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The application of spinors to pulse synthesis and analysis
Author(s) -
Shinnar Meir,
Leigh John S.
Publication year - 1989
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.1910120112
Subject(s) - spinor , pulse (music) , simple (philosophy) , notation , inversion (geology) , bloch equations , mathematics , pulse sequence , pure mathematics , computer science , physics , mathematical physics , quantum mechanics , telecommunications , arithmetic , nuclear magnetic resonance , paleontology , philosophy , epistemology , structural basin , biology , detector
We show how spinors may be used to solve many problems in pulse synthesis and analysis. They provide an elegant simple notation for many problems. We show how one can specify the component of a spinor and then, by exactly solving the Bloch equations, synthesize a hard pulse sequence or a soft pulse which will yield the desired spinor. This is done by generalizing our previous approach to inverting the Bloch equations. This can be applied to synthesizing refocusing pulses. Finally, some simple consequences about symmetric pulses are derived. It is shown that given a symmetric inversion pulse, one can always synthesize an asymmetric inverting pulse of the same duration, which, as an inversion, is better. © 1989 Academic Press, Inc.