Capacitive sensor arrays in dimensional analysis of surfaces

The theoretical aspects of dimensional analysis and shape reconstruction of surfaces by means of displacement sensor arrays are investigated. Although this analysis is focused on surface profiles and linear arrays of capacitive sensors, its results could be easily extended to surfaces and bidimensional arrays of displacement sensors. Capacitance variations related to sensor-to-surface displacements during array scanning are used in the reconstruction equations obtained from the analysis. The reconstruction accuracy depends mainly on the dimensional stability of the array, and it is independent from the array trajectory. The problems raised by nonideal array and sensor behavior, such as fringe effects and geometry deviations are discussed. Capacitance variations due to such effects are calculated and taken into account by means of an energy method. A reconstruction system based on the theoretical results is proposed, and its performance in the reconstruction process is evaluated by a computer simulation which accounts for measurement uncertainties. Simulation results confirm both the effectiveness of the method and the feasibility of the system. Its features are compared with those of other noncontact surface-measuring instruments, and possible applications are outlined