RESUMEN
We report development of a highly accurate (parts per billion) absolute magnetometer based on ^{3}He NMR. Optical pumping polarizes the spins, long coherence times provide high sensitivity, and the ^{3}He electron shell effectively isolates the nuclear spin providing accuracy limited only by corrections including materials, sample shape, and magnetization. Our magnetometer was used to confirm calibration, to 32 ppb, of the magnetic-field sensors used in recent measurements of the muon magnetic moment anomaly (g_{µ}-2), which differs from the standard model by 2.4 ppm. With independent determination of the magnetic moment of ^{3}He, this work will lead the way to a new absolute magnetometry standard.
RESUMEN
Pulsed nuclear magnetic resonance (NMR) is widely used in high-precision magnetic field measurements. The absolute value of the magnetic field is determined from the precession frequency of nuclear magnetic moments. The Hilbert transform is one of the methods that have been used to extract the phase function from the observed free induction decay (FID) signal and then its frequency. In this paper, a detailed implementation of a Hilbert-transform based FID frequency extraction method is described, and it is briefly compared with other commonly used frequency extraction methods. How artifacts and noise level in the FID signal affect the extracted phase function are derived analytically. A method of mitigating the artifacts in the extracted phase function of an FID is discussed. Correlations between noises of the phase function samples are studied for different noise spectra. We discovered that the error covariance matrix for the extracted phase function is nearly singular and improper for constructing the χ2 used in the fitting routine. A down-sampling method for fixing the singular covariance matrix has been developed, so that the minimum χ2-fit yields properly the statistical uncertainty of the extracted frequency. Other practical methods of obtaining the statistical uncertainty are also discussed.