# Magnetic Induction Tomography Spectroscopy for Structural and Functional Characterization in Metallic Materials

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

_{0}), whereas the phase spectrum is the difference between the measured phase in the presence of an object (θ) and that of free space (θ

_{0}), shown in Figure 2 and Figure 3.

## 3. Sensor Modelling

## 4. Spatio-Spectral Image Reconstruction Algorithm

## 5. Results and Analysis

#### 5.1. Single Metal Sample

#### 5.2. Different Samples at Different Locations

#### 5.3. Non-Conductive Inclusion in Conductive Liquid

#### 5.4. Spectral Derivative for Structural and Functional Classification

#### 5.5. Complex Plot from Reconstruction

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Measurement setup: (

**a**) sketch of the sensor array and object in the sensing region, switch, LCR meter and PC connection (signal, solid-line; control, dashed-line); (

**b**) photograph of the system.

**Figure 2.**Free space background measurement of amplitude (

**left**) and phase (

**right**) for 28 coil-pair combinations.

**Figure 3.**Amplitude (

**left**) and phase (

**right**) spectrum of a test sample plotted against the background.

**Figure 4.**Spectral plot for metallic samples (conductivity variations). Solid line for amplitude ratio (left vertical axis); dashed line for phase difference (right vertical axis).

**Figure 5.**Spectral plot for size variations. Solid line for amplitude ratio (left vertical axis); dashed line for phase difference (right vertical axis).

**Figure 6.**Spectral plot for metallic structure. Solid line for amplitude ratio (left vertical axis); dashed line for phase difference (right vertical axis).

**Figure 7.**Spectral derivative for metallic samples with conductivity variations (

**left**: amplitude,

**right**: phase).

**Figure 11.**Spectral profile and its derivative (data and reconstructed image values) for a 0.25 inch copper rod (σ = 58.4 MS/m).

**Figure 12.**Spectral profile and its derivative (data and reconstructed image values) for a 0.25 inch aluminum rod (σ = 26.3 MS/m).

**Figure 13.**Spectral profile and its derivative (data and reconstructed image values) for brass (σ = 16.1 MS/m) rod 0.25 inch.

**Figure 14.**Spectral profile and its derivative (data and reconstructed image values) for liquid GaInSn (σ = 3.2 MS/m) in a 0.25 inch tube.

**Figure 15.**Spectral profile and its derivative (data and reconstructed image values) for (

**a**) copper (σ = 58.4 MS/m) rod 0.25 inch at pos = 10 and brass (σ = 16.1 MS/m) rod 0.25 inch at pos = 40; (

**b**) brass (σ = 16.1 MS/m) rod 0.25 inch at pos = 10, aluminum (σ = 26.3 MS/m) rod 0.25 inch at pos = 25, and copper (σ = 58.4 MS/m) rod 0.25 inch at pos = 40.

**Figure 16.**Spectral profile and its derivative (data and reconstructed image values) for wood cube 1 cm

^{3}at pos = 10 in liquid GaInSn 35 mL 1 inch tube.

**Figure 17.**Spectral profile and its derivative (data and reconstructed image values) for plastic rods 0.25 inch at pos = 10, pos = 25, pos = 40 in liquid GaInSn 35 mL in a one-inch tube.

**Figure 18.**Z (

**left**) and θ (

**right**) spectral gradient (df) metallic samples with conductivity variations.

**Figure 22.**Combination of normalised Z-θ spectrum metallic structures: hollow, hollow-with-inclusion, solid.

**Figure 26.**(

**a**) Complex plot of the impedance for inclusions; (

**b**) focusing on one void, but various background data.

**Figure 27.**Complex plot of impedance for different samples at different locations: (

**a**) two samples at left and right side; (

**b**) three samples located at left, centre and right side.

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**MDPI and ACS Style**

Muttakin, I.; Soleimani, M.
Magnetic Induction Tomography Spectroscopy for Structural and Functional Characterization in Metallic Materials. *Materials* **2020**, *13*, 2639.
https://doi.org/10.3390/ma13112639

**AMA Style**

Muttakin I, Soleimani M.
Magnetic Induction Tomography Spectroscopy for Structural and Functional Characterization in Metallic Materials. *Materials*. 2020; 13(11):2639.
https://doi.org/10.3390/ma13112639

**Chicago/Turabian Style**

Muttakin, Imamul, and Manuchehr Soleimani.
2020. "Magnetic Induction Tomography Spectroscopy for Structural and Functional Characterization in Metallic Materials" *Materials* 13, no. 11: 2639.
https://doi.org/10.3390/ma13112639