Investigating the effect of thickness and frequency spacing on multi-frequency acoustic kinoforms

The generation of complex diffraction limited acoustic fields from a simple planar transducer is possible using cheap 3-D printable kinoforms. This approach is extremely promising for several areas of physical acoustics. However, one drawback is that the acoustic field generated from a given kinoform is fixed, limiting flexibility. In this work, multi-frequency acoustic kinoforms are investigated as a means to circumvent that limitation. These are kinoforms designed to generate different distributions of pressure at a target depth when driven at particular design frequencies. An optimisation approach based on direct search for the design of these structures from a set of input frequencies and target distributions is briefly described. The effect of different parameters of the kinoform on the performance are then established. These include the maximum thickness, frequency spacing and target depth. It is found that the maximum thickness has to be limited to avoid significant aberrations, the frequency spacing should be maximised within the usable bandwidth of the transducer, and the optimal thickness is influenced by the choice of target depth. The thin phase approximation is also shown to be increasingly inaccurate for increasing element thicknesses.