A downhole tool includes circumferentially spaced and/or angled transducer elements. In one embodiment a standoff sensor has at least three piezoelectric transducer elements, at least a first element of which is configured to both transmit and receive ultrasonic energy. At least second and third of the elements are configured to receive ultrasonic energy transmitted by the first element in pitch catch mode. An electronic controller is configured to calculate a standoff distance from the ultrasonic waveforms received at the first, the second, and the third piezoelectric transducer elements. The controller may further be configured to estimate the eccentricity of a measurement tool in the borehole. Exemplary embodiments of the invention may improve borehole coverage and data quality and reliability in LWD caliper logging. In particular, the invention may advantageously reduce or even eliminate blind spots when logging eccentric bore holes.