Multiplicative or t 1 Noise in NMR Spectroscopy

Abstract

The signal in a nuclear magnetic resonance (NMR) experiment is highly sensitive to fluctuations of the environment of the sample. If, for example, the static magnetic field B 0, the amplitude and phase of radio frequency (rf) pulses, or the resonant frequency of the detection circuit are not perfectly stable and reproducible, the magnetic moment of the spins is altered and becomes a noisy quantity itself. This kind of noise depends on the presence of a signal, to which it is usually proportional. Since all the spins at a particular location in a sample experience the same environment at any given time, such multiplicative noise primarily affects the reproducibility of an experiment. It is mainly of importance in the indirect dimensions of a multidimensional experiment, when intense lines are suppressed with a phase cycle, or for difference spectroscopy techniques. Equivalently, experiments which are known to be problematic with regard to their reproducibility, like flow experiments or experiments with a mobile target, tend to be affected more strongly by multiplicative noise. In this article it is demonstrated how multiplicative noise can be identified and characterized using very simple, repetitive experiments. An error estimation approach is developed to give an intuitive, yet quantitative understanding of its properties. The consequences for multidimensional NMR experiments are outlined, implications for data analysis are shown, and strategies for the optimization of experiments are summarized.