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.
Electrical capacitance tomography (ECT) is a so-called 'soft-field' tomography technique. The linear back-projection (LBP) method is used widely for image reconstruction in ECT systems. It is numerically simple and computationally fast because it involves only a single matrix-vector multiplication. However, the images produced by the LBP algorithm are generally qualitative rather than quantitative. This paper presents an image-reconstruction algorithm based on a modified Landweber iteration method that can greatly enhance the quality of the image when two distinct phases are present. In this algorithm a simple constraint is used as a regularization for computing a stabilized solution, with a better immunity to noise and faster convergence. Experimental results are presented.
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.
Purpose-The purpose of this paper is to present the sensing mechanism, design issues, performance evaluation and applications for planar capacitive sensors. In the context of characterisation and imaging of a dielectric material under test (MUT), a systematic study of sensor modelling, features and design issues is needed. In addition, the influencing factors on sensitivity distribution, and the effect of conductivity on sensor performance need to be further studied for planar capacitive sensors. Design/methodology/approach-While analytical methods can provide accurate solutions to sensors of simple geometries, numerical modelling is preferred to obtain sensor response to different design parameters and properties of MUT, and to derive the sensitivity distributions of various electrode designs. Several important parameters have been used to evaluate the response of the sensors in different sensing modes. The designs of different planar capacitive sensor arrays are presented and experimentally evaluated. Findings-The response features and design guidelines for planar capacitive sensors in different sensing modes have been summarised, showing that the sensor in the transmission mode or the single-electrode mode is suitable for material characterisation and imaging, while the sensor in the shunt mode is suitable for proximity/displacement measurement. The sensitivity distribution of the sensor depends largely on the geometry of the electrodes. Conductivity causes positive changes for the sensor in the transmission and single-electrode mode, but negative changes for the sensor in the shunt mode. Experimental results confirm that sensing depths of the sensor arrays and the influence of buried conductor on capacitance measurements are in agreement with simulations. Research limitations/implications-Experimental verification is needed when a sensor is designed. Originality/value-This paper provides a comprehensive study for planar capacitive sensors in terms of sensor design, evaluation and applications.
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