Optimized coherence selection.

A theoretical framework for optimized coherence order selection in regards to cogwheel phase cycling is developed based on analysis of solutions of the associated homogeneous linear Diophantine equation. The empirical Hughes-Carravetta-Levitt conjectures are derived. A general formula is constructed that is guaranteed to provide valid phase cycles. Optimality of this formula is proven for non-sparse sets of coherence levels with relatively prime lower absolute bounds. Smaller phase cycles can be constructed when these conditions do not hold. The resultant formula can be incorporated into NMR spectrometer software to automatically generate cogwheel phase cycles.