Sandia National Laboratories, Albuquerque, NM 87185, USA.
Department of Neuroscience and Biomedical Engineering, Aalto University School of Science, FI-00076 Aalto, Finland.
Sensors (Basel). 2022 Apr 15;22(8):3059. doi: 10.3390/s22083059.
In this paper, we propose a method to estimate the position, orientation, and gain of a magnetic field sensor using a set of (large) electromagnetic coils. We apply the method for calibrating an array of optically pumped magnetometers (OPMs) for magnetoencephalography (MEG). We first measure the magnetic fields of the coils at multiple known positions using a well-calibrated triaxial magnetometer, and model these discreetly sampled fields using vector spherical harmonics (VSH) functions. We then localize and calibrate an OPM by minimizing the sum of squared errors between the model signals and the OPM responses to the coil fields. We show that by using homogeneous and first-order gradient fields, the OPM sensor parameters (gain, position, and orientation) can be obtained from a set of linear equations with pseudo-inverses of two matrices. The currents that should be applied to the coils for approximating these low-order field components can be determined based on the VSH models. Computationally simple initial estimates of the OPM sensor parameters follow. As a first test of the method, we placed a fluxgate magnetometer at multiple positions and estimated the RMS position, orientation, and gain errors of the method to be 1.0 mm, 0.2°, and 0.8%, respectively. Lastly, we calibrated a 48-channel OPM array. The accuracy of the OPM calibration was tested by using the OPM array to localize magnetic dipoles in a phantom, which resulted in an average dipole position error of 3.3 mm. The results demonstrate the feasibility of using electromagnetic coils to calibrate and localize OPMs for MEG.
在本文中，我们提出了一种使用一组（大型）电磁线圈估计磁场传感器位置、方向和增益的方法。我们将该方法应用于光泵磁强计（OPM）的校准，以用于脑磁图（MEG）。我们首先使用经过良好校准的三轴磁强计在多个已知位置测量线圈的磁场，并使用矢量球谐（VSH）函数对这些离散采样的磁场进行建模。然后，我们通过最小化模型信号与 OPM 对线圈磁场的响应之间的平方和误差来定位和校准 OPM。我们表明，通过使用均匀和一阶梯度场，可以从一组具有两个矩阵的伪逆的线性方程中获得 OPM 传感器参数（增益、位置和方向）。可以基于 VSH 模型确定应施加到线圈以近似这些低阶场分量的电流。然后可以得出 OPM 传感器参数的计算简单的初始估计。作为该方法的首次测试，我们将磁通门磁强计放置在多个位置，并估计该方法的 RMS 位置、方向和增益误差分别为 1.0 毫米、0.2°和 0.8%。最后，我们校准了一个 48 通道的 OPM 阵列。通过使用 OPM 阵列在体模中定位磁偶极子来测试 OPM 的校准精度，结果导致平均偶极子位置误差为 3.3 毫米。结果表明，使用电磁线圈来校准和定位 MEG 的 OPM 是可行的。
