Magic-angle rotating-frame imaging

In the presence of dipolar couplings the total spin Hamiltonian in the rotating reference frame is given by 

Here the initial density matrix po(x) corresponds to the spin density (cf. eqn (8.1.1)). 

Evaluation of the density matrix is facilitated by transformation of the spin Hamiltonian into the rotating frame, the z -axis of which is tilted at the magic angle tilted rotating frame), 

2 2D MARF images of compressed polycrystalline adamantane. Left MARF images obtained by reconstruction from projections. Right shapes of the objects and dimensions. Adapted from i Mar2] with permission from the author. 

Line narrowing by multiple-puhe techniques (cf Section 3,3.4) is a promising approach to solid-state imaging with good spatial re.solution. However, high demands on experimental set-up and equipment hamper the use of the technique. Moreover, for line narrowing by multiple-pulse techniques the data points of the free-induction decay are acquired between pulses (cf. Fig. 3.3.10), and the efficiency depends on the quality of the rf pulses [Hael, Mehl. Radio-frequency pulse.s with short rise and fall times require a low quality factor of the rf coil which, at the same time, reduces the sensitivity and therefore limits the. spatial resolution. 

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Multiple-pulse sequences based on off-resonance excitation - where the effective interaction frame rotates at the magic angle and dipolar interactions can be made to vanish. Imaging in this interaction frame requires a combination of matched RF and d.c. gradients. 

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