title: Direct optimization of signal-to-noise ratio of CPMG-like sequences in inhomogeneous fields.
abstract: The performance of the standard CPMG sequence in inhomogeneous fields can be improved with the use of broadband excitation and refocusing pulses. In previous work we have developed short composite broadband refocusing pulses together with practical excitation pulses to realize such performance gains, and quantified them using the ratio of signal to noise power (SNR). In this work we systematically explore the performance of refocusing pulses as a function of the overall pulse length up to ten times the length of the regular 180° pulse. This is in the regime of non-adiabatic pulses. We introduce a new performance functional for numerical pulse optimization that directly maximizes SNR and study the effect of symmetry constraints on the pulses. We find that for the optimal pulses, the SNR per asymptotic echo increases with pulse length but, for typical echo spacings, the SNR per unit time is maximized for refocusing pulses that are between two and four times longer than the duration of the standard rectangular 180° pulse. The performance is limited by the control bandwidth and the inability of finding the global maximum. The best performance was obtained with symmetric phase-alternating (SPA) refocusing pulses optimized with our novel performance functional. To test them in the CPMG sequence, we also developed axis-matching excitation (AMEX) pulses for use with these SPA refocusing pulses and tested the new AMEX-SPA sequences experimentally in a grossly inhomogeneous field, observing excellent agreement with the theoretical expectations. One of these sequences produced over 4.5 times higher SNR per asymptotic echo and 3.9 times higher SNR per unit time than the standard CPMG sequence with the same instantaneous RF power level. We also found that the new sequences are at least as robust to changes in the RF field strength as the standard CPMG sequence.
authors.affiliation: Schlumberger-Doll Research, One Hampshire Street, Cambridge, MA 02139, United States.
authors.forename: Soumyajit
authors.initials: S
authors.lastname: Mandal
authors.affiliation: Institute for Quantum Computing, 200 University Ave. W., Waterloo, ON N2L 3G1, Canada; Department of Physics and Astronomy, University of Waterloo, Waterloo, ON N2L 3G1, Canada.
authors.forename: Troy W
authors.initials: TW
authors.lastname: Borneman
authors.affiliation: Schlumberger-Doll Research, One Hampshire Street, Cambridge, MA 02139, United States; School of Engineering and Applied Sciences, Harvard University, 33 Oxford Street, Cambridge, MA 02138, United States.
authors.forename: Van D M
authors.initials: VDM
authors.lastname: Koroleva
authors.affiliation: Schlumberger-Doll Research, One Hampshire Street, Cambridge, MA 02139, United States. Electronic address: hurlimann@slb.com.
authors.forename: Martin D
authors.initials: MD
authors.lastname: Hürlimann
keywords: CPMG; Inhomogeneous fields; Optimal control; Relaxation