Symmetrical composite pulse sequences for NMR population inversion. I. Compensation of radiofrequency field inhomogeneity

Abstract

The interaction of a nuclear spin system with an inhomogenous or misset radio-frequency field is described by means of rotation operators. It is shown that it is possible to construct sequences of small numbers of pulses which rotate the magnetization vector in a manner analogous to a single pulse, but which have the advantage of being less sensitive to deviations in the radiofrequency field strength. Two new “composite pulses” are proposed which have this property and which convert longitudinal magnetization into transverse magnetization—a two-pulse sequence employing a 27π 3 radian phase shift, and a four-pulse sequence. The problem of inversion of spin populations by a composite pulse is then addressed. It is shown that composite pulse sequences can be constructed which take magnetization vectors from the z axis to the − z axis via trajectories possessing either approximate reflection symmetry, or approximate rotational symmetry. It is shown that this symmetry may cause additional error compensation, and two new pulse sequences are suggested for NMR population inversion—one of three pulses, and one of nine pulses. The sensitivity of these sequences to off-resonance effects is discussed.