# FPGA Implementation of ECT Digital System for Imaging Conductive Materials
## 1 Introduction  
The Electrical Capacitance Tomography (ECT) is one of the recent techniques applied for visualizing industrial applications. It has the ability to generate images capturing the dynamic behavior of the process [1]. The ECT is a non-invasive and non-intrusive modality which measures capacitance data from an array of electrodes evenly mounted around a vessel. Dielectric permittivity properties of materials inside the imaging area change the measured data and enable the ECT to generate tomographic images describing these materials' distribution [2]. Compared with the other electrical tomography techniques such as Magnetic Resonance Imaging (MRI) and Computed Tomography (CT), the ECT has a high temporal resolution [3]. Some of the advantages of the ECT technique over the other methods are low cost, high speed, and robustness [4]. Typically, the ECT system has an array of electrodes mounted around an object to measure the capacitance values across that object to build an image describing its dielectric distribution [2]. The array contains 8-12 electrodes separated by an earthed ring to eliminate any interference between the electrodes. The mutual capacitance is measured between each different pair of the electrodes where one electrode, in turn, is raised as a transmitter and the rest as receivers. Some recent ECT systems have high measurements' sensitivity in a range of femto-Farads (fF) to atto-Farads (aF). However, one challenge is the long time consumed in the data acquisition process (average 1.15 ms) and the image reconstruction procedure around 1.25-1.4 ms [5]. The ECT system can visualize distribution of dielectric or conductive materials [6; 7]. Multi-phase flows such as oil/gas in oil pipelines and gas/solid in fluidization processes are common dielectric ECT applications. One ECT application for conductive materials is casting process where the generated images describe a distribution of metal inside a flask [8]. The capacitance measurements are affected by the amount of the metal between the electrodes. The collected data are used by a proper image reconstruction algorithm to generate the images [9; 10; 11]. The cross-section view of the ECT system for imaging the Lost Foam Casting (LFC) process is shown in Figure 1. There are 12 electrodes attached to the wall of the flask surrounding a foam pattern, embedded in compressed sand, where a molten metal will be poured. The boundaries of the foam pattern represent the imaging area. Each capacitive sensor (S1 to S6) is a pair of electrodes [12]. In order to eliminate the outside disturbance, the flask is grounded. The measurements are wirelessly sent based on Mote technology to a base station connected to a PC where the images will be generated. The system is flexible and portable because it uses wireless technology. The sensors operate simultaneously at different operating frequencies [13]. Two consecutive procedures have to be followed to create the images: the first is called a forward problem and the second is called an inverse problem. The forward one concerns creating a Finite Element Model (FEM) simulating the real ECT system taking spatial materials' distribution and generates corresponding capacitance measurements. While the inverse problem takes the measurements as inputs and applies an image reconstruction algorithm to create a tomographic image [14]. The image reconstruction algorithms are classified into two categories: linear and nonlinear. The linear ones are simple and fast; therefore, they are applied for high temporal and fast dynamic applications, but, usually, output images from these algorithms are blurred. While nonlinear reconstruction algorithms are complex and iteratively solve linear algebra transformations in order to generate high-quality images. The ECT system has been widely implemented with software algorithms running on general-purpose processors. Commands are sent by the processor to measure the capacitance between sensors, construct the tomography images, and display it.