Sidelobe Suppression for a Steerable Parametric Source Using the Sparse Random Array Technique

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.