3.1 System performance
Gradiometers suppress correlated noise, including laser frequency and intensity noise, fiber polarization noise, and common-mode magnetic noise. The pump/probe light is delivered to each sensor via a polarization-maintaining fiber, which picks up a large amount of mechanical noise due to fiber movement. Some of the mode-competition noise can be suppressed by modulating the laser frequency at 1 MHz, which helps to average out the index changes due to mechanical fluctuations. We have previously shown that the common-mode rejection ratio of the gradiometers increased from 70 to 500–1000, by operating under negative feedback [12]. This is due to much lower drifts of the magnetic calibration factors of each of the two magnetometer arms. Open-loop scale factors depend on laser and cell parameters as well as the magnetic field environment, while closed-loop scale factors largely depend on the coil geometry only.
First, the noise floors of all magnetometers and gradiometers were individually measured inside a table-top magnetic shield. Figure 3 shows a histogram of sensor sensitivity values, measured as the average magnetic field equivalent noise between 10–50 Hz for magnetometers (red) and gradiometers (blue). For easier direct comparison with the magnetometer, we are showing gradiometer noise in units of fT/Hz1/2 (gradiometer noise in fT/cm/Hz1/2 × 2 cm baseline). A synthetic gradiometer built out of two magnetometers, each having an uncorrelated noise floor of 10 fT/Hz1/2 in a noiseless homogenous field is expected to have a gradiometer noise of \(\sqrt{2}\) × 10 fT/Hz1/2, independent of the baseline, since the noise of the two magnetometers adds in quadrature.
Nevertheless, it can be seen from Fig. 3 that the OPM gradiometers perform better than the OPM magnetometers. This is largely due to additional noise on the light of the pump/probe fiber, which is suppressed by the gradiometers. It can also be seen that the gradiometers all have noise floors of 7 fT/cm/Hz1/2 × 2 cm = 14 fT/Hz1/2 of lower, some as low as 10 fT/Hz1/2. This implies that the individual magnetometers support a sensitivity of 7 fT/Hz1/2 (since the noise of both magnetometers add in quadrature) in a small sensitive volume of 3 × 3 × 2 mm3, which is consistent with our previous results [26].
After individual testing, the gradiometers were assembled into an array driven by one common pump/probe laser. The system was placed onto a helmet-shaped holder inside a human-sized cylindrical shield can consisting of 2 layers of mu-metal, of diameters 86 cm and 97 cm respectively, and 2 layers of aluminum (shown in Fig. 2). Figure 4 shows the simultaneous averaged sensitivity of 42 magnetometers in comparison with 21 gradiometers. Note that the system is capable of supporting 24 gradiometers (48 magnetometers) but we only had 21 pairs of OPMs available at the time of this measurement. This is due mainly to the fact that our first iteration of vacuum-packaged cells resulted in some cells whose vacuum seal degraded such that the light from the 1540 nm diodes was not sufficient to heat the vapor into the SERF regime.
The gradiometer sensitivity ranged from 10–24 fT/Hz1/2, with a median of 15.4 fT/Hz1/2, averaged from 10–50 Hz in the human-sized shield. Evoked responses typically have signal strengths of several hundred fT and up to several pT at the scalp, which are not only well above the noise floor of our system but are also detectable by sensors several cm away from the source. The gradiometer signals remain relatively flat, excluding a large vibrational noise peak between 40–80 Hz that the magnetometers exhibit. The system is located in a very mechanically and magnetically noisy environment and the shield is only slightly passively vibration-isolated from the ground.
The degradation of the array performance as compared to that of the individual gradiometers was caused by the use of one common pump/probe laser. Variations in the nitrogen buffer gas pressure of each cell led to a slightly different atomic resonance frequency spanning 10 GHz, as can be seen in Fig. 5. The cells were paired into gradiometers with similar pressures to match the FM-AM noise conversion of the two cells to reduce this noise source. The pump/probe light was tuned to an average frequency of 377.095 THz. This sacrificed about 10% sensitivity for those cells where the pump/probe laser and resonant frequency were mismatched.
The setup was complicated by an unequal pump/probe power split delivered by the 1 × 24 fiber splitter to each gradiometer. Because the sensors were assembled by hand, some of the beam paths were better aligned than others and so required less pump/probe power to perform optimally. Gradiometers requiring more power were paired with higher-power splitter ports and those requiring less power were paired with lower-power ports. This left some gradiometers with less-than-ideal power which also led to a decrease in sensitivity.
3.2 Operation in a high-field environment
Another relevant test of sensor performance is its operating range. Many magnetic shields have residual magnetic fields and gradients present, which presents a problem for SERF magnetometers. The four on-board coils in each of our sensors are integral in compensating for excess fields to keep the atomic vapor operating in the SERF regime.
To test the DC dynamic range of the OPM sensors, one gradiometer was placed into a 4-layer mu-metal shield with one pair of Helmholtz coils along cylindrical shield can axis and two pairs of saddle coils in the transverse directions to control offset fields inside of the shield. (Fig. 6(a)). DC fields were applied to one of three large external offset coils embedded in the shield. The sensor then compensated for these fields with its on-board Helmholtz and saddle coils. In the sensitive direction (z-direction), a field offset of up to 80 nT was compensated for with the two on-sensor Helmholtz coils without noticeable degradation of the gradiometer performance. Current fluctuations in the offset coils caused global magnetic fluctuations which were common to both magnetometers and subtracted in the gradiometer signal. Saddle coils shared between the two magnetometers making up the gradiometer compensated for the field offsets in the two transverse directions (x and y). As the field was increased, the on-board saddle coils could not compensate for this field uniformly and so could not simultaneously null the field across the two vapor cells. At 70 nT transverse field, a degradation of the gradiometer sensitivity of 50% was measured. This is due mainly to the broadening of the magnetic resonance line as the high magnetic field transitions the atomic vapor out of the SERF regime. Independent control of the transverse fields across each magnetometer, for example, with independent saddle coil pairs around each cell, would reduce the inhomogeneity and improve performance at larger offset fields.
3.3 Closed-loop operation
The OPM sensors are operated in a closed feedback loop, where the internal field is continuously zeroed and the magnetometer outputs represent the coil-generated fields required to compensate the ambient fields. The two field readings (one per OPM in each sensor) are digitally subtracted to form the gradiometer output. Operating under negative feedback yields a better response linearity with increasing magnetic signal amplitude. In open-loop mode, by contrast, the atomic response becomes nonlinear at a few nanotesla as atoms are driven near the edges of the atomic resonance. In closed-loop mode, the lock-in output signal is fed back on the Helmholtz coils, keeping the atoms at zero field and in the center of the resonance.
To demonstrate the superiority of closed-loop operation, we placed one of our gradiometers in the same 4-layer mu-metal shield as in the previous section and applied a 30 Hz magnetic signal of various amplitudes via the shield’s Helmholtz coils. In closed-loop mode, the relation between measured and actual magnetic signal amplitude remains linear (with a deviation from ideal linearity of <10%) even in the presence of signals >10 nT. In comparison, deviation of 10% from ideal linearity is surpassed already at a 5 nT signal field in open-loop mode (see Fig. 7). While the closed-loop operation increased the linearity, we still measure a significant degradation at larger signal fields. This region could be expanded further with more gain in the feedback loops.
Operation under negative feedback is a robust measurement technique which improves functionality in a non-ideally shielded environment. Scale factors for closed-loop OPMs are more stable than open-loop scale factors since they depend predominantly on the Helmholtz coil geometry. Closed-loop OPMs require a single calibration and magnetic field readings remain stable despite drifts in laser and cell parameters and the external magnetic field environment. This is due to the fact that, even though the lock-in signal slope changes (which impacts open-loop calibration factors), the zero-field point does not change. Thus, any external fields can be zeroed using the Helmholtz coils, whose calibration factor does not change.
In our closed-loop operation the bandwidth of the gradiometers is decreased from 230 Hz (in open-loop mode) to 150 Hz due to the increased latency of the electronics. We believe that this is not a fundamental issue but highlights a specific limitation of our electronics and feedback implementation. Because of the addition of transfer function poles introduced by the feedback, the latency increases. This can be remedied by additional zeros and poles designed specifically to increase bandwidth (i.e., decrease rise time in response to a unit step).
When operating under negative feedback, cross-talk between magnetometers becomes a larger concern. Increasing the density of magnetometers reduces the error in magnetic source localization for MEG. However, as the distance between magnetometers decreases, the modulating coils from one sensor start to influence the measurements of nearby sensors [27]. To address this problem in hardware, we have developed more sophisticated feedback coils than a simple Helmholtz geometry and have reduced the crosstalk from 8% to 0.8% at the closest possible sensor spacing of 1.25 cm and from 2% to 0.1% between the two magnetometers that constitute a gradiometer with 2 cm spacing [28]. This has not yet been implemented in this array but is a crucial next step in advancing OPM-based MEG technology.