# A Review on Electrical Impedance Tomography Spectroscopy

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Physical Principles of EITS

## 3. Electrical Characteristics of Materials

## 4. Sensing Methods

#### 4.1. Electrode Geometry

#### 4.1.1. Two-Dimensional EITS

#### 4.1.2. Three-Dimensional EITS

#### 4.2. Measurement Systems

#### 4.3. Measurement Noise and Error

## 5. Image Reconstruction Algorithm

#### 5.1. Main Algorithms Used for EITS

#### 5.2. Recent Developments

## 6. Image Representation

#### 6.1. Absolute

#### 6.2. Time Difference

#### 6.3. Frequency Difference

#### 6.3.1. Traditional Frequency Difference

#### 6.3.2. Relative Frequency Difference

#### 6.3.3. Weighted Frequency Difference

#### 6.3.4. Adjacent Frequency Difference

#### 6.4. Frequency-Time Difference

#### 6.4.1. Traditional Frequency-Time Difference

#### 6.4.2. Relative Frequency-Time Difference

#### 6.5. Material Fraction

#### 6.6. Model Based Representation

#### 6.7. 3D Imaging

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. List of Symbols

Symbol | Description | Unit |
---|---|---|

$\mathbf{E}$ | Electric Field | $\frac{V}{m}$ |

$\varphi $ | Electric Potential | V |

$\mathbf{J}$ | Current Density | $\frac{A}{{m}^{-2}}$ |

$\sigma $ | Conductivity | $\frac{S}{m}$ |

$\gamma $ | Admittivity | $\frac{S}{m}$ |

$\epsilon $ | Permittivity | $\frac{F}{m}$ |

$\mathbf{P}$ | Polarization | $\frac{A}{{m}^{-2}}$ |

$\chi $ | Susceptibility | 1 |

$\omega $ | Angular Frequency | $\frac{rad}{s}$ |

${\tau}_{0}$ | Relaxation Time | s |

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**Figure 4.**Differential measurement setup example with four electrodes. The equivalent impedances for the first transmitter electrode are shown, these values together with the equivalent impedances obtained with the other transmitter electrodes will generate the measurement matrix.

**Figure 5.**Example of 2D electrode geometries with eight electrodes. (

**a**) Traditional circular electrode geometry, (

**b**) planar electrode geometry. Field lines are exemplified for one electrode considering differential measurement with respect to the other electrodes. Typically, all combinations between electrodes are evaluated for Electrical Impedance Tomography Spectroscopy (EITS).

**Figure 6.**Example of 3D electrode geometries with electrodes shown in black. (

**a**) Traditional circular electrode geometry, (

**b**) planar electrode geometry. Field lines are exemplified for one electrode and one layer, considering differential measurement. Depending on the evaluation circuitry, the coupling between different layers can also be utilized.

**Figure 7.**Example of an EITS system consisting of eight electrodes, a single source, and which is digital Field Programmable Gate Arrays (FPGA)-based.

**Figure 8.**Example of absolute permittivity variation over frequency for an ice and water mixture considering: (

**a**) 100 Hz, (

**b**) 1 kHz, (

**c**) 10 kHz, (

**d**) 100 kHz, and (

**e**) 1 MHz.

Publication | Year | System | Technology | Source | Frequency Range | Frequency Signal | Drive Pattern/Sensing Strategy | Total of Electrodes | Electrode Geometry | Average SNR |
---|---|---|---|---|---|---|---|---|---|---|

[37] | 2001 | Sheffield Mk 3.5 | DSP | Single | 2 kHz to $1.6$ MHz | Discrete Sinusoidal (30 frequencies), up to 10 simultaneous frequencies | Adjacent | 8 | 2D Circular | 40 dB |

[14] | 2003 | UCLH Mk 2 | DSP | Single | 20 Hz to 1 MHz | Discrete Sinusoidal (30 frequencies), up to 10 simultaneous frequencies | Opposite | 64 | 3D Circular | 40 dB |

[36] | 2006 | UCLH Mk 2.5 | DSP | Single | 20 Hz to 1 MHz | Discrete Sinusoidal (30 frequencies), up to 10 simultaneous frequencies | Opposite | 32 | 2D Circular | 40 dB |

[18] | 2008 | - | DSP/FPGA | Multiple | 10 kHz to 10 MHz | Discrete Sinusoidal (20 frequencies) | Adjacent | 64 | 3D Circular | 84 dB |

[39] | 2008 | OXBACT-5 | FPGA | Multiple | 1 kHz to 100 kHz | Discrete Sinusoidal (16 frequencies) | - | 64 | 2D or 3D Circular | - |

[42] | 2014 | KHUMark2.5 | DSP/FPGA | Multiple | 10 Hz to 500 kHz | Discrete Sinusoidal (9 frequencies), up to 6 simultaneous frequencies | Adjacent or Opposite | 16 | 2D Circular | 90 dB |

[44] | 2015 | - | FPGA | Single | 100 Hz to 10 MHz | Discrete Sinusoidal (47 frequencies) | Adjacent | 32 | 2D or 3D Circular | 90 dB |

[46] | 2019 | SWEIT | FPGA | Single | 1 kHz to $1.1$ MHz | Continuous Chirp | Adjacent | 16 | 2D Circular | 56 dB |

Algorithm | Type | Classification | Publications |
---|---|---|---|

Singular Value Decomposition | Non-iterative | Regularization-Based | [21,42,51] |

Newton-Raphson | Iterative | Regularization-Based | [17] |

Gauss-Newton | Iterative | Regularization-Based | [43] |

D-Bar | Non-iterative | Direct | [52] |

Optimal First Order Approximation | Non-iterative | Statistical | [23,53] |

Group Sparse Reconstruction Algorithm | Iterative | Regularization-Based | [54] |

Reconstruction-Classification | Non-iterative | Machine Learning | [55] |

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Padilha Leitzke, J.; Zangl, H. A Review on Electrical Impedance Tomography Spectroscopy. *Sensors* **2020**, *20*, 5160.
https://doi.org/10.3390/s20185160

**AMA Style**

Padilha Leitzke J, Zangl H. A Review on Electrical Impedance Tomography Spectroscopy. *Sensors*. 2020; 20(18):5160.
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**Chicago/Turabian Style**

Padilha Leitzke, Juliana, and Hubert Zangl. 2020. "A Review on Electrical Impedance Tomography Spectroscopy" *Sensors* 20, no. 18: 5160.
https://doi.org/10.3390/s20185160