t. This paper surveys some of the work our group has done in electrical impedance tomography.

Electrical Impedance Tomography

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Art of electronics

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

A software tool that facilitates the development of image reconstruction algorithms, and the design of optimal capacitance sensors for a capacitance-based 12-electrode tomographic flow imaging system are described. The core of this software tool is the finite element (FE) model of the sensor, which is implemented in OCCAM-2 language and run on the Inmos T800 transputers. Using the system model, the in-depth study of the capacitance sensing fields and the generation of flow model data are made possible, which assists, in a systematic approach, the design of an improved image-reconstruction algorithm. This algorithm is implemented on a network of trans- puters to achieve a real-time performance. It is found that the selection of the geometric param- eters of a 12-electrode sensor has significant effects on the sensitivity distributions of the capacitance fields and on the linearity of the capacitance data. As a consequence, the fidelity of the reconstructed images are affected. Optimal sensor designs can, therefore, be provided, by accommodating these effects.

/pdf/electrical-capacitance-tomography-for-flow-imaging-system-2a4ajtiapy.pdf

Electrical capacitance tomography for flow imaging: system model for development of image reconstruction algorithms and design of primary sensors

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.

https://iopscience.iop.org/article/10.1088/0957-0233/10/11/315/pdf

An image-reconstruction algorithm based on Landweber's iteration method for electrical-capacitance tomography

Describes a tomographic flow imaging system based on capacitance sensors. It uses eight capacitance electrodes to perform a 'body scan' of the fluid-conveying pipe, and a linear back projection algorithm is developed to reconstruct the cross-sectional image of the two-component flow from the measured capacitance values. A prototype system has been successfully assembled and reconstructed images of static distribution models are presented. Possible industrial applications and practical limitations of the system are discussed.

https://iopscience.iop.org/article/10.1088/0022-3735/22/3/009/pdf

Tomographic imaging of two-component flow using capacitance sensors

Reviews existing instrumental techniques suitable for industrial measurement of capacitance in the range 0.1-10 pF, including resonance, oscillation, charge/discharge and AC bridge methods. It shows that in order to achieve high measurement sensitivity and good signal-to-noise ratio, the effects of stray capacitances on the measurement systems must be minimised. Several intrinsically stray-immune measuring circuits are described, including an audio-frequency transformer-ratio-arm bridge and a charge/discharge measuring circuit capable of operating at frequencies up to several MHz. The active guard method and suitable guard driving techniques for reducing the effects of strays on the measurement of grounded capacitances sensors are described. Techniques for reducing the baseline drift of the capacitance measuring circuits, such as auto-balancing and auto-calibration, etc., are also discussed.

https://iopscience.iop.org/article/10.1088/0022-3735/21/3/001/pdf

Electronic transducers for industrial measurement of low value capacitances

The design of the sensor electronics for a tomographic imaging system based on electrical capacitance sensors is described. The performance of the sensor electronics is crucial to the per- formance of the imaging system. The problems associated with such a measurement process are discussed and solutions to these are described. Test results show that the present design has a resolution of 0.3 femtofarad (For a 12-electrode system imaging an oil/gas flow, this represents a 2% gas void fraction change at the centre of the pipe) with a low noise level of 0.08 fF (rms value), a large dynamic range of 76 dB and a data acqui- sition speed of 6600 measurements per second. This enables sensors with up to 12 electrodes to be used in a system with a maximum imaging rate of 100 frames per second, and thus provides an improved image resolution over the earlier 8- electrode system and an adequate electrode area to give sufficient measurement sensitivity.

/pdf/design-of-sensor-electronics-for-electrical-capacitance-4w3gbgtdv0.pdf

Design of sensor electronics for electrical capacitance tomography

An instrumentation system for obtaining cross-sectional images of two-component flows is described. It uses measurements made with capacitance electrodes mounted on the outer surface of the fluid-conveying pipe, and an image reconstruction algorithm based on backprojection. Images of static physical models simulating a stratified solids/air flow are presented.

S.M. Huang

Papers

Electrical capacitance tomography for flow imaging: system model for development of image reconstruction algorithms and design of primary sensors

Tomographic imaging of two-component flow using capacitance sensors

Electronic transducers for industrial measurement of low value capacitances

Design of sensor electronics for electrical capacitance tomography

Capacitance-based tomographic flow imaging system