Lesson plan
Angular spectrum method
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 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. 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) 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) of the resulting data set to yield the field over the prediction plane.…
Article summary
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 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. 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) 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) of the resulting data set to yield the field over the prediction plane.…
Key claims
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.