K-space data

Fig. 3.4.3 (a) Two-dimensional k-space acquisition using SPI or SPRITE. The k-space data acquisition is indicated numerically. High magnetic field gradient amplitudes are applied at the extremities of k-space. (b) A generic two-dimensional centric scan SPRITE method. The... 

As we have seen, conventional spin-echo imaging (Section II.A.3) typically takes the order of a few minutes. As shown in Fig. 6, an independent r.f. excitation is required for acquisition of each row of k-space data. Hence sampling of the complete raster is limited by the repetition/recycle time of the pulse sequence used, which in turn is governed by the inherent relaxation time(s) of the system. In... 

Sederman et al. (51) recently implemented a variant of RARE, which yields multiple images from full k-space data at multiple echo times following a single r.f. 

Fourier transforms of the k-space data are depicted as solid curves in figure 4. To obtain the actual distances, r, a phase-shift factor must be added to the apparent distance, r, in the Fourier transform. This phase-shift may be estimated from model compounds. However, more accurate values for r can be obtained from curve-fitting as described below. 

A set of best-fit values (denoted by subscript bf) were obtaind by curve-fitting the filtered k-space data. Plots of the filtered data (solid curve) and associated best-fit values (dashed curve) are shown in Figure 5. These results, which are based upon theory, and hence totally independent of "model" compounds, are listed in the left-hand portion of Table I, under the heading "BFBT results" (best-fit based upon theory). 

The Fourier transform amplitude peaks at the characteristic distances i + a, where a is directly related to the phase shift a j k) in Eq. (11), and it is a powerful visual tool in providing a simple physical picture of the local structure of the metal site. The Fourier transform provides a spectrum which is similar to a radial distribution function with peaks at R, which are shifted from R by a, but which correspond to the shells of backscatterers around the central absorbing atom. The Fourier transform of the k-space data is shown in Fig. 14. Three distinct Fourier peaks are resolved above the noise level in Fig. 14 at 7 less than 4 A. 

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