Imaging with noise excitation

Stochastic excitation in NMR denotes excitation of the spin system with noise [Em3, Kail], which is, in general, white within the spectral region of the linear response. White means that the average of the power spectral density is independent of frequency. This is automatically fulfilled for a delta pulse. For noise this is valid only if successive values 

3 5 Relating-[Vami imaging of Milvenl penetration into reelangular polymer rods, (a) 

The spin sy.stem contains four input signals. These are the rf excitation. r(f) and the three gradient modulation signals G., Cy, and G-. The four input signals can be combined into one excilalinn function 

Cross-correfatfon of the system response yi (r) defined in (5.4.7) with pj (r, /, p) over a finite time T produces the correlation function 

Spectroscopic resolution is obtained by systematic variation of cr in the cross-correlation function (6.4.3) and subsequent Fourier transformation over a. In this way, resonance frequency and 72 relaxation time or spectroscopic lineshape become part of a localization function b[(r — r, 2l — Tif), which now determines not only the spatial but also the spectroscopic resolution, 

---

Fig. 6.4.1 [Blul] In imaging with noise excitation the spin density convolved by a localization function can be retrieved by linear cross-correlation of the system response with a function of the space coordinate r = (x, y, z ) and the time delay

Fig. 6.4.2 (a) Timing diagram for imaging with noise excitation and oscillating gradients. The... 

---