruyama.8n@stu.hosei.ac.jp, b iliana@tu-sofia.bg, c ysaito@hosei.ac.jp

Keywords: ECT, resonance, sensibility.
Abstract. Eddy current testing (ECT) is one of the most representative nondestructive testing

methods for metallic materials, parts, structures and so on. This paper proposes improvement ofsensibility of the impedance sensing type ECT. Sensibility of the ECT is improved by means of threesteps. One is an optimum exciting frequency selection. We employ the natural parallel resonant
frequency of ECT coil. The second is to increase the sharpness of the resonance curve on impedance
versus frequency characteristic by changing the coil connection. Finally, we attach externallycapacitor to reduce the resonance frequency into low. This makes it possible to enhance thesensibility of the impedance sensing type ECT operating at the resonant frequency.
Introduction
Modern engineering products such as air-plane, automobile, smart building, high speed train andso on are essentially composed of metallic materials for forming the shape of product, suspending themechanical stress and constructing the structural frames.
Among various nondestructive methods, ECT does not require complex electronic circuits anddirect contact to target. Furthermore, target whose major frame parts are composed of conductive
metallic materials can be selectively inspected by ECT.
Operating principle of the ECT is based on the two major properties of magnetic field. One is that
exposing the conductive materials to the alternating magnetic fields induces eddy current in all of the
conducting materials. Thereby, the input impedance of the magnetic field source, i.e., electric source,
can detect the change of the target impedance caused by defects blocking eddy current flowing. The
ECT based on this principle is called impedance sensing type. The other type utilizes a separately
installed sensor coil to detect the leakage magnetic flux change. The magnetic field of ECT iscomposed of two components: one is the exciting and the other is the reactive component of magnetic
fields. The reactive component of magnetic field is caused by the eddy currents in the target so thatchange of eddy current paths changes the reactive magnetic fields. Thus, the independently installed
sensor detects this magnetic field change. This type is called a separately sensing coil type.
This paper proposes improvement of sensibility of the impedance sensing method. Improvementof the sensibility is carried out in the three major steps. The first is to select the optimum exciting
frequency. We select the natural parallel resonant frequency of the ECT sensor coil when facing witha wholesome part of target. A system comprising the ECT facing with the wholesome part of target
takes the maximum pure resistive impedance. When the ECT sensor coil meets with a defect of target,
this resonance condition is essentially not satisfied. This makes it possible to maximize thedifference between the resonance and not resonance impedances. The second step is to increase theresonant impedance as well as to sharpen the peaky impedance versus frequency characteristic bychanging the coil connection. Since the natural parallel resonant impedance become larger, then thedeviation between the resonant and not resonant impedances is essentially larger. This essentiallyenhances the sensibility of ECT sensor. Finally we attach an external capacitor to reduce the resonant
frequency into low and also to enhance the sensibility.

Enhancement of ECT Sensibility

Operating principle of ECT. Let anarbitrary finite length solenoid coil shown in
Fig. 1(a) be an eddy current sensor coil. When
we put this sensor coil on a copper plate as
shown in Fig. 1(b) and apply an alternating
current to the sensor coil, because of the
Faraday’s law, eddy current is induced as areaction of the alternating magnetic fields.
Measure the input impedance of the sensor coil
is able to diagnose a difference of the target
copper plate condition between no defects (Fig.
1(b)) and 2mm crack defect (Fig. 1(c)). This issimilar to the secondary impedance change
detection from primary input terminal in aconventional single phase transformer. Thus, it
is obvious that a simple finite length solenoid
coil can detect the defects of the target
conducting materials. This is the operating
principle of impedance sensing type ECT.
Natural resonance phenomena of ECT
coil. Any of the coils always exhibit an
inductive property because of the magnetic
fields around them by applying a current into
the coil. However, any of the coils have thecapacitances among the coils. Even though asimple finite length solenoid coil shown in Fig.
1(a), it is possible to observe its natural
resonance phenomena as shown in Fig. 2. Figs
2(a) and 2(b) are the frequency f versus
impedance |Z| and the frequency f versus phaseψcharacteristics, respectively.
Optimum operation frequency. Decisionof ECT operation frequency is of paramountimportance, because sensibility and searching
depth of ECT are greatly depending on theoperation frequency. Theoretically, theoperation frequency of ECT can be decided bytaking the target conductivity and its skin-depth
into account. However, final selection ofoperation frequency is determined by the pastexperiences and the practical tests.
In the present paper, we select the naturalparallel resonant frequency of the ECT sensor
coil when facing with a wholesome part of target. The ECT facing with the wholesome part of target
takes the maximum pure resistive impedance. When the ECT sensor coil meets with a defect of target,
the resonance condition is essentially not established. Therefore, the input impedance from sensor
coil input terminals is also reduced to small in value compared with those of the resonant one. Namely,
a deviation between the resonance and not resonance impedances becomes maximum value.
A sensibility ε of ECT is defined by,(1)where the reference and measured in (1) refer tothe input impedances from the ECT coilterminals when facing the ECT coil with thewholesome and defect parts of target,
respectively.
Enhancement of quality factor Q. The
sensibility of (1) is intrinsically depended
on the quality factor Q of the parallel resonancedefined by
,

(2)

where
and
are the resonant frequency
and the half width, respectively.
The quality factor Q represents a sharpnessof the resonance curve on the impedance
versus frequency coordinate. So that high Q in(2) means high sensibility in (1).
To increase the quality factor Q, we employ
the resonant connection shown in Fig. 3. Figs.
3(a) and 3(b) are the two parallel conductors
and their resonant connection, respectively.
Denoting R, L, M as the resistance,
self-inductance and, mutual inductance, it ispossible to draw an equivalent circuit of theresonant connected two conductors as shown in
Figs. 3(c), 3(d). Fig.4 shows a difference
between the normal and resonant coilconnection [4].
Practically, the resonant connection is carriedout by twisting the two coils to uniform thefacing side of both conductors as shown in Fig.
5 [5].
Reduction of the resonant frequency. As
mentioned above, the ECT operation
frequency is of paramount importance, because
sensibility and searching depth of ECT are
greatly depending on the operation frequency.
Therefore, we employ the natural parallel
resonant frequency of ECT coil as operation
frequency. But the resonantce frequency of
ECT coil is relatively high. This means a low skin depth of the eddy currents in target. Thereby,
searching depth is limited to only the vicinity of target surface. To overcome this problem, we
attach externally capacitor Ca in parallel to the originally sensor coil circuits as shown in Fig.6.
The resonant mode in Fig.2 is one of the parallel resonance phenomena so that attachment ofcapacitor Ca reduces the resonance frequency to low.

Experiment

Tested target piece and tested ECT coils.
Fig. 7 shows a target piece whose material is
SUS304 steel. A vertical line shape artificial
crack having 10mm length, 0.2mm width and
0.5mm depth had been made to the sandwiched
SUS by the electrical discharge machining.
Hereby, there is a junction of SUS at the bothends of the defect. In Fig. 7 a red square shows a
20mm by 20mm target area. The ECT sensors
measured at the 9 by 9 sampling points with
2.5mm regular spacing on this 20mm by 20mm
square area.
Table 1 lists the various constants of thetested ECT coils. The tested coil was woundaround the Manganese-Zinc type ferrite bar used
as an axial Ferrite core. Further, the coil was
twisted 175/m to compose the resonant
connection as described in Fig.3.
Reduction of the resonant frequency. We
compare the resonance frequencies when
attaching the external capacitors Ca and without
external capacitor. Fig. 8 shows the effect of Ca
to the resonant frequencies when facing on thetarget without any defects. Obviously, larger
external capacitor Ca makes it possible to reduce
the resonant frequency.
Eventhough, we have succeeded in reducing
the resonant frequency into low, the resonant
impedance becomes smaller inversely proportion
to the magnitude of attached capacitance Ca. Thismay mean that the sensibility defined by (1) may
be smaller in value when attaching a larger
capaciatnce Ca.
To check this more specifically, we evaluatedthe quality factor Q defined by (2). Fig. 9 shows
the quality factor Q when attaching the external
capacitors Ca. According to the results in Fig. 9,
it is found that an attachment of larger
capacitance Ca improves the quality factor Q but
too large capacitor Ca reduces the quality factor Q.
This is because attachment of the very large
capacitor Ca to the sensor circuit in parallel shownin Fig. 6 dominates an entire impedance, i.e.,major current flows through the externallyattached capacitor Ca but through not the sensor
circuits.
Resonance type ECT operating at 256kHz. Since the 256kHz operation frequency is oneof the most conventional operating frequencies on the current used ECTs, we have

carried out the defect serchings employing the 256kHz operating frequency to checkthe effect of externallty attached capacitor Ca in parallel to the sensor coils.
Fig.10 shows the results of defect searching facing the target having the defect locatedat 0.1mm liftoff. Observe the results in Fig. 10 suggests that any of the results visualize the
H character shape composed of the artificial defect and two mechanical junctions.
In addition, the results in Fig. 10 suggest that the sensibilities are not dependingon the attached externally capacitors Ca, i.e., any externally attached capacitors
Ca in parallel to the sensor coils hardly change the original sensibility when
operating 256kHz frequency.
R
e
s
o
n
a
n
c
e
t
y
p
e
E
C
T
operating at the resonant frequency. When the tested ECT coil is facing to the target
having the defect located at 0.1mm liftoff, attach externally capacitors Ca having
the 0pF, 100pF, 470pF, 1020pF yields the resonant frequency 2350kHz,
1700kHz, 985kHz, 860kHz, respectively.

Fig.
11
shows
each
of thedefectsearching
results
emplo
ying
their
distinctnaturalresonant
frequencies. Comparison the quality factor Q in Fig. 9 and the detected results in Fig. 11 suggeststhat there is the optimum capacitance to reduced the resonant frequency, i.e. theCa =470pF, to obtain the best detecting result. Also it has been confirmed that
attachment of the very large capacitor Ca to the sensor circuit in parallel shown in Fig. 6 dominats anentire impedance, i.e., major current flows through the externally attached capacitor Ca but not thesensor circuits.
Conclusion

New innovative idea to enhance the sensibility of ECT sensor has been proposed in this paper.
Our idea needs not any special tools but requires a consideration of natural resonance phenomena,
i.e.utilization of the resonant impedance, frequency and capacitive effect among the coils and an
externally attached capacitor.
We have selected the natural parallel resonant frequency of the ECT sensor coil when facing witha wholesome part of target. When the ECT sensor coil has met with a defect of target, the resonancecondition has not been established. This led that the impedance reduced to small in value comparedwith those at resonance condition. As a result, a deviation between the resonant and not resonant
impedances has become the maximum. Thus, the sensibility of ECT sensor has been enhanced.
Further, connection of the conductors to be applied a half of the source voltage to adjacentconductors has made it possible to enhance the capacitive effect among the conductors. Practically,
this connection has been carried out by twisting the two coils to uniform the facing side of bothconductors.
Finally, we have attached externally capacitors in parallel to the original ECT sensor coils.
Attaching external capacitor has made it possible to increase the sensibility when a optimum
external capacitance has been selected.
Thus, we have succeeded in working out one of the ultimate high sensibility resonancetype ECT sensors.
References[1] I.Marinova, S.Hayano and Y.Saito, Ployphase eddy current testing, Journal of Applied Physics,
Vol. 75, No.10, pp.5904-5906, 1994.

[2] N.Burais and A.Nicolas,Electromagnetic field analysis in remote field eddy current testing
systems,IEEE Transactionson Magnetics, Vol.25, No.4, pp.3010-3012, 1989.
[3] S.McFee and J.P.Webb, Automatic mesh generation for h-p adaption, IEEE Transactions
on Magnetics, Vol.29, No.2, pp.1894-1897, 1993.
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