Calculation of Volumetric Sound Field of Pulsed Air-Coupled Ultrasound Transducers Based on Single-Plane Measurements

Quantitative and reproducible air-coupled ultrasound (ACU) testing requires characterization of the volumetric pressure fields radiated by ACU probes. In this paper, a closed-form reradiation method combining the Rayleigh-Sommerfeld integral and time-reversal acoustics is proposed, which allows calculation of both near- field and far-field based on a single-plane measurement. The method was validated for both 3-D (circular, square) and 2-D (rectangular) planar transducers in the 50-230 kHz range. The pressure fields were scanned with a calibrated microphone. The measurement window was at least four times the size of the transducer area and the grid step size was one third of the wavelength. Best results were observed by acquiring the measurement plane at near-field distance. The method accurately reproduces pulsed ultrasound waveforms and pressure distributions (RMSE <;2.5% in far field and <;5.5% in near field), even at the transducer radiation surface. The effects of speed of sound drifts during the scan in the pressure were negligible (RMSE <;0.3%). The reradiation method clearly outperforms conventional baffled piston models. Possible applications are transducer manufacture control (imperfections at radiation surface) and calibration (on-axis pressure, side lobes, and beamwidth) together with generation of accurate source functions for quantitative nondestructive evaluation inverse problems.