A steerable parametric source is designed to steer an audio beam without mechanically rotating the source. To achieve this without the generation of grating lobes requires an ultrasonic array with interelement spacing that is less than half the wavelength of the carrier ultrasound because of the spatial Nyquist criterion. However, ultrasonic wavelengths are typically smaller than the size of an ultrasonic transducer and this generates grating lobes in the radiation pattern, which is known as the spatial aliasing effect. This work proposes a method to suppress sidelobes including these grating lobes by optimizing the position and weight coefficients of the array elements by using a sparse random array technique. This is achieved by using the peak sidelobe level as the objective function and the simulated annealing algorithm for the optimization. Both simulation and experimental results demonstrate the sidelobe level can be effectively suppressed when the average interelement spacing is two wavelengths. It is also found that Westervelt directivity has a significant effect on the spatial aliasing, because it serves as a spatial filter on the product directivity of the ultrasound. Accordingly, the sidelobe suppression performance deteriorates at low audio frequencies and high ultrasound frequencies where Westervelt directivity tends to be broader. However, this deterioration in performance can be addressed by increasing the number of the array elements.

In this paper, the audio sound field generated by a focusing parametric array loudspeaker (PAL) is investigated both numerically and experimentally. A computationally efficient method is developed to calculate the quasilinear solution of both the Westervelt and Kuznetsov equations. The accuracy of generated sound field using Westervelt equation is initially examined, and the results are then compared with those obtained using the Kuznetsov equation. It is found that the focusing on the true focal location deteriorates the prediction accuracy using the Westervelt equation due to the strong and complicated local effects. To validate the numerical results against experimental data, a 37-channel focusing PAL prototype is constructed by using a field programmable gate array, metal-oxide semiconductor field-effect transistor drivers and the pulse train signal technique. Both the simulation and experimental results show that the audio sound pressure around the true focal location is increased, and the increment becomes larger at low audio frequencies and when the focal point moves close to the radiation surface, which is attributed to the strong local effects in the near field. It has been shown that a focusing PAL can improve the poor low frequency response for a conventional PAL without focusing, and the generated audio sound decays rapidly with the distance in the far field when compared to that without focusing.