The angular spectrum method is a technique for modeling the propagation of a wave field. This technique involves expanding a complex wave field into a summation of infinite number of plane waves of the same frequency and different directions. Its mathematical origins lie in the field of Fourier optics[1][2][3] but it has been applied extensively in the field of ultrasound. The technique can predict an acoustic pressure field distribution over a plane, based upon knowledge of the pressure field distribution at a parallel plane. Predictions in both the forward and backward propagation directions are possible.[4]
Modeling the diffraction of a CW (continuous wave), monochromatic (single frequency) field involves the following steps:
In addition to predicting the effects of diffraction,[5][6] the model has been extended to apply to non-monochromatic cases (acoustic pulses) and to include the effects of attenuation, refraction, and dispersion. Several researchers have also extended the model to include the nonlinear effects of finite amplitude acoustic propagation (propagation in cases where sound speed is not constant but is dependent upon the instantaneous acoustic pressure).[7][8][9][10][11]
Backward propagation predictions can be used to analyze the surface vibration patterns of acoustic radiators such as ultrasonic transducers.[12] Forward propagation can be used to predict the influence of inhomogeneous, nonlinear media on acoustic transducer performance.[13]
