Self-Adaptive Loop for External-Disturbance Reduction in a Differential Measurement Setup

We present a method developed to actively compensate common-mode magnetic disturbances on a multisensor device devoted to differential measurements. The system uses a field-programmable-gated-array card, and operates in conjunction with a high-sensitivity magnetometer: compensating the common mode of magnetic disturbances results in a relevant reduction of the difference-mode noise. The digital nature of the compensation system allows for the use of a numerical approach aimed at automatically adapting the feedback-loop filter response. A common-mode-disturbance attenuation exceeding 50 dB is achieved, resulting in a final improvement of the differential noise floor by a factor of 10 over the whole spectral interval of interest.

Figure 1

The single-channel OAM schematics. The Cs cell is illuminated by two types of co-propagating radiation, which are appropriately polarized to pump (red curved arrow) and probe (blue curved arrows) the atomic magnetization. The pump and probe beams denoted as CP are co-propagating through the Cs cell. An interference filter (IF) is used to block the pump beam. The Faraday rotation of the probe’s polarization (from $P_{\mathrm{in}}$ to $P_{\mathrm{out}}$) is measured by a balanced polarimeter (BP).

Figure 2

The single-channel noise-amplitude spectral density (ASD), the square root of the power spectral density.

Figure 3

The block diagram of the feedback loop. The system contains three main units: the experiment module—the magnetometer and the field control (current amplifier and coils); the real-time module (FPGA); and the computer for online data analysis and optimization. The elements in the dashed box constitute a linear time-invariant (LTI) system. A linear control approach for field stabilization through a feedback loop is implemented in the FPGA. An optimization procedure running on the personal computer (PC) determines the infinite-impulse-response (IIR) filter coefficients for the best noise rejection.

Figure 4

A sketch of the whole setup. The Cs cell is merged in a field $\overrightarrow{B}$ made of a static term – controlled by the coil DC – and of time-dependent external-disturbances that are counteracted by the compensation coils (CC). The sensor output is digitized both by the FPGA ADC and by a PCI-ADC. The FPGA elaborates the signal to provide a real-time output at the DAC board, which is used to feed the CC through a voltage-to-current converter (V2I); the PC elaborates finite-time traces to extract the spectral information to evaluate the cost function used in the optimization procedure (OPT). The latter provides loop-filter coefficients to the FPGA and searches for their optimal values.

Figure 5

The power spectra, in a wide (upper plot) and a narrow (lower plot) frequency range, of the polarimetric signal of a single magnetometer channel in open loop (a) and in closed loop with an FIR loop filter designed according to the magnetometer frequency response (b).

Figure 6

A sample of a few significative steps in the optimization procedure. Starting from the uncompensated case (step 0), a progressive improvement of the polarimetric signal spectra is achieved. The improvement appears in the power spectrum (PS) and consists in the fact that both the pedestal and the peaks around the carrier frequency are lower than in the uncompensated case. The CF reduction is represented in the blue plot on the left vertical plane.

Figure 7

The power spectrum of the polarimetric signal of a single magnetometer channel obtained with an IIR filter after optimization. Both plots show the same signal in different frequency ranges. The most prominent feedback-loop instability can be seen in the upper plot—around 4 kHz away from the carrier frequency at about 14 kHz.

Figure 8

The amplitude spectral density of the DM signal.