## 3 Electrical Tomography Principles and Applications
### Fundamentals of Electrical Tomography
#### 3.2.2 Resistivity/Impedance Tomography
An additional limitation of using discrete electrodes mounted in the pipe wall, the surface of which is parallel to the inner pipe wall (as required by resistive/impedance tomography), is their surface modification over time, particularly when used for evaluation processes that operate under extreme conditions. Temperature is one example of such conditions: temperature changes can dramatically cause fluid conductivity to alter, and consequently fluid temperature compensation mechanisms have to be applied to \"correct\" current/voltage measurements. Looking now to the evolution of acquisition systems, recent developments in the electronics field have made it possible to achieve frame acquisition speeds of 1000 frames/s [73; 74]. In acquisition systems, a good excitation strategy is also vital, and these are typically current-based ones. However, the use of voltage-based excitation strategies, where a voltage-controlled source (typically with low output impedance) combined with an equal width pulse synthesiser, generates a subset of waveforms used for exciting the domain and to implement demodulation, have attracted increasing attention, since they produce less noisy data [73]. The use of voltage-controlled sources in the domain excitation causes electrical currents inside the domain that increase with the increase in suspension fluid conductivity; this fact is very important for highly conductive suspensions, above 2 S/m, which are quite typical of industrial processes [67; 74]. In addition to the shape and size of the electrodes, and the material from which they are made, when using ERT/EIT, other characteristics must be considered, such as the spacing between electrodes, and for EIT the frequency of the electrical excitation signal. Altogether, these characteristics condition the electric field distribution along the domain and determine the true measuring volume and overall sensitivity [74; 75]. However, some of the negative effects of these characteristics can be overcome; for instance, the effect of the electrode dimensions can be reduced by using appropriate calibration procedures [76]. EIT, similar to ECT, can also be used to obtain disperse phase velocity by using a pair of data acquisition planes and applying cross-correlation algorithms to the acquired data [77; 78]. However, to properly estimate velocity, a minimum frame rate acquisition of 100 frames per second is needed [78]. Demodulation has to be performed through software to overcome the problem of the low settling time of the low-pass filters. Figure 2: EIT/ERT adjacent injection and measurement protocol for the first (**A**) and second (**B**) projections (reproduced with permission from [PERSON] et al. [71]). The way electrodes are combined to introduce the electrical signal into the domain is designated by the Injection Protocol. Thorough studies on injection and measurement protocols or patterns can be found in the literature. The most common strategy is referred to as the four-electrode method, where the signal is injected through some electrodes and the voltages are measured from the remaining electrodes. Different patterns for using this strategy can be found in the literature [79; 80]: (a) Adjacent Pattern: where the signal is injected through neighbouring or adjacent electrodes and the resulting electrical potential differences are measured in the remaining pairs of electrodes, in a similar adjacent combination; (b) Opposite Pattern: In this pattern, the signal is injected through opposite electrodes and the electrical potential is measured with respect to one reference electrode adjacent to the injecting electrode. In addition to the above-mentioned strategies, which are the most frequently used, others have been employed, such as the Cross or Diagonal Pattern [80], which is a combination of the two described above, and the Trigonometric or Adaptive Pattern [81].