Feed-forward active magnetic shielding

TL;DR

Brain-field measurements require suppression of ambient magnetic noise, which this paper addresses with a feed-forward active shielding approach augmented by a decoupling matrix to counter coil–reference coupling. The authors formulate a linear data model linking ambient sources, main sensors, reference sensors, and shielding coils, and derive a procedure to compute the gain ${\bf M}$ using drive and ambient data, augmented by a PCA-derived decoupling transform ${\bf U}$ when coil–reference coupling ${\bf D}$ is non-negligible. In toy 2D and 3D Biot–Savart simulations, the method achieves ambient-field attenuation factors exceeding $10^5$ and $10^7$, respectively, suggesting feasibility for hardware implementation and potential to enable cheaper, flexible magnetometry with optically-pumped sensors. The work is data-driven, avoids precise geometric calibration, and could impact MEG, MCG, and related sensing domains by enabling high-quality shielding in portable or clinical settings.

Abstract

Magnetic fields from the brain are tiny relative to ambient fields which therefore need to be suppressed. The common solution of passive shielding is expensive, bulky and insufficiently effective, thus motivating research into the alternative of active shielding which comes in two flavours: feed-back and feed-forward. In feed-back designs (the most common), corrective fields are created by coils driven from sensors within the area that they correct, for example from the main sensors of an MEG device. In feed-forward designs (less common), corrective fields are driven from dedicated reference sensors outside the area they correct. Feed-forward can achieve better performance than feed-back, in principle, however its implementation is hobbled by an unavoidable coupling between coils and reference sensors, which reduces the effectiveness of the shielding and may affect stability, complicating the design. This paper suggests a solution that relies on a ``decoupling matrix," inserted in the signal pathway between sensors and corrective coils, to counteract the spurious coupling. This allows feed-forward shielding do reduce the ambient field to zero across the full frequency range, in principle, although performance may be limited by other factors such as current noise. The solution, which is fully data-driven and does not require geometric calculations, high-tolerance fabrication, or physical calibration, has been evaluated by simulation, but not implemented in hardware. It might contribute to the deployment of a new generation of measurement systems based on optically-pumped magnetometers (OPM). The lower cost and reduced constraints of those systems are a strong incentive to likewise reduce the cost and constraints of the shielding required to operate them, hence the appeal of active shielding.

Figures (7)

• Figure 1: A: Magnetic fields from the brain are dwarfed by fields from ambient sources, including the earth's magnetic field and fields from electrical circuits and machinery. B: Classic approaches to the problem: passive magnetic shielding, subtraction of signals from reference sensors, active magnetic shielding with coils, downstream signal processing.
• Figure 2: Two basic topologies for active shielding of an MEG system. A: Feed-back: coils are driven from the main sensors via a matrix M tuned to minimize the field at the main sensors. B: Feed-forward: coils are driven from an array of reference sensors via a matrix M tuned to minimize the field at the main sensors.
• Figure 3: A: An array of correction coils is driven from an array of reference sensors via a feed-forward sensor-to-coil transform matrix ${\bf M}$ that is tuned to minimize the field at the primary sensors in the absence of brain activity. B: Block diagram of quantities and transforms. C: To estimate coil-to-sensor matrices ${\bf C}$ and ${\bf D}$, coils are driven with a current ${\bf Q}_d$ large enough that the ambient field can be ignored. D: To estimate the reference-to-main sensor coupling matrix ${\bf P}$, sensor outputs are observed in response to the ambient field, in the absence of coil current. E: If the coil-to-reference matrix ${\bf D}$ is small enough be ignored, ${\bf M}$ can be estimated from ${\bf C}$ and ${\bf P}$. F: If ${\bf D}$ is non-negligible, its effect can be removed by applying a "shielding" matrix ${\bf U}$ (see text). G: Structure of the system.
• Figure 4: Toy world simulation. A: Ambient sources (black circles) are located on the edges of a large square, main sensors (black crosses) on the edge of a small square. Reference sensors (red circles) and coils (red crosses) occupy intermediate positions. B: Amplitude of the field of a single ambient source. C: RMS amplitude of the field of 8 concurrently active ambient sources. D: Amplitude of the ambient field in the presence of active shielding.
• Figure 5: Effect of the decoupling matrix. A: The color at each point represents the maximum gain from that point to any reference sensor (crosses). B: Same, when the decoupling matrix is applied. At each coil (circles) the maximum gain to any sensor approaches zero (blue dots).