Electrical capacitance tomography (ECT) is used to image cross-sections of industrial processes containing dielectric material. This technique has been under development for more than a decade. The task of image reconstruction for ECT is to determine the permittivity distribution and hence material distribution over the cross-section from capacitance measurements. There are three principal difficulties with image reconstruction for ECT: (1) the relationship between the permittivity distribution and capacitance is non-linear and the electric field is distorted by the material present, the so-called 'soft-field' effect; (2) the number of independent measurements is limited, leading to an under-determined problem and (3) the inverse problem is ill posed and ill conditioned, making the solution sensitive to measurement errors and noise. Regularization methods are needed to treat this ill-posedness. This paper reviews existing image reconstruction algorithms for ECT, including linear back-projection, singular value decomposition, Tikhonov regularization, Newton–Raphson, iterative Tikhonov, the steepest descent method, Landweber iteration, the conjugate gradient method, algebraic reconstruction techniques, simultaneous iterative reconstruction techniques and model-based reconstruction. Some of these algorithms are examined by simulation and experiment for typical permittivity distributions. Future developments in image reconstruction for ECT are discussed.

https://iopscience.iop.org/article/10.1088/0957-0233/14/1/201/pdf

Image reconstruction algorithms for electrical capacitance tomography

Electrical capacitance tomography (ECT) has been developed since the late 1980s for visualization and measurement of a permittivity distribution in a cross section using a multi-electrode capacitance sensor. While the hardware and image reconstruction algorithms for ECT have been published extensively and the topics have been reviewed, few papers have been published to discuss ECT sensors and the design issues, which are crucial for a specific application. This paper will briefly discuss the principles of ECT sensors, but mostly will address key issues for ECT sensor design, with reference to some existing ECT sensors as a good understanding of the key issues would help optimization of the design of ECT sensors. The key issues to be discussed include the number and length of electrodes, the use of external and internal electrodes, implications of wall thickness, earthed screens (including the outer screen, axial end screens and radial screens), driven guard electrodes, dealing with high temperature and high pressure, twin planes for velocity measurement by cross correlation and limitations in sensor diameter. While conventional ECT sensors are circular with the electrodes in a single plane or in twin planes, some non-conventional ECT sensors, such as square, conical and 3D sensors, will also be discussed. As a practical guidance, the procedure to fabricate an ECT sensor will be given. In the end are summary and discussion on future challenges, including re-engineering of ECT sensors.

https://iopscience.iop.org/article/10.1088/0957-0233/21/4/042001/pdf

Design of electrical capacitance tomography sensors

In this paper a novel ultrasound tomography imaging system is presented. It employs a relatively small number of transducers that produce fan-shaped beam profile to effectively insonify the cross-section. The impact on the image quality due to the reduction of the number of transducers is discussed, and different approaches such as multiple receiver data acquisition and nonlinear thresholding are explored. A prototype of a tomographic imaging system with only 36 transducers has been constructed, and processing rates of up to 100 frames per second have been achieved using a parallel processing technique. Good image reconstructions based on simulations and real objects also are provided to confirm the principles of the theoretical analysis.

Real-time ultrasound process tomography for two-phase flow imaging using a reduced number of transducers

Recent Advances in Flame Tomography

Disclosed herein is a novel sensing technique, termed Multiple Excitation Capacitance Polling (MECaP), that improves the efficiency of Electrical Capacitance Tomography (ECT). Unlike traditional alternating current techniques, where excitation signal is applied to an electrode one at a time, MECaP involves simultaneously applying multiple excitation signals, in a progressively increasing fashion, to multiple electrodes on an ECT sensor. The received signals are filtered or otherwise decomposed (e.g., Fourier transformed) into different components, and the individual components are used to generate an image of the article or substance disposed between the electrodes. Because multiple capacitances can be simultaneously measured as a consequence, scanning with MECaP can significantly increase the image scanning speed. For example, scanning with MECaP may enable frames rates of tens of kHz for imaging dynamic processes such as engine combustion.

Multiple excitation capacitance polling for enhanced electronic capacitance tomography

The development of stray-immune circuits to measure very small floating capacitances has enabled the technique of electrical capacitance tomography (ECT) to be developed. Burning fuel, for example in an internal combustion engine, produces a high concentration of ions, thus modifying the dielectric constant of the combustion volume. Thus ECT can be applied to produce tomographic images inside a combustion chamber, independent of flame luminosity. However, the major effect of the increase in ion concentration is to increase the conductivity of the volume. The ECT technique has been extended to measure both the change in permittivity and change in conductivity, yielding additional information on the flame composition. Current spatial and temporal resolution is poor but developments are in hand to overcome these limitations. Alternatively, the way forward may well be to abandon images and instead use extremely simple and cheap sensors to monitor knock on a cycle-by-cycle basis. An alternative use of such a simple sensor would be to monitor cycle dispersion in a lean burn engine. Both these techniques could help minimize fuel consumption, whilst maximizing power output and keeping emissions low.

http://iopscience.iop.org/article/10.1088/0957-0233/7/3/018/pdf

N B White

Papers

Combustion imaging from electrical impedance measurements