<i>In Situ</i> Measurement of Nonorthogonal Angles of a Three-Axis Vector Optically Pumped Magnetometer
Siran Li, Jixi Lu, Danyue Ma, Kun Wang, Yanan Gao, Chang Sun, Bangcheng Han
Abstract
An <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> method has been proposed for measuring all nonorthogonal angles of the beams and triaxial coils in a three-axis vector optically pumped magnetometer (OPM). Based on the combination and alignment of two pump beams, each of which can achieve biaxial transverse measurement in a time-sharing regime under modulated magnetic fields, a 3-D orthogonal coordinate measurement system is obtained, and the measurement models for three categories (six types) of nonorthogonal angles are established theoretically. On this basis, we experimentally measured the nonorthogonal angles along with related uncertainties at different modulated frequencies and strengths of the magnetic fields. The nonorthogonal angles were (3.65° ± 0.52°) between the two pump beams before compensation. They were (7.05° ± 0.23°) between the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula> - and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Y$ </tex-math></inline-formula> -axis coils, (8.89° ± 0.21°) between the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Y$ </tex-math></inline-formula> - and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Z$ </tex-math></inline-formula> -axis coils, (5.23° ± 0.27°) between the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula> - and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Z$ </tex-math></inline-formula> -axis coils, (7.24° ± 0.24°) between the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x$ </tex-math></inline-formula> -direction pump beam and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula> -axis coil, and (9.10° ± 0.22°) between the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$z$ </tex-math></inline-formula> -direction pump beam and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Z$ </tex-math></inline-formula> -axis coil. This study measures the magnitudes of six types of nonorthogonality, without making an assumption of ideal orthogonality or using auxiliary calibration equipment. Moreover, this method can be extended to several other kinds of OPMs with simple modifications. This study is critical for evaluating and reducing the misalignment error to improve the accuracy of three-axis vector OPMs.