Categories of coherence pathways for the CPMG sequence

The CPMG sequence has been extremely useful for efficient measurements of NMR signal, spin-spin relaxation, and diffusion, particularly in inhomogeneous magnetic fields, such as when samples are outside the magnet and RF coil. Due to the inaccuracy of the pulses and the off-resonance effects, the CPMG echoes have contributions from the Hahn echo as well as signals that are similar to stimulated echoes. The systematic understanding of the CPMG pulse sequence requires decomposing the magnetization dynamics into different coherence pathways. In this paper, we describe a method to classify the CPMG coherence pathways and illustrate the nature of these types of pathways. This classification shows that direct echo and stimulated echoes are the major contribution to the CPMG signal. It also provides a clear understanding of the effect of restricted diffusion in porous media.