Time-of-Flight Based Calibration of an Ultrasonic Computed Tomography System

The paper presents a novel method for calibration of measuring geometry and of individual signal delays of transducers in ultrasonic computed tomography (USCT) systems via computational processing of multiple time-of-flight measurements of ultrasonic (US) impulses. The positions and time-delay parameters of thousands of ultrasonic transducers inside the USCT tank are calibrated by this approach with a high precision required for the tomographic reconstruction; such accuracy cannot be provided by any other known method. Although utilising similar basic principles as the global positioning system (GPS), the method is importantly generalised in treating all transducer parameters as the to-be calibrated (floating) unknowns, without any a-priori known positions and delays. The calibration is formulated as a non-linear least-squares problem, minimizing the differences between the calculated and measured time-of-arrivals of ultrasonic pulses. The paper provides detailed derivation of the method, and compares two implemented approaches (earlier calibration of individual transducers with the new approach calibrating rigid transducer arrays) via detailed simulations, aimed at testing the convergence properties and noise robustness of both approaches. Calibration using real US signals is described and, as an illustration of the utility of the presented method, a comparison is shown of two image reconstructions using the tomographic US data from a concrete experimental USCT system measuring a 3D phantom, without and after the calibration.