Nonlinear characterization of NMR systems by Wiener kernels

Abstract

Stochastic excitation of nuclear magnetic resonance, NMR, systems is a relatively new technique used to obtain NMR spectra. Instead of the conventional monochromatic radiation sources, samples are excited with a band limited white noise spectrum. The familiar Bloch equation can be derived for a nucleus in a constant magnetic field subjected to a stochastic perturbation. The method employed by Ernst (1) to solve these equations is examined in this report. In order to characterize an NMR system, the magnetization is expressed as an infinite sum of increasing order functionals called the Wiener series. Equations, which may be solved on a computer, are derived for the first and third Wiener kernel. Computer programs to implement these equations are written and tested with several test systems. The programs are applied to NMR signals obtained from a water sample using various values of input intensity to verify the saturation curve predicted from the theory. An NMR spectrum is also obtained for noise excitation of the hydrogen nuclei in a sample of 2, 3-dibromothiophene.