Optimal control of the signal to noise ratio per unit time for a spin 1/2 particle

TL;DR

This paper applies optimal control techniques to maximize the signal-to-noise ratio per unit time in spin 1/2 particles, confirming the optimality of the Ernst angle solution and providing a geometric framework for control design.

Contribution

It introduces a geometric description of the optimal control problem and demonstrates the optimality of the Ernst angle solution within a broad control space.

Findings

Optimal control techniques identify the best pulse sequences for maximum SNR.

The Ernst angle solution is proven to be optimal in the unbounded control case.

Shaped pulses can be used to improve signal-to-noise performance.

Abstract

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.