# Pulsed Optically Pumped Magnetometers: Addressing Dead Time and Bandwidth for the Unshielded Magnetorelaxometry of Magnetic Nanoparticles

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Setup Overview

#### 2.2. MNP Excitation Circuit

#### 2.3. MNP

#### 2.4. OPM: Optical Magnetic Gradiometer (OMG)

^{87}Rb). After pumping, the atoms freely precess and their projection is monitored by optical rotation of a linearly polarized probe beam light. The off-resonance $100\mathsf{\mu}\mathrm{W}$ probe beam light is generated by a single mode, polarization stable vertical-cavity surface-emitting laser (VCSEL). Both, the pump and probe laser are tuned near the 795 $\mathrm{n}$$\mathrm{m}$ rubidium resonance manually. The rubidium polarization relaxation rate is dominated by spin-exchange relaxation. With the pump beam shut off for the duration of the measurement a class of systematic errors from pump lightshift to pointing noise are completely eliminated, resulting in a very clean and high precision frequency-based magnetic field measurement. The high power optical pumping substantially resets and erases the time history of the alkali polarization, rendering an independent magnetic field measurement each $\mathrm{m}\mathrm{s}$. It should be noted that there is no frequency feedback or resonance tracking as used in other types of self-oscillating magnetometers. This also enhances OPM bandwidth. The different elements of the commercially available sensor are sketched in Figure 3. The sensor is composed of two magnetometers; i.e., it houses two vapor cells. The pump beam and probe beam are split and distributed to the two cells, enabling a future common laser noise reduction as in [49]. The two amplified photodiode signals are available as analog outputs of the OPM control electronics. Additionally, the signals are filtered with a passband between 100 and $500\mathrm{kHz}$ and are fed into an FPGA inside the OMG control electronics, which measures the frequency and sends the result via USB connection.

#### 2.5. Data Acquisition, System Synchronization and Mains Synchronization

#### 2.6. Data Processing: Raw Photodiode Data

^{87}Rb ($\gamma /2\pi =7\mathrm{Hz}/\mathrm{n}\mathrm{T}$). Iterating over each data chunk gives magnetic field readings at a sample rate of $1\mathrm{kHz}$.

#### 2.7. Data Processing: FPGA Data

#### 2.8. Data Processing: MRX Data

#### 2.9. Proof of Principle Unshielded OPM-MRX with 100 mT Pulsed Fields

## 3. Results and Discussion

#### 3.1. OMG Characterization and Performance

^{87}Rb and corresponds to the Earth’s magnetic field of $43.6\mathsf{\mu}\mathrm{T}$. The harmonic at $610\mathrm{kHz}$ may arise due to orientation-to-alignment conversion due to the linearly polarized probe laser or due to a background magnetic field with a vector component parallel to the pump beam [56,57].

#### 3.2. Unshielded MRX with OMG

#### 3.3. Proof of Principle Unshielded OPM-MRX with 100 mT Pulsed Fields

## 4. Conclusions and Outlook

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Schematic drawing of the pulsed optically pumped magnetometers (OPM), consisting of two pulsed magnetometers enclosed in a compact sensor head.

**Figure 4.**Summary of the raw photodiode processing techniques used: (

**a**) free-precession decay fit ($1\mathrm{kHz}$ sample rate); (

**b**) Hilbert transform; (

**c**) sliding window cosine fit.

**Figure 5.**Unshielded OPM-MRX setup with possible MRX excitation fields of up to 100 mT. The battery powered notebook, the USB-oscilloscope and the OMG control electronics are visible on the upper part of the figure. The OMG’s sensor head and the MRX excitation-coil are visible in the lower part of the figure. The position where the MNP sample was later placed is indicated by an arrow. The power amplifier is not visible, as it is located at a distance of about 3 m.

**Figure 6.**(

**a**) Unshielded raw OMG photodiode signal as output by the OPM electronics and recorded using an oscilloscope. (

**b**) Amplitude noise spectral densities (ANSD) of the raw OMG analog output: blue—normal operation; red—pump laser always off; black—OMG unpowered. The data used for the calculation of the ANSD were recorded $100\mathsf{\mu}\mathrm{s}$ to $700\mathsf{\mu}\mathrm{s}$ after the pump pulse.

**Figure 7.**Amplitude noise spectral density (ANSD) of the unshielded OPM in a laboratory environment. The OMG was configured to pump for $22\mathsf{\mu}\mathrm{s}$. The software gradiometer baseline is $2.3\mathrm{c}\mathrm{m}$.

**Figure 8.**Unshielded magnetometer noise spectral densities using free-precession decay fits (brown), sliding window fits (green) and Hilbert transform (red). Unshielded gradiometer noise spectral densities using free-precession decay fits (green), sliding window fits (blue), Hilbert transform (black) and linear fit to the Hilbert transform (purple).

**Figure 9.**Magnetometer amplitude response over OMG bandwidth for both magnetometer channels using Hilbert transform.

**Figure 10.**Coil current and OPM photodiode output. The optical pumping started $28\mathsf{\mu}\mathrm{s}$ after initiating the coil shut-off. The signal distortion prior the pump pulses (i.e., periods $-0.2\mathrm{m}\mathrm{s}$ to $0\mathrm{m}\mathrm{s}$ and $0.8\mathrm{m}\mathrm{s}$ to $1\mathrm{m}\mathrm{s}$) is caused by the electrical heater of the OMG.

**Figure 11.**Unshielded OPM-MRX measurements of BNF-MNP (sample with dilution factor 1:20). The excitation coil is on when no FPGA data are available, e.g., in the time span from $20\mathrm{m}\mathrm{s}$ to $30\mathrm{m}\mathrm{s}$. The FPGA data were not averaged.

**Figure 12.**Unshielded OPM-MRX measurements of a BNF-MNP dilution series. The excitation coil was switched off a few $\mathsf{\mu}\mathrm{s}$ before the timestamp $0\mathrm{s}$. The gradiometric data were averaged 100-times and an averaged empty measurement was subtracted. Individual FPGA-data-points are indicated by crosses, solid lines are the corresponding exponential fits (compare Table 1). (

**a**) FPGA data. (

**b**) FPGA data and instantaneous magnetic field obtained via Hilbert transform of 1:20 BNF sample; top: logarithmical time axis, bottom: linear time-axis.

**Figure 13.**(

**a**) FPGA-data of MRX of MNP embedded in gypsum at different excitation fields of up to $100\mathrm{m}\mathrm{T}$. The inset shows a zoom of the first $30\mathrm{m}\mathrm{s}$ of the relaxations. Please note the different time scale of the figure and inset. The data were not averaged. (

**b**) Pickup loop voltage during the shut-off of the different excitation fields.

**Table 1.**Estimated relaxation amplitudes $\Delta B$, relaxation times ${t}_{1/e}$ and fit parameters for double exponential fits (Equation (9)) to relaxation curves of liquid BNF MNP and Perimag${}^{\circledR}$ MNP. The values are extracted from FPGA data and from magnetic field readings obtained via Hilbert transform (HT).

Data | MNP | Dilution | Fe | $\mathsf{\Delta}\mathit{B}$ | ${\mathit{t}}_{1/\mathit{e}}$ | ${\mathit{B}}_{1}$ | ${\mathit{\tau}}_{1}$ | ${\mathit{B}}_{2}$ | ${\mathit{\tau}}_{2}$ | O | R${}_{\mathbf{adj}}^{2}$ |
---|---|---|---|---|---|---|---|---|---|---|---|

from | Type | Factor | ($\mathsf{\mu}\mathbf{g}$) | ($\mathbf{n}\mathbf{T}/\mathbf{c}\mathbf{m}$) | ($\mathbf{m}\mathbf{s}$) | ($\mathbf{n}\mathbf{T}/\mathbf{c}\mathbf{m}$) | ($\mathbf{m}\mathbf{s}$) | $(\mathbf{n}\mathbf{T}/\mathbf{c}\mathbf{m}$) | ($\mathbf{m}\mathbf{s}$) | ($\mathbf{n}\mathbf{T}/\mathbf{c}\mathbf{m}$) | |

FPGA | BNF | 1:1 | 1370 | 321.23 | 1.35 | 72.57 | 5.20 | 389.62 | 1.10 | 26.98 | 1.00 |

FPGA | BNF | 1:2 | 685 | 189.21 | 0.84 | 45.51 | 3.51 | 290.86 | 0.70 | 10.71 | 1.00 |

FPGA | BNF | 1:10 | 137 | 44.89 | 0.64 | 9.58 | 3.25 | 84.19 | 0.56 | 2.30 | 1.00 |

FPGA | BNF | 1:20 | 68.5 | 14.44 | 0.62 | 3.19 | 3.05 | 27.90 | 0.54 | 1.23 | 1.00 |

FPGA | BNF | 1:100 | 13.7 | 2.73 | 0.64 | 0.74 | 3.09 | 4.98 | 0.54 | 0.30 | 1.00 |

FPGA | BNF | 1:200 | 6.85 | 1.40 | 0.72 | 0.23 | 4.39 | 2.48 | 0.64 | 0.12 | 1.00 |

FPGA | BNF | 1:1000 | 1.37 | 0.28 | 0.75 | 0.05 | 8.62 | 0.49 | 0.65 | 0.01 | 1.00 |

HT | BNF | 1:1 | 1370 | 265.18 | 0.18 | 298.19 | 1.94 | 1214.60 | 0.13 | 33.42 | 0.99 |

HT | BNF | 1:2 | 685 | 164.52 | 0.35 | 120.89 | 1.86 | 457.98 | 0.25 | 12.00 | 1.00 |

HT | BNF | 1:10 | 137 | 39.68 | 0.42 | 21.98 | 1.81 | 95.46 | 0.32 | 2.64 | 1.00 |

HT | BNF | 1:20 | 68.5 | 12.77 | 0.42 | 7.00 | 1.78 | 31.17 | 0.32 | 1.41 | 0.99 |

HT | BNF | 1:100 | 13.7 | 2.43 | 0.42 | 1.52 | 1.76 | 5.68 | 0.31 | 0.28 | 0.61 |

HT | BNF | 1:200 | 6.85 | 1.25 | 0.42 | 0.65 | 1.92 | 3.05 | 0.33 | 0.10 | 0.31 |

FPGA | Perimag${}^{\circledR}$ | 1:1 | 850 | 132.99 | 1.43 | 66.40 | 4.88 | 128.91 | 0.81 | 30.72 | 1.00 |

FPGA | Perimag${}^{\circledR}$ | 1:10 | 85 | 16.07 | 1.08 | 6.86 | 4.74 | 19.18 | 0.70 | 3.28 | 1.00 |

HT | Perimag${}^{\circledR}$ | 1:1 | 850 | 124.23 | 0.73 | 54.94 | 4.97 | 191.99 | 0.49 | 30.78 | 1.00 |

HT | Perimag${}^{\circledR}$ | 1:10 | 85 | 14.96 | 0.69 | 9.06 | 3.56 | 22.24 | 0.40 | 3.44 | 0.99 |

**Table 2.**Estimated relaxation parameters $\Delta B$, ${t}_{1/e}$ and offset O of relaxation curves with excitation fields ranging from $1\mathrm{m}\mathrm{T}$ to $100\mathrm{m}\mathrm{T}$. The sample consists of gypsum-immobilized MNP with a total iron amount of $6.4\mathrm{m}\mathrm{g}$.

${\mathit{B}}_{\mathbf{excitation}}$ | $\mathsf{\Delta}\mathit{B}$ | ${\mathit{t}}_{1/\mathit{e}}$ | O |
---|---|---|---|

($\mathbf{m}\mathbf{T}$) | ($\mathbf{n}\mathbf{T}/\mathbf{c}\mathbf{m}$) | ($\mathbf{m}\mathbf{s}$) | $(\mathbf{n}\mathbf{T}/\mathbf{c}\mathbf{m}$) |

100 | 120.98 | 6 | −50.01 |

40 | 69.98 | 48 | −50.09 |

20 | 92.34 | 16 | −50.14 |

10 | 68.30 | 58 | −50.07 |

2 | 43.66 | 58 | −51.24 |

1 | 28.65 | 40 | −51.94 |

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Jaufenthaler, A.; Kornack, T.; Lebedev, V.; Limes, M.E.; Körber, R.; Liebl, M.; Baumgarten, D.
Pulsed Optically Pumped Magnetometers: Addressing Dead Time and Bandwidth for the Unshielded Magnetorelaxometry of Magnetic Nanoparticles. *Sensors* **2021**, *21*, 1212.
https://doi.org/10.3390/s21041212

**AMA Style**

Jaufenthaler A, Kornack T, Lebedev V, Limes ME, Körber R, Liebl M, Baumgarten D.
Pulsed Optically Pumped Magnetometers: Addressing Dead Time and Bandwidth for the Unshielded Magnetorelaxometry of Magnetic Nanoparticles. *Sensors*. 2021; 21(4):1212.
https://doi.org/10.3390/s21041212

**Chicago/Turabian Style**

Jaufenthaler, Aaron, Thomas Kornack, Victor Lebedev, Mark E. Limes, Rainer Körber, Maik Liebl, and Daniel Baumgarten.
2021. "Pulsed Optically Pumped Magnetometers: Addressing Dead Time and Bandwidth for the Unshielded Magnetorelaxometry of Magnetic Nanoparticles" *Sensors* 21, no. 4: 1212.
https://doi.org/10.3390/s21041212