Estimation and Utilization of the Geomagnetic Field Inhomogeneities Using the Relaxation Characteristics of the FID Signal in an Overhauser Magnetometer

Accurate measurement of geomagnetic field inhomogeneity commonly necessitates the use of two or more magnetic sensors for differential measurements, and most of the geomagnetic sensors are unusable in large inhomogeneous fields. To address these issues, this article presents a new approach for estimating the geomagnetic field's inhomogeneities based on a single Overhauser magnetometer. First, we establish the improved free induction decay (FID) signal model by integrating the phases of all protons over the entire Overhauser sensor in arbitrary inhomogeneous fields, which enables the inversion of the geomagnetic field gradient using the relaxation characteristics of the FID signal. Then, we propose a composite algorithm designed to accurately derive the relaxation parameters of the FID signal by carefully extracting and denoising its envelope and after that calculate the gradient of the geomagnetic field by the above FID signal model. Moreover, we designed a specialized Overhauser magnetic sensor prototype for measuring geomagnetic gradients and conducted experiments on a dedicated experimental platform. The designed prototype successfully measured the magnetic gradient even under high gradients of up to 10 005 nT/m, yielding a measurement error of 15.83%, with one sensor in the experiments. In addition, we employed this method to successfully detect unexploded ordnance (UXO) using the transverse relaxation time of the FID signal as an indicator. This application further validates the effectiveness and practicality of our proposed methodology.