238 R Reinaldo / Study of Planar Magnetic Induction Tomography Depth Detection Capability

and Its Imaging Quality Evaluation

Prosiding Pertemuan Ilmiah XXVIII HFI Jateng & DIY, Yogyakarta, 26 April 2014

ISSN : 0853-0823

Study of Planar Magnetic Induction Tomography Depth Detection

Capability and Its Imaging Quality Evaluation

R Reinaldo

1, M R Baidillah

2, Warsito Purwo Taruno

2, Agus Setyo Budi

1

1Department Of Physics, Universitas Negeri Jakarta, Jakarta Timur, Indonesia 2CTECH Labs Edwar Technology. Co, Alam Sutera, Tanggerang, Indonesia

rifkyreynaldo@gmail.com

Abstrak – Planar Magnetic Induction Tomography (PMIT) merupakan sebuah pengembangan mutakhir sistem

pencitraan Magnetic Induction Tomography (MIT). PMIT pada dasarnya dikembangkan untuk mengatasi permasalahan

pencitraan bahan konduktif yang mana pengukuran hanya dapat dilakukan pada salah satu permukaan bahan.

Konfigurasi desain planar yang dimiliki PMIT menjadikannya sangat cocok untuk diterapkan pada bidang-bidang

aplikasi seperti pengujian tak-merusak (NDT) dan Geofisika. Hasil riset terbaru memperlihatkan bahwa sistem PMIT

memiliki kelemahan dalam hal mencitrakan objek yang berada pada kedalaman tertentu dari permukaan sensor sistem.

Namun demikian, akan lebih baik apabila hal ini dapat dinyatakan secara kuantitatif, sehingga kelemahan tersebut

dapat terukur dan terjelaskan dengan baik. Dalam makalah ini, akan didemonstrasikan simulasi pengujian kemampuan

deteksi kedalaman sistem PMIT serta evaluasi kualitas hasil pencitraan yang didapat secara kuantitatif menggunakan

beberapa teknik pemrosesan citra digital.

Kata kunci: magnetic induction tomography, planar, sensor, pengujian tak-merusak, pemrosesan citra digital

Abstract – Planar Magnetic Induction Tomography (PMIT) is an emerging development of Magnetic Induction

Tomography (MIT) imaging system that is developed to overcome imaging process restriction that the measurements can

only be taken from one surface of conductive materials under testing. The planar design configuration makes it quite

attractive to be applied in fields such as Non-Destructive Testing (NDT) and Geophysics. The recent study shows that

PMIT has a weakness in terms of detecting object that is located at a particular distance from the sensor. However, it

would be better if it can be represented quantitatively, so the weakness can be measured and well explained. In this

paper, simulation of a PMIT system is demonstrated to test its depth detection capability and its imaging quality is also

evaluated quantitatively using several digital image processing techniques.

Key words: magnetic induction tomography, planar, sensor, non-destructive testing, digital image processing

I. INTRODUCTION

Planar Magnetic Induction Tomography (PMIT) is an

emerging development of Magnetic Induction

Tomography (MIT) [1] imaging system that is developed

to overcome imaging process restriction that the

measurements can only be taken from one surface of

materials under testing [2-3]. The planar configuration of

PMIT makes it quite attractive to be applied in Non-

Destructive Testing (NDT) and Geophysics, besides its

contact-less and non-invasive features [4]. The most

recent study of PMIT is the one that carried out by

Soleimani et all [5]. According to the results, PMIT has

an unsatisfactory performance because of its week depth

detection capability. It means, for objects under testing

that are located at a particular distance from the sensor,

the image that its produce can experience quality

degradation. In specific, this occurs when the objects are

not located in the sensitive region of the sensor.

Soleimani et all discovered that the maximum

detectability depth of PMIT is less than 5 cm. This

disadvantage definitely can reduce the potential of PMIT

to be applied for instance in geophysics to detect metallic

objects that far away bellow the ground surface.

However, from a fundamental point of view, no matter

how week the system capability, it should always be

represented quantitatively. Therefore, the weakness can

be measured and well explained.

II. SYSTEM DESCRIPTION

The simulated PMIT system used in the perfect study

consists of 16 identical and equally spaced transmitter-

sensor coils that are arranged in 4 × 4 matrix as can be

seen in Figure 1(a) and Figure 1(b) for the coil sequence.

Each coil is designed has 3.9 cm inner diameter, 4.1 cm

outer diameter, 3.4 cm length and 100 numbers of turns.

These parameters are chosen based on what can be found

on the literature [5]. Each of these16 coils is driven

individually with harmonic signal of 1A current, 50 KHz.

According to sensitivity model theory [6], for a 16-

channels system, total number of induced voltage

measurements will be (16 × 15)/2 = 120.

(a)

(b)

Figure 1. (a) Coil Array. (b) Coil Sequence.

R Reinaldo / Study of Planar Magnetic Induction Tomography Depth Detection Capability

and Its Imaging Quality Evaluation

239

Prosiding Pertemuan Ilmiah XXVIII HFI Jateng & DIY, Yogyakarta, 26 April 2014

ISSN : 0853-0823

III. METHODOLOGIES A. Forward Model

Forward problem of MIT is an eddy current problem

that can be derived mathematically from Maxwell’s

equation for quasi-static approximation [7]. This

derivation can be written in terms of the magnetic vector

potential, A for the harmonic excitation cases using

complex phasor notation as:

(1)

Where µ is magnetic permeability, σ is electrical

conductivity, and Js is driving current density applied at

an excitation coil. If the total current at an excitation coil

is 1A, the sensitivity map also known as the Sensitivity

matrix can be defined as [8]:

(2)

Where Vij is the measured voltage for i-j coil pair, σk is

the conductivity of k-th voxel, Ωk is the volume of k-th

voxel, Ai and Aj are respectively solutions of the forward

problem when the excitation coil i is excited with 1A

current and sensing coil j is excited with unit current. The

number of voxels in this simulation is chosen to be

32x32x32. Figure 2 shows the Sensitivity map coupling

for several coil pairs in the simulated system.

(a) (b)

(c) (d)

Figure 2. Sensitivity map coupling for coil pair (a) 1-3, (b) 1-

16, (c) 4-13, and (d) 4-16 in the simulated system.

B. Inverse Solver

To solve inverse problem of the system, in this

simulation we use a well-known inverse technique that is

widely used in electrical tomography cases, that is

Lanbewer algorithm which is also known as Iterative

Linear Back-Projection technique. It is noted that, inverse

problem in electrical tomography systems are mainly ill-

posed. Therefore, it will need a regularization. The

Iterative Linear Back-Projection technique aims to find

the minimum least square error of a function through an

iterative regularized manner [6]. The algorithm procedure

of the technique is given by:

(3)

Where x is the reconstructed parameter vector, S is the

system’s sensitivity matrix, V is the measurement vector,

and λ is the regularization parameter. Actually, in this

algorithm we are free to choose whatever value for the

number of iteration and regularization parameter.

However, in this occasion we find the parameter value

and the number of iteration based on the smallest image

error and the fastest convergence rate criteria that can be

seen on Figure 3.

Figure 3. Convergence plot of Iterative Linear Back-Projection

Algorithm in this simulation.

C. Image Quality Measures

The imaging quality of the system in this simulation is

evaluated by measuring several image quality parameters

that had been already proposed and used by Adler et all

and Soleimani et all [9-10]. These parameters are

resolution (RES), positioning error (PE), and shape

deformation (SD). Procedure that is used to implement

this method, as follow: the chosen layer of the

reconstructed image first is converted to a binary image

that is defined as:

(4)

Where [.] is the truth statement that will give 1 if the

condition is satisfied, else 0. RES is defined as:

(5)

Where A0 is the pixel area of true conductivity

distribution. RES value should be close to 1 in order for

the algorithm correctly represents true area of the

distribution. In this occasion, we define our own

formulation to calculate SD as:

(6)

Where C is the boundary region of A0. So, the first term

in (6) means the total pixel amplitude of b outside C. The

value of SD should be close to 0, which shows there is no

degradation in the reconstructed shape. PE measures the

extent to which a reconstructed image faithfully

represents the position of the image target based on the

Center of Mass (CoM) of both images [9].

240 R Reinaldo / Study of Planar Magnetic Induction Tomography Depth Detection Capability

and Its Imaging Quality Evaluation

Prosiding Pertemuan Ilmiah XXVIII HFI Jateng & DIY, Yogyakarta, 26 April 2014

ISSN : 0853-0823

Figure 4. Depth detection capability imaging test setup and result.

Table 1. Imaging quality evaluation result.

Inclusion depth (cm) Image RES RES error (%) CoM (x,y) PE error (%) SD (%)

1 True 1.00 0.00 (16.50, 16.50) 0.00 0.00

Reconstructed 1.38 27.45 (16.50,16.50) 0.00 3.66

2 True 1.00 0.00 (16.50, 16.50) 0.00 0.00

Reconstructed 1.22 18.35 (16.50, 16.50) 0.00 17.15

3 True 1.00 0.00 (16.50, 16.50) 0.00 0.00

Reconstructed 1.30 23.30 (16.50, 16.74) 1.00 16.34

4 True 1.00 0.00 (16.50, 16.50) 0.00 0.00

Reconstructed 0.92 8.47 (16.50, 24.30) 29.77 58.17

5 True 1.00 0.00 (16.50, 16.50) 0.00 0.00

Reconstructed 0.91 10.10 (20.58, 16.09) 16.57 95.65

Inclusion depth Experiment setup Sliced true image Sliced reconstructed image

1 cm

2 cm

3 cm

4 cm

5 cm

R Reinaldo / Study of Planar Magnetic Induction Tomography Depth Detection Capability

and Its Imaging Quality Evaluation

241

Prosiding Pertemuan Ilmiah XXVIII HFI Jateng & DIY, Yogyakarta, 26 April 2014

ISSN : 0853-0823

III. RESULTS AND DISCUSSION Several simulation experiments were conducted to test

depth detection capability of the PMIT system. Five

experiments were conducted and the setup can be seen in

the second column of Figure 4. The system is tested to

detect two identic inclusions that are steel cube with the

side length of 3 cm, electrical conductivity of 4.02×106

S/m, and relative permittivity and permeability of 1. The

depth of the inclusions to the coil array are varied for

each simulation, which are 1,2…5 cm. Third and fourth

column in Figure 4 are respectively sliced true and

reconstructed images of the inclusions.

It can be seen that reconstructed images for the depth

cases 1, 2 and 3 cm give satisfactory results. These

images are correctly represent where the inclusions are

located. However, for the depth cases of 4 and 5 cm, the

results are in contras. Table 1 shows the imaging quality

evaluation result for each depth variation. It can be

inferred from the result that the greater the depth of the

inclusions, the larger the PE and SD that occurs in the

reconstructed images. For the depth cases of 4 and 5 cm,

the PE and SD are greater compared to the others, which

means the reconstructed images are not capable anymore

to correctly represent the inclusions. These give us an

intuition that the system capability to maintain its

imaging performance degrades when detecting inclusions

that depth are greater than the maximum of the system

can reach, in this case, 3 cm. According to literature,

what can affect the depth detection capability of PMIT is

not the image reconstruction algorithm or the number of

inclusions. PMIT system detectability depends on its

sensitivity and location of the inclusion(s). It had been

discovered that the sensitive region of PMIT tends to

have a trapezoidal or spherical shape [2]. Working

frequency of 50 KHz also made the system obtained less

information about the inclusion, because the eddy current

can only penetrate 0.112 cm. In every experiment, the

skin effect is not neglected. Therefore, it is clear that the

larger the depth, the less the information can be obtained

from the inclusions.

IV. CONCLUSION

This study has shown the depth detection capability of

PMIT system and evaluation of its imaging quality. The

depth detectability performance of the system is highly

depending on its sensitivity and the location of the

object(s) under testing. The farther the object(s) from the

system sensitive region, the lower the quality of the

reconstructed image that will be produced. How good or

bad the imaging quality can be measured quantitatively

through evaluating several image quality parameters.

Nevertheless, further development has to be concerned

about how to increase the sensitivity range of the system,

so its maximum detectability depth can be enhanced.

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