  We investigate the maximum signal to noise ratio per unit time that can be
achieved for a spin 1/2 particle subjected to a periodic pulse sequence.
Optimal control techniques are applied to design the control field and the
position of the steady state, leading to the best signal to noise performance.
A complete geometric description of the optimal control problem is given in the
unbounded case. We show the optimality of the well-known Ernst angle solution,
which is widely used in spectroscopic and medical imaging applications, over a
large control space allowing use of shaped pulses.
