International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2010 
International Tables for Crystallography (2010). Vol. B, ch. 1.3, p. 101

Let ρ be the electrondensity distribution in a fibre, which is assumed to have translational periodicity with period 1 along z, and to have compact support with respect to the (x, y) coordinates. Thus ρ may be writtenwhere is the motif.
By the tensor product property, the inverse Fourier transform may be writtenand hence consists of `layers' labelled by l:with
Changing to polar coordinates in the (x, y) and planes decomposes the calculation of F from ρ into the following steps:and the calculation of ρ from F into:
These formulae are seen to involve a 2D Fourier series with respect to the two periodic coordinates ϕ and z, and Hankel transforms along the radial coordinates. The two periodicities in ϕ and z are independent, so that all combinations of indices (n, l) occur in the Fourier summations.