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 wave In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space. For any position \vec x in space and any time t, ...

s of the same frequency and different directions. Its mathematical origins lie in the field of

Fourier optics Fourier optics is the study of classical optics using Fourier transforms (FTs), in which the waveform being considered is regarded as made up of a combination, or '' superposition'', of plane waves. It has some parallels to the Huygens–Fresnel pri ...

but it has been applied extensively in the field of

ultrasound Ultrasound is sound waves with frequencies higher than the upper audible limit of human hearing. Ultrasound is not different from "normal" (audible) sound in its physical properties, except that humans cannot hear it. This limit varies ...

. 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. Modeling the diffraction of a CW (continuous wave), monochromatic (single frequency) field involves the following steps: # Sampling the complex (real and imaginary) components of a pressure field over a grid of points lying in a cross-sectional plane within the field. # Taking the 2D-

FFT A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in the ...

(two dimensional

Fourier transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed ...

) of the pressure field - this will decompose the field into a 2D "angular spectrum" of component plane waves each traveling in a unique direction. # Multiplying each point in the 2D-FFT by a propagation term which accounts for the phase change that each plane wave will undergo on its journey to the prediction plane. # Taking the 2D-IFFT (two dimensional inverse

) of the resulting data set to yield the field over the prediction plane. In addition to predicting the effects of diffraction, 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). Backward propagation predictions can be used to analyze the surface vibration patterns of acoustic radiators such as

ultrasonic transducer Ultrasonic transducers and ultrasonic sensors are devices that generate or sense ultrasound energy. They can be divided into three broad categories: transmitters, receivers and transceivers. Transmitters convert electrical signals into ultrasoun ...

s. Forward propagation can be used to predict the influence of inhomogeneous, nonlinear media on acoustic transducer performance.

References

{{DEFAULTSORT:Angular Spectrum Method Physical optics Ultrasound

See also

References