Level-set shape reconstruction of binary permittivity distributions using near-field focusing capacitance measurements

A near-field focusing capacitance sensor consists of an array of long, coplanar electrodes offset by a small interface gap from an identical orthogonal array of electrodes. The sensor may be used to characterize permittivity inhomogeneities in thin dielectric layers. The sensor capacitance measurements represent a tessellated matrix of integral-averaged values describing void content in a series of zones corresponding to the electrode crossing points (junctions) of the sensor. The sensor does not lend itself to computed tomography because the individual capacitance measurements do not represent overlapping regions of sensitivity. An evolving level-set algorithm is proposed to reconstruct a binary permittivity distribution. A mathematical construct, based on the physics of inverse-square fields, is used to approximately reconstruct shape features too small to be captured by the raw measurements. The method accommodates the non-uniform area-sensitivity of the junction capacitance measurement. Effective use of the algorithm requires active management of the convergence criterion and evolution rate. The algorithm is demonstrated on a series of phantoms as well as measurements of a voided dielectric thermal interface material using a near-field focusing sensor. (paper)