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
Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of ...
s of the same frequency and different directions. Its mathematical origins lie in the field of
Fourier optics but it has been applied extensively in the field of
ultrasound
Ultrasound is sound with frequency, frequencies greater than 20 Hertz, kilohertz. This frequency is the approximate upper audible hearing range, limit of human hearing in healthy young adults. The physical principles of acoustic waves apply ...
. 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 (two dimensional
Fourier transform
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the tr ...
) 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
Fourier transform
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the tr ...
) 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 signal (electrical engineering), ...
s. Forward propagation can be used to predict the influence of inhomogeneous, nonlinear media on acoustic transducer performance.
See also
*
Wave field synthesis
References
{{DEFAULTSORT:Angular Spectrum Method
Physical optics
Ultrasound