Capacitive sensor setup for the measurement and tracking of edge angles

In this paper we propose a capacitive sensor setup for measuring the geometry of an edge consisting of electroconductive material. The Laplace equation for the electric field in the proposed setup is solved by conformal mapping methods. This unusual approach provides the analytic equations which describe the electric field in terms of the geometric parameters. An in depth analysis of these equations enables the fast and simple evaluation of measurement results. An additional sensitivity analysis leads to optimizations in the placement of the sensor array.