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Title: Optimal control of the signal-to-noise ratio per unit time of a spin 1/2 particle: The crusher gradient and the radiation damping cases

We show to which extent the signal to noise ratio per unit time of a spin 1/2 particle can be maximized. We consider a cyclic repetition of experiments made of a measurement followed by a radio-frequency magnetic field excitation of the system, in the case of unbounded amplitude. In the periodic regime, the objective of the control problem is to design the initial state of the system and the pulse sequence which leads to the best signal to noise performance. We focus on two specific issues relevant in nuclear magnetic resonance, the crusher gradient and the radiation damping cases. Optimal control techniques are used to solve this non-standard control problem. We discuss the optimality of the Ernst angle solution, which is commonly applied in spectroscopic and medical imaging applications. In the radiation damping situation, we show that in some cases, the optimal solution differs from the Ernst one.
Authors:
;  [1] ;  [2] ;  [3] ;  [2]
  1. Department of Chemistry, Technische Universität München, Lichtenbergstrasse 4, D-85747 Garching (Germany)
  2. Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 6303 CNRS-Université de Bourgogne, 9 Ave. A. Savary, BP 47 870, F-21078 Dijon Cedex (France)
  3. (Israel)
Publication Date:
OSTI Identifier:
22416044
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 4; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; DAMPING; EXCITATION; FERMIONS; MAGNETIC FIELDS; NUCLEAR MAGNETIC RESONANCE; OPTIMAL CONTROL; PERFORMANCE; PERIODICITY; RADIOWAVE RADIATION; SIGNAL-TO-NOISE RATIO; SPIN