Hyperpolarization and sensitivity in nuclear magnetic resonance

Hyperpolarization can boost the sensitivity of nuclear magnetic resonance. Other things being equal, a polarization increase by one order of magnitude leads to a time saving by two orders of magnitude. However, other things are rarely equal, and in this tutorial article we calculate how side effects of hyperpolarization, namely changes in duty cycle, dilution, and resolution, influence the net sensitivity and time savings of the (hyperpolarized) NMR experiment. The signal-to-noise ratio is calculated both in time- and frequency-domain for a sample at thermal equilibrium using the principle of reciprocity. The hyperpolarized time gain (HYTIGA) is calculated separately for concentration- and mass-limited samples. The article includes a detailed appendix on the measurement of the coil’s $Q$-factor.