A Tensor Model for the Calibration of Air-Coupled Ultrasonic Sensor Arrays

Air-coupled ultrasonic sensor arrays are suitable for inexpensive three-dimensional (3D) imaging, however, production tolerances of the transceivers and insufficient array geometry knowledge cause amplitude and phase errors that deteriorate the imaging performance. We introduce a tensor signal model based on piezoelectric ultrasonic transducer (PUT) characteristics and propose to calibrate the multiple-input multiple-output (MIMO) array with measurements. Simulations and real experiments evaluate the calibrated array parameters that are solutions of an optimization problem subject to our tensor model.