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In this paper we introduce an image reconstruction technique for imaging permittivity distributions using electrical capacitance tomography, based on global optimization by very fast simulated annealing. Electrical capacitance measurement data are obtained between electrodes placed around the outer wall of an electrically insulating pipe. Such data are used to infer material distributions inside the pipe. The data are processed in order to reconstruct an image of the spatial distribution of the relative electrical permittivity (also known as dielectric constant) inside the pipe, which reflects a material distribution. In the very fast simulated annealing method, the permittivity image is reconstructed by minimizing iteratively a cost function related to the difference between the measured data and those calculated for an estimated permittivity distribution that is repeatedly updated, in a semi-random search process that mimics the thermodynamic phenomena of annealing (as metals slowly cool down) or crystallization (as liquids freeze). The images are refined until their calculated capacitance data match the measured data, in which case it is considered that such images properly resemble the permittivity distribution that produced the measured capacitance data.

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In conventional electrical capacitance tomography (ECT) systems the single-electrode excitation scheme is used in which an excitation signal is applied to each of the sensor electrodes in turn. This conventional ECT sensor is more sensitive in the wall area than the central area and consequently the signal-to-noise ratio (SNR) in the central area is poor. To improve this situation, a scheme called parallel field excitation has recently been proposed. This paper analyses the sensitivity distributions of the parallel field sensors. Analytical, simulation and experimental results show that the sensitivity maps of the parallel field sensors are simply the linear superimpositions of those of the conventional sensor, and give inferior image reconstructions.

An ac-based capacitance transducer has been designed for use in electrical capacitance tomography systems. It has a high signal-to-noise ratio and good stray-immunity, compared with a charge/discharge transducer designed for the same purpose. However, the non-ideal characteristics of amplifiers and CMOS switches limit the performance of the ac-based transducer. This paper analyses the effects of the frequency-dependent gain of the amplifiers and the finite 'on' resistance of the CMOS switches. It is shown that the non-ideal characteristics restrict the frequency response of the transducer by introducing extra poles, which depend not only on the parameters of the devices but also on the stray capacitance. Mathematical expressions quantifying these effects are presented.

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Multiple-electrode excitation methods in electrical capacitance tomography (ECT) are analysed and compared with the conventional single-electrode excitation strategy. A series of experiments carried out employing a purpose-built flexible-excitation ECT system, showed a variable (11–125%) but consistent increase in the detection signals when using ‘optimum’ excitation patterns, compared with the single-electrode case. However, for most applications this advantage of multiple-electrode excitation may not justify the price that must be paid in terms of higher system complexity.