Calibrating position and orientation of multiple ultrasound phased array units using Bayesian optimization

Airborne ultrasound phased arrays (AUPAs) generate non-contact tactile sensations and enable acoustic levitation with specific focus fields. Using multiple units together offers numerous advantages, such as increased stimulus intensity and the ability to overcome occlusion. The AUPA units are typically mounted on a fixed frame, with their poses manually measured using tools such as a ruler for calibration. However, to increase the degrees of freedom for these units, a more flexible calibration method is required. With a wavelength of 8.5 mm, a 4 mm deviation in propagation distance from the two phased arrays can weaken the pressure at the focus position. Hence, in this study, calibration based on pose and focus information obtained through image processing was performed. First, augmented reality markers are attached to each AUPA unit for rough estimation of pose parameters. Second, using these approximate poses, the pressure distribution generated on a specific plane is estimated through thermal imaging. Finally, Bayesian optimization is employed to efficiently explore the pose parameters to minimize the error between the desired position and generated focal point. This approach enables the efficient calibration of the relative poses of AUPA units, even when they are placed in challenging-to-measure locations.