A QUATERNION ANALYSIS OF TIME SYMMETRY IN SPIN-1 EXCITATION

The role of time symmetry in composite-pulse design is examined by con sidering a phase-alternating composite pulse pair {pi(I = 1/2), pi/2(I = 1)}, where the spin-1 excitation pulse has been derived from its sp in-1/2 progenitor by halving the pulse durations, The quaternion calcu lus is used to define the quaternion elements (Euler-Rodrigues paramet ers) of each composite pulse, In this manner, it is shown how an Euler -Rodrigues (ER) parametrization of the consecutive rotations implicit in each composite pulse can be used to derive simple phase and amplitu de relationships between the members of such a {pi(I = 1/2), pi/2(I = 1)} pulse pair. The simplicity and compactness of the ER parametrizati on is then used to identify optimal time-symmetric sequences for spin- 1 excitation by using the Lagrange multiplier method. (C) 1996 Academi c Press, Inc.