Spherical harmonic-domain acousto-optic tomography for three-dimensional sound-field reconstruction

Acousto-optic tomography (AOT), a technology that reconstructs two- or three-dimensional sound fields from optically measured sound-field projections, has been widely studied as an efficient and high-spatial-resolution method for sound field observations. Recently, physical-model-based approaches have made significant progress, with higher accuracy and fewer sampling requirements than conventional methods. Nevertheless, it remains a challenge to reconstruct three-dimensional outgoing sound waves in the volume surrounding a sound source due to constraints on existing methods both in mathematical formulation and measurement systems. In this paper, we propose spherical harmonic-domain AOT, a three-dimensional reconstruction of sound fields by combining instantaneous sound-field imaging using parallel phase-shifting interferometry with a physics-based reconstruction using spherical wave function expansions. We formulated two problems: one for the sound field radiated by a transducer and the other for the sound field scattered by an object. Through experiments, we demonstrated the successful reconstruction of the two types of three-dimensional sound fields: one radiated from two ultrasonic transducers and the other scattered by an ellipsoid.