Aspects of NMR reciprocity and applications in highly conductive media

In the context of NMR spectroscopy and MRI, the principle of reciprocity provides a convenient method for determining the reception sensitivity from the transmitted rf field pattern. The reciprocity principle for NMR was originally described by Hoult et al (J Magn Reson. 1976;24:71) and is related to the broader Lorentz reciprocity principle and similar theorems from antenna theory. One frequent application of the reciprocity principle is that for a single coil used for both transmission and detection, the transmit and receive fields can be assumed to be equal. This aspect is also where some of the conceptual difficulty of applying the theorem may be encountered. For example, the questions of whether one should use the complex conjugate field for detection or whether one should apply the theorem in the rotating frame or in the laboratory frame may give rise to considerable confusion. We attempt here to provide a helpful discussion of the application of the reciprocity principle in such a way as to clarify some of the confounding questions. In particular, we avoid the use of the “negatively rotating frame,” which is frequently mentioned in this context, since we consider it to unnecessarily complicate the matter. In addition, we also discuss the implications of the theorem for magnetic resonance experiments on conducting samples, and metals, in particular.