Tomographic study of acoustic emission by parametric arrays for airborne sound

Ultrasonic parametric arrays are used for the nonlinear generation of highly directional airborne audio sound. Often they are composed of up to several hundred individual piezoelectric transducers. The ultrasonic field is effected by intrinsic phase shifts between the transducers. These can be compensated by active phase adjustments – provided the ultrasonic field near the array is known. Optical monitoring of the propagating sound wave makes use of the corresponding refractive index variations. We use time-averaged Electronic Speckle Pattern Interferometry (ESPI – TV-holography) with sinusoidal reference wave modulation and phase-shifting. The primary results are amplitude and phase maps of the refractive index modulation integrated along the viewing path. The three-dimensional field is obtained from many projections through the sound field at different viewing angles and tomographic back-projection. For this purpose the sound source is placed on a precision rotation stage and the measurement is repeated for 180 angular orientations. The algorithm of filtered back projection is used to calculate phase and amplitude distributions for arbitrarily oriented planes in the field.