Insko E K, Elliott M A, Schotland J C, Leigh J S
Department of Radiology, University of Pennsylvania, 422 Curie Boulevard, Philadelphia, Pennsylvania 19104-6100, USA.
J Magn Reson. 1998 Mar;131(1):111-7. doi: 10.1006/jmre.1997.1355.
The remarkable theorem of reciprocity as described by D. I. Hoult and R. E. Richards (J. Magn. Reson. 24, 71 (1976)) may be generalized to account for the near, intermediate, and radiation zone fields of a magnetic dipole. This form of reciprocity may be important when the wavelength of the NMR signal is not large compared to the distance scale of the system. In these situations the effects of interference may be significant. In addition, both the frequency dependence and distance dependence of the NMR signal amplitude are altered. In general, the distance dependence of the signal follows a weighted sum of 1/r3, 1/r2, and 1/r dependence. The frequency dependence of the signal amplitude is a function of omega, omega2, and omega3. Finally, the signal reflects the full vector field nature of the magnetic dipole. The mathematical expression of generalized reciprocity is completely equivalent to that of Hoult and Richards if the appropriate retarded potential form of the magnetic field is utilized.
D. I. 霍尔特（Hoult）和R. E. 理查兹（Richards）（《磁共振杂志》24, 71 (1976)）所描述的著名互易定理可以推广，以考虑磁偶极子的近场、中场和辐射场。当NMR信号的波长与系统的距离尺度相比不大时，这种互易形式可能很重要。在这些情况下，干涉效应可能很显著。此外，NMR信号幅度的频率依赖性和距离依赖性都会改变。一般来说，信号的距离依赖性遵循1/r³、1/r²和1/r依赖性的加权和。信号幅度的频率依赖性是ω、ω²和ω³的函数。最后，信号反映了磁偶极子的全矢量场性质。如果使用磁场的适当推迟势形式，广义互易的数学表达式与霍尔特和理查兹的完全等价。
