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.
Watson,A Treatise on the Theory of Bessel Functions, Cambridge Mathematical Library (Cambridge University Press, 1995)
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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.