A study of angular spectrum and limited diffraction beams for calculation of field of array transducers

Angular spectrum is one of the most powerful tools for field calculation. It is based on linear system theory and the Fourier transform and is used for the calculation of propagating sound fields at different distances. In this report, the generalization and interpretation of the angular spectrum and its intrinsic relationship with limited diffraction beams are studied. With an angular spectrum, the field at the surface of a transducer is decomposed into limited diffractions beams. For an array transducer, a linear relationship between the quantized fields at the surface of elements of the array and the propagating field at any point in space can be established. For an annular array, the field is decomposed into limited diffraction Bessel beams [P. D. Fox and S. Holm, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 85–93 (2002)], while for a two‐dimensional (2‐D) array the field is decomposed into limited diffraction array beams [J‐y. Lu and J. Cheng, J. Acoust. Soc. Am. 109, 2397–2398 (2001)]. The angular spectrum reveals the intrinsic link between these decompositions. [Work supported in part by Grant 5RO1 HL60301 from NIH.]