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.
Osgood,Lectures on the Fourier transform and its applications, Sally series (Providence, R.I.) (American Mathematical Society, Providence, Rhode Island, 2019)
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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.