A sensor has a sensing region that responds to a surface property by producing an output signal. The sensor has a spatially distributed shape or sensitivity so that the output decreases away from a central part of the sensor, and thus the outputs of plural sensors combined have finite spatial transform as well as high roll off in spatial frequency. Preferably the output decreases to zero at edges of the sensor, and conditions of continuity or vanishing may be imposed on first or higher order derivatives. An edge sensor suitable for mounting at the edge of the structure has its weight function obtained by processes of reflecting and inverting the weight function at an edge. A sensor system employs plural such sensors and edge sensors to produce bounded spatial transfer functions for characterizing the structure. Embodiments of piezeoelectric, resistive, capacitive and thermal sensors are described.