Toward electric field tomography

This thesis addresses the problem of recovering three-dimensional location and shape information from measurements made with Electric Field Sensors. A single sensor functions as a proximity detector; two can be used as a mouse; three allow tracking of the hand in three dimensions, and each additional sensor allows us to extract additional shape information. The ultimate goal of this work is to understand the entire hierarchy, from a single sensor up to an array of sensors. In this thesis, we take the rst steps toward imaging, moving from simple proximity detection to imaging a single point in three dimensions. At every step along the hierarchy, we are interested in two questions: i) given a xed number of sensors, how should they be arranged in space to enable us to extract the most information, and ii) given an arrangement of sensors, how should we infer \what's out there" from the data they return? We describe a probabilistic framework that can be used to answer these questions for any sensor con guration, from a single sensor to an array. The thesis describes the physics of Electric Field Sensing, uses this discussion to nd an approximate analytical solution to the forward problem of determining the sensor values from a conductivity distribution, shows how to use this analytical model in conjunction with probability theory to design optimal electrode layouts, and presents several methods of inverting the signals to recover information about a conductivity distribution from sensor values. As an example application, we present a non-contact three-dimensional mouse. Thesis Supervisor: Neil Gershenfeld Title: Assistant Professor of Media Arts and Sciences