Objective. Our objective is to formulate the problem of the magnetoencephalographic (MEG) sensor array design as a well-posed engineering problem of accurately measuring the neuronal magnetic fields. This is in contrast to the traditional approach that formulates the sensor array design problem in terms of neurobiological interpretability the sensor array measurements. Approach. We use the vector spherical harmonics (VSH) formalism to define a figure-of-merit for an MEG sensor array. We start with an observation that, under certain reasonable assumptions, any array of m perfectly noiseless sensors will attain exactly the same performance, regardless of the sensors' locations and orientations (with the exception of a negligible set of singularly bad sensor configurations). We proceed to the conclusion that under the aforementioned assumptions, the only difference between different array configurations is the effect of (sensor) noise on their performance. We then propose a figure-of-merit that quantifies, with a single number, how much the sensor array in question amplifies the sensor noise. Main results. We derive a formula for intuitively meaningful, yet mathematically rigorous figure-of-merit that summarizes how desirable a particular sensor array design is. We demonstrate that this figure-of-merit is well-behaved enough to be used as a cost function for a general-purpose nonlinear optimization methods such as simulated annealing. We also show that sensor array configurations obtained by such optimizations exhibit properties that are typically expected of 'high-quality' MEG sensor arrays, e.g. high channel information capacity. Significance. Our work paves the way toward designing better MEG sensor arrays by isolating the engineering problem of measuring the neuromagnetic fields out of the bigger problem of studying brain function through neuromagnetic measurements.
To detect a specific radio-frequency (rf) magnetic field, rf optically pumped magnetometers (OPMs) require a static magnetic field to set the Larmor frequency of the atoms equal to the frequency of interest. However, unshielded and variable magnetic field environments (e.g., an rf OPM on a moving platform) pose a problem for rf OPM operation. Here, we demonstrate the use of a natural-abundance rubidium vapor to make a comagnetometer to address this challenge. Our implementation builds upon the simultaneous application of several OPM techniques within the same vapor cell. First, we use a modified implementation of an OPM variometer based on 87Rb to detect and actively cancel unwanted external fields at frequencies 60Hz using active feedback to a set of field control coils. We exploit this stabilized field environment to implement a high-sensitivity rf magnetometer using 85Rb. Using this approach, we demonstrate the ability to measure rf fields with a sensitivity of approximately 9fTHz-1/2 inside a magnetic shield in the presence of an applied field of approximately 20μT along three mutually orthogonal directions. This demonstration opens up a path toward completely unshielded operation of a high-sensitivity rf OPM.
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.