Compensation for Pulse Imperfections in NMR Spin-Echo Experiments

Abstract The refocusing pulse R Y ( π ) of a Carr-Purcell spin-echo experiment may be replaced with a composite sequence of three pulses, R X ( π /2) R Y ( π ) R X ( π /2), which compensates the effects of pulse length errors due to spatial inhomogeneity of the radiofrequency field. An analysis in terms of rotation operators indicates that the overall effect of the sequence R X ( π /2 + Δ ) R Y ( π + 2 Δ ) R X ( π /2 + Δ ) is equivalent to an exact π pulse applied about an axis in the XY plane which is phase shifted by an angle Δ with respect to the Y axis. Good spin state inversion is therefore achieved, but there is a phase shift of 2Δ for odd-numbered echoes, which is canceled on even-numbered echoes. For spin systems with no homonuclear coupling, the degree of compensation exceeds that of the well-known Meiboom-Gill modificaation, while for coupled spin systems the composite pulse scheme provides effective compensation whereas the Meiboom-Gill method breaks down. The technique has been tested on the proton spectrum of 1,1,2-trichloroethane with deliberately misset refocusing pulses; gross fluctuations in intensity are observed unless the composite pulses are used. A slightly different composite pulse sequence is proposed for situations where radiofrequency offset effects are the dominant source of error.

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