A focal expansion approximates the Hankel transforms of angular modes to give a single accurate Fourier transform for ring-like images across all spatial frequencies.
We assumea >0 and a/b >1, the latter condition coming from requiring the lima¸ con to be a smooth, non-self-intersecting curve [25]
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Approximating the Fourier Transform of Ring-Like Images: the Focal Expansion
A focal expansion approximates the Hankel transforms of angular modes to give a single accurate Fourier transform for ring-like images across all spatial frequencies.