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The synthesis of pulse sequences yielding arbitrary magnetization vectors
Author(s) -
Shinnar Meir,
Eleff Scott,
Subramanian Harihara,
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.1910120109
Subject(s) - pulse sequence , fourier transform , fourier series , pulse (music) , sequence (biology) , magnetization , excitation , offset (computer science) , generalization , series (stratigraphy) , physics , mathematics , fourier analysis , mathematical analysis , function (biology) , nuclear magnetic resonance , magnetic field , quantum mechanics , chemistry , computer science , evolutionary biology , biology , programming language , paleontology , biochemistry , voltage
A new procedure and algorithm are presented to allow the synthesis of a pulse sequence which will generate an arbitrary frequency‐dependent spin excitation. This procedure is a generalization of our previous paper, where this was done subject to the restriction that the spin excitation was symmetric about zero offset frequency, and pulses were restricted to being about a fixed axis. The required final z‐magnetization vector ( M z ) is expressed as a function of the off‐resonance frequency as an N th order complex Fourier series. We then form a consistent Fourier series for ( M xy ). As many as 2 2N different pulse sequences may be directly generated all of which produce a different M xy (f ), but the same M z (f). A pulse sequence is then generated which will yield the desired M z (f ) and M xy (f). This is done by an analytic inversion of the Bloch equation, not by the classical Fourier approximation. This technique enables us to generate any M z which is potentially realizable by a pulse sequence. © 1989 Academic Press, Inc.