Parametric array in air: Distortion reduction by preprocessing

Abstract

In a parametric array, highly directional low-frequency sound is generated by the self-demodulation of an intense, amplitude-modulated high-frequency sound beam as a result of nonlinear propagation effects. The term ‘‘audio spotlight’’ was introduced by Yoneyama et al. [J. Acoust. Soc. Am. 73, 1532 (1983)] for a parametric array in air used to generate directional audio frequency sound with an ultrasonic primary beam. Berktay’s far-field solution [Berktay, J. Sound Vib. 2, 435 (1965)] predicts a demodulated secondary waveform along the axis of the beam that is proportional to the second time derivative of the square of the modulation envelope. The secondary wave is therefore generated with high levels of harmonic distortion, even at moderate modulation indexes [Blackstock, J. Acoust. Soc. Am. 102, 3106(A) (1997)]. Integrating the modulation signal twice and taking the square root removes this distortion; however, the resulting reduction in distortion due to taking the square root is severely limited by the bandwidth of the primary beam transducer. Here, the characteristics of the transducer are taken into account in developing an appropriate predistortion scheme to achieve high quality reproduction. Relationships between distortion, modulation index, secondary bandwidth, and secondary sound-pressure level are also discussed, and results of simulations are presented. [Work supported in part by ARL:UT IR&D.]