Field-Noise Effects on NMR Signals: Hahn Echoes and CPMG

 Stanislav Sykora

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presented at

XXXII Congress on Magnetic Resonance, GIDRM, Pavia (Italy) 2002, Sept.18-21.

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Using the techniques developed in Part I, this study investigates the effects of various types of field fluctuations on Hahn echos and CPMG echo trains. Compared to an FID, the echos (both single and multiple) refocus a substantial part of the induced phase errors, provided the field noise is Gaussian and its mean correlation time is not much smaller than tau (the time interval between the 90 and 180-degree pulses). For a normally distributed field noise, the echo-phase errors never exceed those of an FID at the same total time elapsed since the excitation pulse.

When the field is subject to a periodic modulation, however, there are values at which the refocussing is very good, alternating with regions where the echo phase errors exceed those encountered in an FID. For a single echo the critical tau values center around odd multiples of T/2, T being the modulation period, while the 'good' ones are in the vicinity of integer multiples of T. This picture changes in a train of n echos. Increasing n beyond 3, ever more ample regions of tau values with excellent field-error refocussing alternate with ever narrower regions of severe resonant error amplification. The critical tau values are centered around odd multiples of T/4 and may all but preclude a successful application of a CPMG sequence. This, among other things, explains some striking and only partially explained CPMG artifacts.

The results provide a basis for the evaluation of errors due to field noise in those experimental techniques which use multiple spin echos and/or spin-locking mechanisms. They are directly applicable also to the T1r experiment which can be viewed as a limit case of CPMG for tau tending to 0. Due to field noise, averaged CPMG and T1r data are biased in a way which increases the apparent decay rate. Since this noise-induced decay factor is non-exponential, it can even simulate/modify non-exponentiality. Methods to estimate, detect and overcome such errors are discussed.


  • A.Allerhand, Effect of Magnetic Field Fluctuations in Spin-Echo NMR Experiments, Rev.Sci.Instr. 41, 269 (1970).
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