Decomposition of acoustic fields in quantised Bessel beams

Bessel beams are non-diffracting solutions to the wave equation, which become limited diffraction beams when implemented on finite apertures. In previous work we have applied Fourier-Bessel theory to deduce theoretically that the quantization of the Bessel beam profile on annular arrays results in a field which is a sum of limited diffraction fields. Here we demonstrate this for a five-ring, 20-mm diameter, 2.5-MHz transducer. The quantized field comprises a weighted sum of a main component corresponding to the desired field, along with three other major components and 28 lesser components representing undesired field components. The three major components correspond to limited diffraction beams with narrower beamwidths and shorter depths of field than the desired beam, and we show that these account for most of the discrepancies between the desired field and actual quantized field. An estimate and an interpretation of the number of field components as a function of the wavenumber are also given.