Objective: In this paper we extend the angular spectrum method to calculate pressure from a curved source. The angular spectrum is calculated for a spherically curved source and then propagated to a plane, after which the angular spectrum can be propagated from plane to plane.

Significance: The angular spectrum method is a fast, accurate and computationally efficient method to model wave propagation. It can only be used for calculation of pressure on a plane and hence it has been restricted to calculation of wave propagation from planar sources. This technique extends the angular spectrum technique to curved sources (radially symmetric) which are used extensively in applications like High Intensity Focused Ultrasound (HIFU).

Results: A method to propagate the angular spectrum from a curved source to a secondary plane was developed. The technique breaks up the curved sources into concentric rings of different radii, each ring a different distance Zi from the secondary plane. Using the Fourier transform to find the angular spectrum of each ring, each angular spectrum is propagated a distance Zi to the secondary plane where all the propagated angular spectra are added together (complex addition) to get the pressure on the secondary plane. The accuracy of this technique was compared to the Rayleigh-Sommerfeld technique and in the focal plane of size 16.75 cms X 16.75 cms (201 X 201 voxels) the difference was 4.1% . The technique also results in a factor of four increases in speed as compared to the Rayleigh-Sommerfeld method.

Conclusion: A purely frequency domain technique using angular spectrum for curved transducers was developed and shown to be fast and accurate.