Sensitivity Enhancement by Remote Detection

The situation is different in an experiment where the acquisition dimension of the conventional, direct detection experiment itself measures only the magnitude of a signal, as opposed to its time evolution. This is the case for example in an MRI experiment with phase encoding in all three dimensions. Here, it is the ID sensitivity that has to be compared between remote and direct detection, because the direct FID is no longer sampled point-by-point. Also, by following the treatment of ID sensitivity in Ref. [20], this yields  

In order to use Eqs. (2.6.1) and (2.6.2) to estimate the sensitivity gain obtained by remote detection, knowledge of the relative sensitivity of the detector and the encoding circuit, A, is required. Here we discuss the sensitivity of an rf coil detector as an example, because all the experiments presented in this text use inductive detection at high field. The signal-to-noise ratio of inductive NMR detection can be approximated by the following simplified equation [12]  

Finally, to estimate A at a given B0 and T, it is sufficient to consider the coil s Q and Vc. The Bi field, and thus the jt/2 pulse length tg0, are directly related to these parameters, as expressed in Ref. [12] 

Consequently, knowledge of the t90 of both coils - for the same applied rf power -allows a rough calculation of the expected signal-to-noise ratio, in agreement with the principle of reciprocity [27]. The sensitivity ratio between the two coils is thus given by 

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