Skip to main content
. Author manuscript; available in PMC: 2008 Feb 1.
Published in final edited form as: J Magn Reson. 2006 Oct 27;184(2):207–221. doi: 10.1016/j.jmr.2006.10.002

Figure 2.

Figure 2

The Fourier Transform of a Ring of Sampling Points. Two examples are shown, each with 72 sampling points (N = 36) and phase 0, one with a radius of 9Δr, the other 14Δr. (a) Positions of the sampling points for the two rings. The axes are measured in multiples of the dwell time Δr. (b) Schematic showing the positions in the frequency domain at which the first of the higher-order Bessel terms (J72) begin for the two rings, relative to the region of interest and the plotted transform size. Note that the ring of smaller radius in the time domain generates the higher-order terms of larger radii. (c) The FT of the r0 = 9Δr ring. Note the J0 “ripple” pattern starting from the center, with the J72 term beginning close to the edge. (d) The FT of the r0 = 14Δr ring.