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Keywords = optically pumped magnetometers

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17 pages, 4943 KiB  
Article
Cost-Reference Particle Filter-Based Method for Constructing Effective Brain Networks: Application in Optically Pumped Magnetometer Magnetoencephalography
by Yuyu Ma, Xiaoyu Liang, Huanqi Wu, Hao Lu, Yong Li, Changzeng Liu, Yang Gao, Min Xiang, Dexin Yu and Xiaolin Ning
Bioengineering 2024, 11(12), 1258; https://doi.org/10.3390/bioengineering11121258 - 12 Dec 2024
Viewed by 474
Abstract
Optically pumped magnetometer magnetoencephalography (OPM-MEG) represents a novel method for recording neural signals in the brain, offering the potential to measure critical neuroimaging characteristics such as effective brain networks. Effective brain networks describe the causal relationships and information flow between brain regions. In [...] Read more.
Optically pumped magnetometer magnetoencephalography (OPM-MEG) represents a novel method for recording neural signals in the brain, offering the potential to measure critical neuroimaging characteristics such as effective brain networks. Effective brain networks describe the causal relationships and information flow between brain regions. In constructing effective brain networks using Granger causality, the noise in the multivariate autoregressive model (MVAR) is typically assumed to follow a Gaussian distribution. However, in experimental measurements, the statistical characteristics of noise are difficult to ascertain. In this paper, a Granger causality method based on a cost-reference particle filter (CRPF) is proposed for constructing effective brain networks under unknown noise conditions. Simulation results show that the average estimation errors of the MVAR model coefficients using the CRPF method are reduced by 53.4% and 82.4% compared to the Kalman filter (KF) and maximum correntropy filter (MCF) under Gaussian noise, respectively. The CRPF method reduces the average estimation errors by 88.1% and 85.8% compared to the MCF under alpha-stable distribution noise and the KF method under pink noise conditions, respectively. In an experiment, the CRPF method recoversthe latent characteristics of effective connectivity of benchmark somatosensory stimulation data in rats, human finger movement, and auditory oddball paradigms measured using OPM-MEG, which is in excellent agreement with known physiology. The simulation and experimental results demonstrate the effectiveness of the proposed algorithm and OPM-MEG for measuring effective brain networks. Full article
(This article belongs to the Section Biosignal Processing)
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<p>OPM-MEG system.</p>
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<p>(<b>a</b>) Auditory oddball experimental paradigm. (<b>b</b>) The position and distribution of OPM magnetometers.</p>
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<p>MVAR model coefficient estimation using different noise conditions and filter methods. (<b>a</b>–<b>c</b>) Comparison between estimated values and ground truth values of MVAR model coefficients using the CRPF method under Gaussian noise, alpha-stable distribution noise, and pink noise, respectively. (<b>d</b>–<b>f</b>) Estimated values and ground truth values of <math display="inline"><semantics> <msub> <mi>d</mi> <mi>t</mi> </msub> </semantics></math> using the KF, MCF, and CRPF methods, respectively. (<b>g</b>–<b>i</b>) Estimation errors across 50 trials under Gaussian noise, alpha-stable distribution noise, and pink noise, respectively.</p>
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<p>Total outflow sPDC values of the cS1 node during unilateral whisker stimulation in rats.</p>
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<p>Connections in effective brain networks during finger movement. (<b>a</b>) MCF method; (<b>b</b>) CRPF method (displays the top 50 connections).</p>
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<p>Source activity and time series of bilateral STG. (<b>a</b>) Standard stimulation; (<b>b</b>) deviant stimulation (significantly different time points are marked with a yellow line along the <span class="html-italic">x</span>-axis, <math display="inline"><semantics> <mrow> <mi>p</mi> <mo>&lt;</mo> <mn>0.001</mn> </mrow> </semantics></math>).</p>
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<p>Time–frequency effective brain network of MMF (white boxes represent statistically significant time–frequency points, <math display="inline"><semantics> <mrow> <mi>p</mi> <mo>&lt;</mo> <mn>0.05</mn> </mrow> </semantics></math>, FDR corrected).</p>
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<p>Connections in effective brain networks of MMF with significant differences. (<b>a</b>) Connections in the theta band (3–8 Hz); (<b>b</b>) Connections in the alpha band (8–13 Hz); (<b>c</b>) Connections in the beta band (13–30 Hz).</p>
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<p>Total inflow sPDC values of MMF. (<b>a</b>) MCF method; (<b>b</b>) CRPF method.</p>
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11 pages, 4652 KiB  
Article
Improving 795 nm Single-Frequency Laser’s Frequency Stability by Means of the Bright-State Spectroscopy with Rubidium Vapor Cell
by Junye Zhao, Yongbiao Yang, Lulu Zhang, Yang Li and Junmin Wang
Photonics 2024, 11(12), 1165; https://doi.org/10.3390/photonics11121165 - 11 Dec 2024
Viewed by 480
Abstract
The utilization of atomic or molecular spectroscopy for frequency locking of single-frequency laser to improve laser frequency stability plays an important role in the experimental investigation of optically pumped atomic magnetometers, atomic clocks, laser cooling and trapping of atoms, etc. We have experimentally [...] Read more.
The utilization of atomic or molecular spectroscopy for frequency locking of single-frequency laser to improve laser frequency stability plays an important role in the experimental investigation of optically pumped atomic magnetometers, atomic clocks, laser cooling and trapping of atoms, etc. We have experimentally demonstrated a technique for frequency stabilization of a single-frequency laser employing the bright state spectroscopy (BSS) with a rubidium atomic vapor cell. By utilizing the counter-propagating dual-frequency 795 nm laser beams with mutually orthogonal linear polarization and a frequency difference of 6.834 GHz, which is equal to the hyperfine splitting of rubidium-87 ground state 5S1/2, an absorption-enhanced signal with narrow linewidth at the center of Doppler-broadened transmission spectroscopy is observed when continuous scanning the laser frequency over rubidium-87 D1 transition. This is the so-called BSS. Amplitude of the absorption-enhanced signal in the BSS is much larger compared with the conventional saturation absorption spectroscopy (SAS). The relationship between linewidth and amplitude of the BSS signal and laser beam intensity has been investigated. This high-contrast absorption-enhanced BSS signal has been employed for the laser frequency stabilization. The experimental results show that the frequency stability is 4.4×1011 with an integration time of 40 s, near one order of magnitude better than that for using the SAS. Full article
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<p>Alkali metal atomic energy level system. <math display="inline"><semantics> <mfenced open="|" close="&#x232A;"> <mn>1</mn> </mfenced> </semantics></math> and <math display="inline"><semantics> <mfenced open="|" close="&#x232A;"> <mn>2</mn> </mfenced> </semantics></math> are the hyperfine states of ground state. <math display="inline"><semantics> <mfenced open="|" close="&#x232A;"> <mn>3</mn> </mfenced> </semantics></math> and <math display="inline"><semantics> <mfenced open="|" close="&#x232A;"> <mn>4</mn> </mfenced> </semantics></math> are the excited states of D1 transition.</p>
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<p>Experimental setup. APP: anamorphic prism pair; ISO: isolator; HWP: half-wave plate; PBS: polarization beam splitter cube; EOPM: electro-optic phase modulator; L: lens; QWP: quarter-wave plate; HR: high reflectivity mirror (T∼5%); PD: photodiode; D: dump.</p>
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<p>(<b>a</b>) Relevant energy level diagram of rubidium-87 atoms D1 line; (<b>b</b>) the CPT spectroscopy detected by PD1 in <a href="#photonics-11-01165-f001" class="html-fig">Figure 1</a> for 6.8 GHz micro-wave frequency optimization; (<b>c</b>) the transmission spectra of the optical etalon for 6.8 GHz micro-wave power optimization. The height of the +1-order and −1-order sideband peaks is roughly equal to that of the carrier peak in center.</p>
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<p>BSS and parameter optimization. (<b>a</b>) Rubidium 87 with different hyperfine BSS; (<b>b</b>) signal amplitude vs. laser beam power; (<b>c</b>) linewidth vs. laser beam power; (<b>d</b>) amplitude/linewidth vs. laser beam power.</p>
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<p>Atomic absorption signal (black) and differential signal (red). (<b>a</b>) The absorption spectroscopy of the laser beam through the rubidium vapor cell; (<b>b</b>) saturation absorption spectroscopy (SAS); (<b>c</b>) bright state spectroscopy (BSS).</p>
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<p>Typical frequency fluctuation. (<b>a</b>) Laser free-running case; (<b>b</b>) laser frequency locked case with the SAS scheme (locked to (F = 2) → (<math display="inline"><semantics> <msup> <mi mathvariant="normal">F</mi> <mo>′</mo> </msup> </semantics></math> = 1) transition); (<b>c</b>) laser frequency locked case with the BSS scheme (locked to (F = 2) → (<math display="inline"><semantics> <msup> <mi mathvariant="normal">F</mi> <mo>′</mo> </msup> </semantics></math> = 1) transition); (<b>d</b>) laser frequency locked case with the BSS scheme (locked to (F = 2) → (<math display="inline"><semantics> <msup> <mi mathvariant="normal">F</mi> <mo>′</mo> </msup> </semantics></math> = 2) transition).</p>
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<p>Beat note experimental setup. L: lens; AOM: acousto-optic modulator; HR: high reflectivity mirror; HWP: half-wave plate; PBS: polarization beam splitter; P: P-polarized light; S: S-polarized light; LPF: low pass filter; AMP: amplifier; D: dump.</p>
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<p>The overlapping Allan deviation values are calculated from the beat note data. The two lasers in free-running case, the locked cases with the same hyperfine transition as the reference using the SAS scheme and the BSS scheme, respectively.</p>
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17 pages, 3073 KiB  
Article
The Gradient of Spontaneous Oscillations Across Cortical Hierarchies Measured by Wearable Magnetoencephalography
by Xiaoyu Liang, Yuyu Ma, Huanqi Wu, Ruilin Wang, Ruonan Wang, Changzeng Liu, Yang Gao and Xiaolin Ning
Technologies 2024, 12(12), 254; https://doi.org/10.3390/technologies12120254 - 9 Dec 2024
Viewed by 945
Abstract
The spontaneous oscillations within the brain are intimately linked to the hierarchical structures of the cortex, as evidenced by the cross-cortical gradient between parametrized spontaneous oscillations and cortical locations. Despite the significance of both peak frequency and peak time in characterizing these oscillations, [...] Read more.
The spontaneous oscillations within the brain are intimately linked to the hierarchical structures of the cortex, as evidenced by the cross-cortical gradient between parametrized spontaneous oscillations and cortical locations. Despite the significance of both peak frequency and peak time in characterizing these oscillations, limited research has explored the relationship between peak time and cortical locations. And no studies have demonstrated that the cross-cortical gradient can be measured by optically pumped magnetometer-based magnetoencephalography (OPM-MEG). Therefore, the cross-cortical gradient of parameterized spontaneous oscillation was analyzed for oscillations recorded by OPM-MEG using restricted maximum likelihood estimation with a linear mixed-effects model. It was validated that OPM-MEG can measure the cross-cortical gradient of spontaneous oscillations. Furthermore, results demonstrated the difference in the cross-cortical gradient between spontaneous oscillations during eye-opening and eye-closing conditions. The methods and conclusions offer potential to integrate electrophysiological and structural information of the brain, which contributes to the analysis of oscillatory fluctuations across the cortex recorded by OPM-MEG. Full article
(This article belongs to the Special Issue Technological Advances in Science, Medicine, and Engineering 2024)
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<p>The flow of the estimation of <math display="inline"><semantics> <mi mathvariant="bold-italic">D</mi> </semantics></math>, <math display="inline"><semantics> <mi mathvariant="bold-italic">β</mi> </semantics></math>, and <math display="inline"><semantics> <mrow> <msup> <mi>σ</mi> <mn>2</mn> </msup> </mrow> </semantics></math>.</p>
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<p>The estimation of cross-cortical gradient of spontaneous oscillations based on OPM-MEG, including MRI segmentation and reconstruction (<b>a</b>), sensors co-registration (<b>b</b>), the acquisition of MEG (<b>c</b>), ROIs parceling and source reconstruction (<b>d</b>), oscillation parameterization (<b>f</b>), and the gradient estimation of parameterized oscillations (<b>e</b>,<b>f</b>).</p>
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<p>Simulation of scalp MEG with simulated oscillatory gradient.</p>
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<p>The oscillations of all ROIs during closed-eye and open-eye states measured by OPM-MEG. (<b>a</b>) The separated periodic time–frequency representation average across 150 ROIs of subject sub01, sub02, sub03, and sub04. (<b>b</b>) The PF and PT values of closed-eye and open-eye OPM-MEG for all ROIs and all subjects.**** means <span class="html-italic">p</span> &lt; 0.0001. ♦ means outlier points.</p>
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<p>The PF gradient of SQUID-MEG (<b>a</b>) and EO OPM-MEG (<b>b</b>) on the fsaverage brain template. Left panel: a cortical map of the cross-cortical gradient of PF on a template brain. Right panel: Dependency between the PF or PT and the ROI’s location along the y-axis (posterior to anterior).</p>
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<p>The cross-cortical gradient of peak frequency (<b>a</b>) and peak time (<b>b</b>) of EO and EC resting-state rhythmics. The upper panels of (<b>a</b>,<b>b</b>) show cortical maps of the cross-cortical gradient of EO and EC spontaneous oscillations on template brains. The bottom panels of (<b>a</b>,<b>b</b>) show the dependency between the PF or PT and cortex along the x-axis (left to right), the y-axis (posterior to anterior), and the z-axis (the bottom to the top), respectively. In (<b>a</b>,<b>b</b>), the dots show the original PFs or PTs obtained with STPPTO and the slopes show <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>β</mi> <mo stretchy="false">^</mo> </mover> <mn>1</mn> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>β</mi> <mo stretchy="false">^</mo> </mover> <mn>2</mn> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>β</mi> <mo stretchy="false">^</mo> </mover> <mn>3</mn> </msub> </mrow> </semantics></math> in Equation (13).</p>
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12 pages, 2324 KiB  
Article
Fast Degaussing Procedure for a Magnetically Shielded Room
by Peter A. Koss, Jens Voigt, Ronja Rasser and Allard Schnabel
Materials 2024, 17(23), 5877; https://doi.org/10.3390/ma17235877 - 30 Nov 2024
Viewed by 1104
Abstract
A demagnetization study was conducted on a magnetically shielded room (MSR) at Fraunhofer IPM, designed for applications such as magnetoencephalography (MEG) and material testing. With a composite of two layers of mu-metal and an intermediate aluminum layer, the MSR must provide a residual [...] Read more.
A demagnetization study was conducted on a magnetically shielded room (MSR) at Fraunhofer IPM, designed for applications such as magnetoencephalography (MEG) and material testing. With a composite of two layers of mu-metal and an intermediate aluminum layer, the MSR must provide a residual field under 5 nT for the successful operation of optically pumped magnetometers (OPMs). The degaussing process, employing six individual coils, reached the necessary residual magnetic field within the central 1 m3 volume in under four minutes. Due to the low-frequency shielding factor of 100, the obtained average residual field is shown to be limited by environmental residual field changes after degaussing and not by the degaussing procedure. Full article
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<p>Schematic illustration of the experiment’s layout established to degauss the MSR. The identically colored coils on the edges are interconnected in a series so that the magnetic field induces a complete magnetic loop inside the shielding material around the inner volume, as indicated by the blue arrows for the blue coils.</p>
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<p>Images of the experimental setup elements: On the left: a picture of the mapping framework using an aluminum rail to adjust the xy-position of the pole, allowing the fluxgate to be positioned at different z-positions. On the right: a photo of the four-quadrant amplifier (black) that drives the degaussing current through the degaussing coil and the 7 Hz transformer (large white box) to eliminate DC offsets.</p>
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<p>Measured shielding factor (SF) curves for the three axes of the two-layer MSR with a 1µT effective excitation field strength. In the inset: dependence of the SF at 0.02 Hz on the amplitude of the excitation field.</p>
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<p>Illustration of the measured 3D field distributions for the three different degaussing configurations: <b>posI</b>, <b>negI</b>, and <b>posZ</b> (top row). Below, the difference between the respective 3D maps is shown. All maps use the same color code. <a href="#materials-17-05877-t001" class="html-table">Table 1</a>a provides characteristic values for these 3D field illustrations. Note that the scaling of the height of the cones relative to the absolute field value reveals minor differences in the maximum amplitude, attributed to a much larger base surface. The difference between <b>negI</b> and <b>posZ</b> is minimal because both fields have a similar direction, whereas <b>posI</b> and <b>negI</b> exhibit slightly different directions.</p>
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<p>Average field map (<b>ave</b>) and the differences between it and the maps <b>posI</b>, <b>negI</b>, and <b>posZ</b>. All maps share the same color code. <a href="#materials-17-05877-t001" class="html-table">Table 1</a>b provides characteristic values for these 3D field maps.</p>
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<p>Illustration of the corrections performed to the measured data (red) based on a simultaneous field measurement with an outside reference fluxgate (green) and the repeated measurement of the magnetic field at the center of the MSR at 7 different times. Blue is the difference between the red and the green curve. The yellow line is the calculated linear fit curve to the blue curve. The black dots are the 7 values of the magnetic field at the MSR center after all corrections are applied.</p>
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16 pages, 4852 KiB  
Article
Applicability of Small and Low-Cost Magnetic Sensors to Geophysical Exploration
by Filippo Accomando and Giovanni Florio
Sensors 2024, 24(21), 7047; https://doi.org/10.3390/s24217047 - 31 Oct 2024
Viewed by 897
Abstract
In the past few decades, there has been a notable technological advancement in geophysical sensors. In the case of magnetometry, several sensors were used, having the common feature of being miniaturized and lightweight, thus idoneous to be carried by UAVs in drone-borne magnetometric [...] Read more.
In the past few decades, there has been a notable technological advancement in geophysical sensors. In the case of magnetometry, several sensors were used, having the common feature of being miniaturized and lightweight, thus idoneous to be carried by UAVs in drone-borne magnetometric surveys. A common feature is that their sensitivity ranges from 0.1 to about 200 nT, thus not comparable to that of optically pumped, standard fluxgate or even proton magnetometers. However, their low cost, volume and weight remain very interesting features of these sensors. In fact, such sensors have the common feature of being very inexpensive, so new ways of making surveys using many of these sensors could be devised, in addition to the possibility, even with limited resources, of creating gradiometers by combining two or more of them. In this paper, we explore the range of applicability of small tri-axial magnetometers commonly used for attitude determination in several devices. We compare the results of surveys performed with standard professional geophysical instruments with those obtained using these sensors and find that in the presence of strongly magnetized sources, they succeeded in identifying the main anomalies. Full article
(This article belongs to the Collection Magnetic Sensors)
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<p>“Area 1” (Naples, Italy) case. (<b>a</b>) the Total field intensity acquired by an MFAM sensor. (<b>b</b>) The total field intensity computed by the three components of a Hall-effect sensor contained in a smartphone. Dashed lines mark the position of the profiles shown in <a href="#sensors-24-07047-f002" class="html-fig">Figure 2</a>.</p>
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<p>Comparison of the total field intensities recorded by an MFAM and a Hall-effect sensor at “Area 1” (Naples, Italy). (<b>a</b>) NW–SE profile located at x = 12 m in the map of <a href="#sensors-24-07047-f001" class="html-fig">Figure 1</a>a. (<b>b</b>) NW–SE profile located at x = 24 m in the map of <a href="#sensors-24-07047-f001" class="html-fig">Figure 1</a>b.</p>
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<p>Verteglia Plain (Italy) case. (<b>a</b>) Total field intensity acquired by an MFAM sensor. (<b>b</b>) Total field intensity computed by the three components of an AMR sensor used as a compass in the MFAM. Dashed lines mark the position of the profiles shown in <a href="#sensors-24-07047-f004" class="html-fig">Figure 4</a>. In both maps, the color bar is optimized to allow visualizing the northern low-amplitude magnetic anomalies.</p>
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<p>Comparison of the total field intensities recorded by an MFAM and an AMR sensor at Verteglia Plain (Italy). (<b>a</b>) S–N profile located at x = 12 m in the map of <a href="#sensors-24-07047-f003" class="html-fig">Figure 3</a>a. (<b>b</b>) S–N profile located at x = 26 m in the map of <a href="#sensors-24-07047-f003" class="html-fig">Figure 3</a>b.</p>
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<p>Comparison of the total field intensities recorded by an MFAM and an AMR sensor at Verteglia Plain (Italy). (<b>a</b>) S–N profile located at x = 12 m in the map of <a href="#sensors-24-07047-f003" class="html-fig">Figure 3</a>a. (<b>b</b>) S–N profile located at x = 26 m in the map of <a href="#sensors-24-07047-f003" class="html-fig">Figure 3</a>b.</p>
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<p>Presenzano quarry drone-borne magnetic datasets. (<b>a</b>) Total field intensity acquired by an MFAM sensor. (<b>b</b>) Total field intensity computed by the three components of an AMR sensor used as a compass in the MFAM. The line at x = 419,500 m marks the profile shown in <a href="#sensors-24-07047-f006" class="html-fig">Figure 6</a>.</p>
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<p>Presenzano quarry drone-borne magnetic datasets. (<b>a</b>) Total field intensity acquired by an MFAM sensor. (<b>b</b>) Total field intensity computed by the three components of an AMR sensor used as a compass in the MFAM. The line at x = 419,500 m marks the profile shown in <a href="#sensors-24-07047-f006" class="html-fig">Figure 6</a>.</p>
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<p>Comparison of the total field intensities recorded by an MFAM and an AMR sensor at Presenzano quarry (Italy). S–N profile located at x = 419,500 m in the map of <a href="#sensors-24-07047-f005" class="html-fig">Figure 5</a>.</p>
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19 pages, 22517 KiB  
Article
Development of a High-Precision Deep-Sea Magnetic Survey System for Human-Occupied Vehicles
by Qimao Zhang, Keyu Zhou, Ming Deng, Qisheng Zhang, Yongqiang Feng and Leisong Liu
Electronics 2024, 13(18), 3611; https://doi.org/10.3390/electronics13183611 - 11 Sep 2024
Viewed by 3385
Abstract
The high-precision magnetic survey system is crucial for ocean exploration. However, most existing systems face challenges such as high noise levels, low sensitivity, and inadequate magnetic compensation effects. To address these issues, we developed a high-precision magnetic survey system based on the manned [...] Read more.
The high-precision magnetic survey system is crucial for ocean exploration. However, most existing systems face challenges such as high noise levels, low sensitivity, and inadequate magnetic compensation effects. To address these issues, we developed a high-precision magnetic survey system based on the manned submersible “Deep Sea Warrior” for deep-ocean magnetic exploration. This system incorporates a compact optically pumped cesium (Cs) magnetometer sensor to measure the total strength of the external magnetic field. Additionally, a magnetic compensation sensor is included at the front end to measure real-time attitude changes of the platform. The measured data are then transmitted to a magnetic signal processor, where an algorithm compensates for the platform’s magnetic interference. We also designed a deep pressure chamber to allow for a maximum working depth of 4500 m. Experiments conducted in both indoor and field environments verified the performance of the proposed magnetic survey system. The results showed that the system’s sensitivity is ≤0.5 nT, the noise level of the magnetometer sensor is ≤1 pT/√Hz at 1 Hz, and the sampling rate is 10 Hz. The proposed system has potential applications in ocean and geophysical exploration. Full article
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<p>Overall architecture of the human-occupied, vehicular platform-based, high-precision, deep-sea magnetic survey system.</p>
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<p>Design of the optically pumped magnetometer sensor.</p>
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<p>Block diagram of the optically pumped magnetometer sensor circuitry.</p>
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<p>Structure of the fluxgate sensor.</p>
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<p>3D model diagram of fluxgate sensor.</p>
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<p>Block diagram of the magnetic compensation circuitry.</p>
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<p>Power management circuit diagram.</p>
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<p>Schematic of waveform generation circuit.</p>
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<p>Block diagram of the magnetic signal processor.</p>
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<p>Functional modules of the magnetic signal processing software.</p>
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<p>Data processing flowchart using the magnetic signal processing software.</p>
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<p>Functional modules of the display and control software.</p>
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<p>User interface of the display and control software.</p>
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<p>3D model of pressure chamber. (<b>a</b>) Electronic pressure chamber. (<b>b</b>) Assembly of the probe pressure chamber.</p>
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<p>Actual manned submersible sampling basket.</p>
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<p>Assembly position of the magnetometer equipment.</p>
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<p>Noise test scenario.</p>
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<p>Noise level spectrum.</p>
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<p>Anti-aliasing filtering and re-sampling process.</p>
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<p>Alternating magnetic field test result.</p>
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<p>The noise levels of compensated magnetic field signals before and after geomagnetic gradient correction.</p>
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<p>Flight trajectory for calibrating magnetic noise compensation.</p>
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<p>Compensation performance before and after calibration flight trial.</p>
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<p>Fluxgate spectrum for the magnetic compensation actions.</p>
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13 pages, 4538 KiB  
Article
Measuring Transverse Relaxation with a Single-Beam 894 nm VCSEL for Cs-Xe NMR Gyroscope Miniaturization
by Qingyang Zhao, Ruochen Zhang and Hua Liu
Sensors 2024, 24(17), 5692; https://doi.org/10.3390/s24175692 - 1 Sep 2024
Viewed by 878
Abstract
The spin-exchange-pumped nuclear magnetic resonance gyroscope (NMRG) is a pivotal tool in quantum navigation. The transverse relaxation of atoms critically impacts the NMRG’s performance parameters and is essential for judging normal operation. Conventional methods for measuring transverse relaxation typically use dual beams, which [...] Read more.
The spin-exchange-pumped nuclear magnetic resonance gyroscope (NMRG) is a pivotal tool in quantum navigation. The transverse relaxation of atoms critically impacts the NMRG’s performance parameters and is essential for judging normal operation. Conventional methods for measuring transverse relaxation typically use dual beams, which involves complex optical path and frequency stabilization systems, thereby complicating miniaturization and integration. This paper proposes a method to construct a 133Cs parametric resonance magnetometer using a single-beam vertical-cavity surface-emitting laser (VCSEL) to measure the transverse relaxation of 129Xe and 131Xe. Based on this method, the volume of the gyroscope probe is significantly reduced to 50 cm3. Experimental results demonstrate that the constructed Cs-Xe NMRG can achieve a transverse relaxation time (T2) of 8.1 s under static conditions. Within the cell temperature range of 70 °C to 110 °C, T2 decreases with increasing temperature, while the signal amplitude inversely increases. The research lays the foundation for continuous measurement operations of miniaturized NMRGs. Full article
(This article belongs to the Special Issue Atomic Magnetic Sensors)
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<p>A simplified schematic of <sup>133</sup>Cs PRM.</p>
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<p>The D1 absorption line of <sup>133</sup>Cs.</p>
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<p>Schematic diagram of the system for achieving wavelength locking of VCSEL in Cs-Xe NMRG. (Parts of the optical path structure and mechanical structure are omitted in the figure.).</p>
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<p>Schematic diagram of the overall experimental system.</p>
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<p>The structure of the probe part of the NMRG. (<b>a</b>) Assembly diagram. (<b>b</b>) The composition of the layers inside the oven. (<b>c</b>) Dual-layer flexible printed circuit heating film.</p>
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<p>VCSEL and its peripheral circuits. (<b>a</b>) The TO-46 package of the VCSEL, with its internal structure (cited from [<a href="#B31-sensors-24-05692" class="html-bibr">31</a>]) highlighted in the red box. NTC: negative temperature coefficient thermistor; Si-HS: silicon-based heat sink; SMD: surface mount devices; TEC: thermoelectric cooler. (<b>b</b>) The driving and frequency locking circuit board for the VCSEL, size 10 × 6 cm<sup>2</sup>.</p>
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<p>Current scanning curve. (<b>Top</b>): absorption curve; (<b>Bottom</b>): demodulation result curve.</p>
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<p>Test results of closed-loop control of VCSEL wavelength within 180 s.</p>
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<p>Results of the FID experiment. (<b>a</b>) Time domain signal. (<b>b</b>) The FFT transform of the time domain signal.</p>
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<p>Comparison of FID signals at different cell temperatures.</p>
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<p>The relationship between <span class="html-italic">T</span><sub>2</sub> and signal amplitude and cell temperature changes.</p>
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<p>The relationship between <span class="html-italic">T</span><sub>2</sub> and different injection currents (<span class="html-italic">I</span><sub>1</sub>~<span class="html-italic">I</span><sub>4</sub>).</p>
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12 pages, 1912 KiB  
Article
Bedside Magnetocardiography with a Scalar Sensor Array
by Geoffrey Z. Iwata, Christian T. Nguyen, Kevin Tharratt, Maximilian Ruf, Tucker Reinhardt, Jordan Crivelli-Decker, Madelaine S. Z. Liddy, Alison E. Rugar, Frances Lu, Kirstin Aschbacher, Ethan J. Pratt, Kit Yee Au-Yeung and Stefan Bogdanovic
Sensors 2024, 24(16), 5402; https://doi.org/10.3390/s24165402 - 21 Aug 2024
Viewed by 1343
Abstract
Decades of research have shown that magnetocardiography (MCG) has the potential to improve cardiac care decisions. However, sensor and system limitations have prevented its widespread adoption in clinical practice. We report an MCG system built around an array of scalar, optically pumped magnetometers [...] Read more.
Decades of research have shown that magnetocardiography (MCG) has the potential to improve cardiac care decisions. However, sensor and system limitations have prevented its widespread adoption in clinical practice. We report an MCG system built around an array of scalar, optically pumped magnetometers (OPMs) that effectively rejects ambient magnetic interference without magnetic shielding. We successfully used this system, in conjunction with custom hardware and noise rejection algorithms, to record magneto-cardiograms and functional magnetic field maps from 30 volunteers in a regular downtown office environment. This demonstrates the technical feasibility of deploying our device architecture at the point-of-care, a key step in making MCG usable in real-world settings. Full article
(This article belongs to the Special Issue Biomedical Imaging, Sensing and Signal Processing)
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<p>Device overview. (<b>a</b>). Photograph of MCG system with critical components indicated. The sensor head and arm can pivot about the points indicated by the circulating red arrows, allowing an operator to position the device optimally over a participant’s chest. Sensors and their control modules are housed within the sensor head assembly, while the data acquisition electronics and other supporting components are placed in the electronics rack indicated at the bottom left. The participant bed is an MRI-compatible hospital-grade bed constructed from non-magnetic PVC. The gantry support is assembled from extruded aluminum. (<b>b</b>). (<b>left</b>) Photograph of the bottom layer of sensors within the sensor housing. The nonmagnetic, 3-D printed sensor mount can accommodate up to 9 sensors per layer. (<b>right</b>) Schematic of both sensor layers indicating dimensions and gradiometric baseline. (<b>c</b>). Photograph of a participant with the sensor array positioned for a measurement. The approximate direction of the Earth’s magnetic field is indicated with the arrow labelled B<sub>earth</sub>.</p>
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<p>Typical power spectral density (PSD) plot of the unshielded system. Magnetometer signals are shown in grey dashed lines. Filtered gradiometer signals are shown in colors. The PSD is calculated via Welch’s method with a Hann window and normalized by the noise bandwidth. Low frequency environmental noise and 60 Hz line noise dominate the magnetometer signal. These are effectively reduced by bandpass filtering, notch filtering and gradiometry, as described in <a href="#sec2dot2-sensors-24-05402" class="html-sec">Section 2.2</a>.</p>
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<p>Signal processing pipeline and example data. (<b>a</b>). Signal processing pipeline flowchart showing processing steps for time-series data acquired from a multi-channel sensor array. After data are loaded from storage, channel synchronization is performed by aligning common signals that were injected in all channels, including the ECG, which is up-sampled to optimize trigger timing. Filtering follows, which consists of a 60 Hz IRR notch filter and 0.5–45 Hz bandpass using a bi-directional Butterworth digital filter. Then bad channels and segments are identified in and removed from the data using automatic power thresholding and basic data checks. The noise rejection step consists of a combination of gradiometry and Principal Component Analysis (PCA), where signal components that have high noise character are removed. MCG epochs are identified using ECG as a trigger, with automated epoch rejection based on signal power and timing criteria. Finally, epochs are averaged together, and the epoch-average is visualized. (<b>b</b>). Epoch-average for each gradiometer channel is displayed based on approximate relative positions over the participant’s chest. The upper right sensor and lower left sensor show inverted features. (<b>c</b>). (<b>Upper</b>) Epoch-average of all five gradiometric signals overlayed. Inset shows SNR scaling as a function of the number of epochs used to average. Each line corresponds to a different ordering of averaging. SNR &gt; 10 can be achieved with 60 s of averaging and reaches 18 after 214 averages. (<b>Lower</b>) Corresponding ECG Lead I trace acquired simultaneously with the MCG data.</p>
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<p>Summary of SNR<sub>max</sub> of the heartbeat averages, separated by experimental condition for all participants. N_participants = 23, N_observations = 92. Recording length = 300 s. The mean number of heartbeats averaged together for each participant is 191, with a standard deviation of 41. Considering the SNR scaling with number of heartbeats shows that differences in the number of heartbeats averaged cannot account for the spread in SNR values. Wings of each violin plot represent an empirical distribution of the participant results, computed by kernel density estimation (KDE). Mean SNR is indicated for each experimental condition with a gold dot, with the asymmetric standard deviation of the participant level distribution from the mean reported with thick black lines. Mixed modeling comparisons across condition-sorted datasets showed that there were no statistically significant differences in the distributions for each condition, indicating that the controlled factors in the study did not meaningfully affect the SNR.</p>
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17 pages, 3167 KiB  
Article
Dynamic Field Nulling Method for Magnetically Shielded Room Based on Padé Approximation and Generalized Active Disturbance Rejection Control
by Jiye Zhao, Xinxiu Zhou and Jinji Sun
Electronics 2024, 13(16), 3163; https://doi.org/10.3390/electronics13163163 - 10 Aug 2024
Viewed by 874
Abstract
Magnetically shielded rooms (MSRs) provide a near-zero field environment for magnetoencephalography (MEG) research. Due to the high cost of high-permeability materials and the weak shielding capability against low-frequency magnetic disturbance, it is necessary to further design active compensation coils combined with a closed-loop [...] Read more.
Magnetically shielded rooms (MSRs) provide a near-zero field environment for magnetoencephalography (MEG) research. Due to the high cost of high-permeability materials and the weak shielding capability against low-frequency magnetic disturbance, it is necessary to further design active compensation coils combined with a closed-loop control system to achieve dynamic nulling of environmental magnetic disturbance. To enhance the performance of the dynamic nulling system, this paper proposes a novel controller design method based on Padé approximation and generalized active disturbance rejection control (GADRC). First, a precise closed-loop model of the dynamic nulling system is established. On this basis, the delay element of the optically pumped magnetometer (OPM) is approximated using the Padé approximation method, and the controller is designed within the GADRC framework. The system’s stability and disturbance suppression capability are analyzed using frequency-domain methods. To validate the effectiveness of the proposed method, simulations and experiments are conducted, achieving a shielding factor greater than 40 dB at 0.1 Hz. After filtering out power frequency interference, the peak-to-peak field fluctuation is reduced from 320.3 pT to 1.8 pT. Full article
(This article belongs to the Section Systems & Control Engineering)
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<p>Composition of the dynamic nulling system for MSR. The OPM is used for dynamic magnetic field detection. The analog-to-digital converter (ADC), controller, and digital-to-analog converter (DAC) are responsible for data acquisition, control program execution, and control voltage output, respectively. The linear power amplifier drives current to the compensation coils, thereby generating a compensating field to achieve dynamic nulling within the MSR.</p>
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<p>Results comparison for square wave input. The blue curve labeled ‘square wave’ represents the input magnetic field, which is calculated by multiplying the coil’s input current by the coil constant. The red curve labeled ‘<math display="inline"><semantics> <mrow> <msub> <mi>G</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>m</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>’ shows the response of the transfer function model <math display="inline"><semantics> <mrow> <msub> <mi>G</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>m</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. This response exhibits a delay of approximately 3.2 ms and a monotonically increasing response without overshoot, corresponding to the first-order inertial element in the model. The yellow curve labeled ‘actual OPM’ represents the response of actual OPM, which closely matches the <math display="inline"><semantics> <mrow> <msub> <mi>G</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>m</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> model, with a nearly identical rise time and final value. The inset illustrates the deviation between the two responses, revealing a small discrepancy at the end of the rise time.</p>
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<p>Closed-loop model of the dynamic nulling system.</p>
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<p>Results of Padé approximation. <math display="inline"><semantics> <mrow> <msub> <mi>G</mi> <mrow> <mi>B</mi> <mi>P</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>G</mi> <mrow> <mi>B</mi> <mi>P</mi> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>G</mi> <mrow> <mi>B</mi> <mi>P</mi> <mn>3</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> represent the results of the 1st–3rd-order Padé approximations, respectively. As shown in the inset, <math display="inline"><semantics> <mrow> <msub> <mi>G</mi> <mrow> <mi>B</mi> <mi>P</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> exhibits the largest overshoot and the slowest convergence rate. Conversely, <math display="inline"><semantics> <mrow> <msub> <mi>G</mi> <mrow> <mi>B</mi> <mi>P</mi> <mn>3</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> demonstrates the smallest overshoot and the fastest convergence. This indicates that increasing the order of the Padé approximation improves fitting accuracy but also increases the system’s order and complexity.</p>
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<p>Dynamic nulling system within the GADRC framework.</p>
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<p>Equivalent two-degrees-of-freedom system.</p>
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<p>Root locus of equivalent control system. (<b>a</b>) Tracking controller <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>; (<b>b</b>) feedback control loop <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mrow> <mn>2</mn> <mi>f</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
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<p>Equivalent disturbance suppression model.</p>
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<p>Bode plot of equivalent disturbance suppression model. (<b>a</b>) Open-loop Bode plot; (<b>b</b>) closed-loop Bode plot. (<b>a</b>) The open-loop crossover frequency of the system is 28.3 Hz, with a phase margin of 62.5 deg. (<b>b</b>) The intersection of the magnitude–frequency response curve with the 0 dB line is at 31.2 Hz, indicating the disturbance rejection bandwidth of the dynamic nulling system. Additionally, a resonance peak is observed at 78.9 Hz, with a peak value of 3.8 dB.</p>
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<p>Bode plot of equivalent disturbance suppression model. (<b>a</b>) Open-loop Bode plot; (<b>b</b>) closed-loop Bode plot. (<b>a</b>) The open-loop crossover frequency of the system is 28.3 Hz, with a phase margin of 62.5 deg. (<b>b</b>) The intersection of the magnitude–frequency response curve with the 0 dB line is at 31.2 Hz, indicating the disturbance rejection bandwidth of the dynamic nulling system. Additionally, a resonance peak is observed at 78.9 Hz, with a peak value of 3.8 dB.</p>
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<p>Simulation results of dynamic nulling system. (<b>a</b>) MESO estimation result; (<b>b</b>) time-domain waveform; (<b>c</b>) power spectral density. <math display="inline"><semantics> <msub> <mi>B</mi> <mi>e</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>B</mi> <mi>r</mi> </msub> </semantics></math> represent the field fluctuations before and after dynamic nulling, respectively.</p>
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<p>Simulation results of dynamic nulling system. (<b>a</b>) MESO estimation result; (<b>b</b>) time-domain waveform; (<b>c</b>) power spectral density. <math display="inline"><semantics> <msub> <mi>B</mi> <mi>e</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>B</mi> <mi>r</mi> </msub> </semantics></math> represent the field fluctuations before and after dynamic nulling, respectively.</p>
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<p>Experimental platform for the dynamic nulling system. (<b>a</b>) MSR and OPM; (<b>b</b>) hardware system.</p>
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<p>Experimental results of dynamic nulling system. (<b>a</b>) Time domain; (<b>b</b>) time domain with 50 Hz notch filter; (<b>c</b>) power spectral density. <math display="inline"><semantics> <msub> <mi>B</mi> <mi>e</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>B</mi> <mi>r</mi> </msub> </semantics></math> represent the field fluctuations before and after dynamic nulling, respectively.</p>
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<p>Experimental results of dynamic nulling system. (<b>a</b>) Time domain; (<b>b</b>) time domain with 50 Hz notch filter; (<b>c</b>) power spectral density. <math display="inline"><semantics> <msub> <mi>B</mi> <mi>e</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>B</mi> <mi>r</mi> </msub> </semantics></math> represent the field fluctuations before and after dynamic nulling, respectively.</p>
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<p>Comparison of shielding factors between MSR, dynamic nulling system, and MSR+dynamic nulling system.</p>
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23 pages, 14496 KiB  
Article
Hardware Design and Implementation of a High-Precision Optically Pumped Cesium Magnetometer System Based on the Human-Occupied Vehicle Platform
by Keyu Zhou, Qimao Zhang and Qisheng Zhang
Appl. Sci. 2024, 14(15), 6778; https://doi.org/10.3390/app14156778 - 2 Aug 2024
Viewed by 842
Abstract
High-precision magnetometers play a crucial role in ocean exploration, geophysical prospecting, and military and security applications. Installing them on human-occupied vehicle (HOV) platforms can greatly enhance ocean exploration capabilities and efficiency. However, most existing magnetometers suffer from low sensitivity and excessively large size. [...] Read more.
High-precision magnetometers play a crucial role in ocean exploration, geophysical prospecting, and military and security applications. Installing them on human-occupied vehicle (HOV) platforms can greatly enhance ocean exploration capabilities and efficiency. However, most existing magnetometers suffer from low sensitivity and excessively large size. This study presents a high-sensitivity, miniaturized magnetometer based on cesium optically pumped probes. The designed magnetometer utilizes a three-probe design to eliminate the detection dead zone of the cesium optically pumped probe and enable three-dimensional magnetic detection. The proposed magnetometer uses a flux gate probe to detect the three-axis magnetic field and ensure that the probe does not enter the dead zone. The three probes can automatically switch by measuring the geomagnetic elements and real-time attitude of the HOV platform. This article primarily introduces the cesium three-probe optically pump, flux gate sensor, and automatic switching scheme design of the above-mentioned magnetometer. Moreover, it is proven through testing that the core indicators, such as the accuracy and sensitivity of the cesium three-probe optically pumped and flux gate sensor, reach international standards. Finally, the effectiveness of the automatic switching scheme proposed in this study is demonstrated through drone-mounted experiments. Full article
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<p>System block diagram.</p>
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<p>The hardware of the optically pumped probe.</p>
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<p>The cesium optically pumped probe.</p>
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<p>A three-dimensional model of the cesium atomic lamp.</p>
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<p>A physical picture of the cesium atomic lamp.</p>
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<p>A cesium absorption cell model.</p>
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<p>A schematic diagram of the signal conditioning process.</p>
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<p>A circuit diagram of the signal conditioning circuit.</p>
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<p>A schematic diagram of the temperature control unit.</p>
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<p>Design diagram of the temperature control circuit.</p>
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<p>A schematic diagram of the RF excitation circuit.</p>
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<p>The structure of the single-axis flux gate probe.</p>
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<p>A schematic diagram of the detection circuit.</p>
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<p>The dimensions of the optical probe unit (unit: mm).</p>
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<p>A three-dimensional diagram of the probe assembly.</p>
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<p>The simulation results.</p>
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<p>A control flowchart for switching between three probes.</p>
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<p>A block diagram of the triaxial flux gate acquisition board.</p>
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<p>The peripheral circuit of the Zynq XC7Z020 processor chip.</p>
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<p>A schematic diagram of the absolute accuracy, sensitivity, and dynamic range testing of the optically pumped cesium magnetometer.</p>
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<p>A photograph of the magnetic shielding cylinder.</p>
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<p>A schematic diagram of gradient tolerance testing for the optically pumped cesium magnetometer.</p>
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<p>Ultra-high-uniformity magnetic field generation system.</p>
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<p>A schematic diagram of zero-field compensation testing for the triaxial flux gate probe.</p>
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<p>A schematic diagram of triaxial flux gate probe noise testing.</p>
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<p>Platform movement trajectory.</p>
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<p>Platform movement attitude.</p>
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<p>Test curves for the automatic probe switching experiment.</p>
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17 pages, 4217 KiB  
Article
One-Step Preparation Method and Rapid Detection Implementation Scheme for Simple Magnetic Tagging Materials
by Xianxiao Song, Weiting Ma, Ping Song and Hongying Wang
Magnetochemistry 2024, 10(7), 44; https://doi.org/10.3390/magnetochemistry10070044 - 22 Jun 2024
Viewed by 1233
Abstract
With the widespread application of tagging materials, existing chemical tagging materials exhibit limitations in stability and detection under field conditions. This study introduces a novel magnetic detection scheme. Hydrophilic material-modified Fe3O4 nanoparticles (COOH-PEG@Fe3O4 NPs) were synthesized using [...] Read more.
With the widespread application of tagging materials, existing chemical tagging materials exhibit limitations in stability and detection under field conditions. This study introduces a novel magnetic detection scheme. Hydrophilic material-modified Fe3O4 nanoparticles (COOH-PEG@Fe3O4 NPs) were synthesized using the co-precipitation technique. The content of Fe3O4 nanoparticles in the magnetic tagging liquid can reach up to 10 wt% and remain stable in an aqueous phase system for seven days. This research details the preparation process, the characterization methods (IR, 1HNMR, EDX, XRD, SEM, TEM, VSM, DLS), and the performance effects of the materials in magnetic tagging. Experimental results indicate that COOH-PEG@Fe3O4 NPs exhibit high remanence intensity (Br = 1.75 emu/g) and considerable stability, making it possible to quickly detect tagged liquids in the field using portable flux meters and optical pump magnetometers. This study provides new insights into the design and application of magnetic tagging materials, making it particularly suitable for long-term tagging and convenient detection in field scenarios. Full article
(This article belongs to the Section Applications of Magnetism and Magnetic Materials)
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<p>Modification mechanism of PEG and Fe<sub>3</sub>O<sub>4</sub> NPs.</p>
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<p>Magnetic stabilizing fluid (COOH-PEG300@Fe<sub>3</sub>O<sub>4</sub> (NPs)).</p>
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<p>(<b>a</b>) <sup>1</sup>H NMR of COOH-PEG300, a corresponds to the hydrogen atom in the PEG segment (-C-C-O-), b corresponds to the hydrogen atom in the PEG segment (-C-O-), and c corresponds to the hydrogen atom in the PEG segment (-C=C-); (<b>b</b>) <sup>1</sup>H NMR of COOH-PEG800, a, b and c correspond to the same as above; (<b>c</b>) IR of COOH-PEG300, PEG300, and maleic anhydride; (<b>d</b>) IR of COOH-PEG800, PEG800, and maleic anhydride; (<b>e</b>) IR of COOH-PEG300@Fe<sub>3</sub>O<sub>4</sub>, COOH-PEG800@Fe<sub>3</sub>O<sub>4</sub>, Fe<sub>3</sub>O<sub>4</sub>, and COOH-PEG300.</p>
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<p>(<b>a</b>,<b>b</b>) SEM images of Fe<sub>3</sub>O<sub>4</sub> (NPs) at different magnifications; (<b>c</b>,<b>d</b>) SEM images of COOH-PEG300@Fe<sub>3</sub>O<sub>4</sub> (NPs) at different magnifications; (<b>e</b>) TEM images of COOH-PEG300@Fe<sub>3</sub>O<sub>4</sub> (NPs); (<b>f</b>,<b>g</b>) HRTEM images of COOH-PEG300@Fe<sub>3</sub>O<sub>4</sub> (NPs).</p>
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<p>XRD patterns of as-synthesized Fe<sub>3</sub>O (NPs), COOH-PEG300@Fe<sub>3</sub>O<sub>4</sub> (NPs), and oleic acid@Fe<sub>3</sub>O<sub>4</sub> (NPs).</p>
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<p>(<b>a</b>) SEM images of Fe<sub>3</sub>O<sub>4</sub> (NPs) (ruler = 2 μm), (<b>b</b>) elemental content within the box in (<b>a</b>) 1 as characterized by EDX, (<b>c</b>) SEM images of COOH-PEG300@Fe<sub>3</sub>O<sub>4</sub> (NPs) (ruler = 2 μm), (<b>d</b>) elemental content within the box in (<b>c</b>) 1 as characterized by EDX, (<b>e</b>) the elemental mapping within the box in (<b>a</b>) 2 as characterized by EDX, (<b>f</b>) the elemental mapping within the box in (<b>c</b>) 2 as characterized by EDX.</p>
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<p>(<b>a<sub>1</sub></b>–<b>a<sub>3</sub></b>) The change graph of COOH-PEG300@Fe<sub>3</sub>O<sub>4</sub> (10 wt%), COOH-PEG300@Fe<sub>3</sub>O<sub>4</sub> (5 wt%), and Fe<sub>3</sub>O<sub>4</sub> (10 wt%) magnetic labeling liquid before and after 7 days; (<b>b</b>) particle size distribution graph of Fe<sub>3</sub>O<sub>4</sub> by DLS; (<b>c</b>) particle size distribution graph of COOH-PEG300@Fe<sub>3</sub>O<sub>4</sub> by DLS; (<b>d</b>) zeta potential distribution graph of COOH-PEG300@Fe<sub>3</sub>O<sub>4</sub> and Fe<sub>3</sub>O<sub>4</sub>; (<b>e</b>) the average zeta potential of COOH-PEG300@Fe<sub>3</sub>O<sub>4</sub> and Fe<sub>3</sub>O<sub>4</sub>.</p>
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<p>(<b>a</b>) Magnetic hysteresis curve of COOH-PEG300@Fe<sub>3</sub>O<sub>4</sub> (NPs) measured by VSM, (<b>b</b>) enlarged local image of curve (<b>a</b>,<b>c</b>) magnetic hysteresis curve of Fe<sub>3</sub>O<sub>4</sub> (NPs) measured by VSM, (<b>d</b>) magnetic hysteresis curve of oleic acid@Fe<sub>3</sub>O<sub>4</sub> (NPs) measured by VSM.</p>
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<p>(<b>a</b>) Simulated marking and detection diagram for COOH-PEG300@Fe<sub>3</sub>O<sub>4</sub> (10 wt%), (<b>b</b>) magnetic signal measured by handheld flux meter, (<b>c</b>) magnetic signal measured by handheld optical pump magnetometer.</p>
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18 pages, 6497 KiB  
Article
Decoding N400m Evoked Component: A Tutorial on Multivariate Pattern Analysis for OP-MEG Data
by Huanqi Wu, Ruonan Wang, Yuyu Ma, Xiaoyu Liang, Changzeng Liu, Dexin Yu, Nan An and Xiaolin Ning
Bioengineering 2024, 11(6), 609; https://doi.org/10.3390/bioengineering11060609 - 13 Jun 2024
Cited by 1 | Viewed by 1173
Abstract
Multivariate pattern analysis (MVPA) has played an extensive role in interpreting brain activity, which has been applied in studies with modalities such as functional Magnetic Resonance Imaging (fMRI), Magnetoencephalography (MEG) and Electroencephalography (EEG). The advent of wearable MEG systems based on optically pumped [...] Read more.
Multivariate pattern analysis (MVPA) has played an extensive role in interpreting brain activity, which has been applied in studies with modalities such as functional Magnetic Resonance Imaging (fMRI), Magnetoencephalography (MEG) and Electroencephalography (EEG). The advent of wearable MEG systems based on optically pumped magnetometers (OPMs), i.e., OP-MEG, has broadened the application of bio-magnetism in the realm of neuroscience. Nonetheless, it also raises challenges in temporal decoding analysis due to the unique attributes of OP-MEG itself. The efficacy of decoding performance utilizing multimodal fusion, such as MEG-EEG, also remains to be elucidated. In this regard, we investigated the impact of several factors, such as processing methods, models and modalities, on the decoding outcomes of OP-MEG. Our findings indicate that the number of averaged trials, dimensionality reduction (DR) methods, and the number of cross-validation folds significantly affect the decoding performance of OP-MEG data. Additionally, decoding results vary across modalities and fusion strategy. In contrast, decoder type, resampling frequency, and sliding window length exert marginal effects. Furthermore, we introduced mutual information (MI) to investigate how information loss due to OP-MEG data processing affect decoding accuracy. Our study offers insights for linear decoding research using OP-MEG and expand its application in the fields of cognitive neuroscience. Full article
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<p>(<b>a</b>) Flowchart of the paradigm. Subjects taking the test were first presented with a sentence main body followed by the final verb after 1 s for comprehension. After another 1 s for thinking, subjects gave their response to the congruity judgement. The whole trial lasted 1.2 s in total, i.e., 0.2 s pre-stimulus and 1 s post-stimulus. The whole experiment consisted of 196 trials in all. (<b>b</b>,<b>c</b>) Subjects were sitting in the middle of MSR to take EEG and OP-MEG recording.</p>
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<p>An overview for data acquisition and decoding options. In preprocessing part, the methods of improving data SNR and reducing dimension are compared. In decoding and testing parts, the decoder types, cross-validation folds and different modalities were used to systematically evaluate decoding performance.</p>
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<p>The effect of DR methods on decoding performance. Overall, DR through univariate statistical methods for channel selection of interest is less effective compared to using PCA or no DR operation. Using PCA (blue line) yields the modest gain in performance. The decoding results obtained without any DR operation (orange line) achieved the highest decoding accuracy. The colored triangles marked at <span class="html-italic">y</span>-axis denotes the maximum value to the corresponding curves and the triangle at <span class="html-italic">x</span>-axis denotes the maximum time. Discs above the <span class="html-italic">x</span>-axis indicate the time points where decoding performance is significantly higher than chance.</p>
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<p>The effect of (<b>left</b>) subsampling and (<b>right</b>) sliding window approaches to improving SNR on decoding accuracy. The two approaches aimed at improving SNR do not yield a significant enhancement of the decoding performance. Discs above the <span class="html-italic">x</span>-axis indicate the time points where the decoding performance is significantly higher than chance.</p>
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<p>The effect of averaging trials on decoding performance. The blue, orange, green and red curves represent, respectively, the decoding accuracy under four conditions: not averaging and averaging over every 2, 4, 6 epochs. The colored triangles marked at the <span class="html-italic">y</span>-axis denote the maximum value to the corresponding curves and the triangles at the <span class="html-italic">x</span>-axis denote the corresponding maximum times. Discs above the <span class="html-italic">x</span>-axis indicate the time points where decoding performance is significantly higher than chance.</p>
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<p>The effect of (<b>left</b>) classifier and (<b>right</b>) cross-validation approaches on decoding accuracy. The colored triangles marked at the <span class="html-italic">y</span>-axis denote the maximum value to the corresponding curves and the triangles at the <span class="html-italic">x</span>-axis denote the corresponding maximum times. Discs above the <span class="html-italic">x</span>-axis indicate the time points where decoding performance is significantly higher than chance.</p>
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<p>The effect of different modalities on decoding accuracy. (<b>a</b>) Grand-averaged time course of decoding for OP-MEG, EEG and OP-MEG and EEG samplings. The colored triangles marked at the <span class="html-italic">y</span>-axis denote the maximum value to the corresponding curves and the triangles at the <span class="html-italic">x</span>-axis denote the corresponding maximum times. (<b>b</b>) Difference curves for the results are shown in (<b>a</b>). Discs above the <span class="html-italic">x</span>-axis indicate the time points where decoding performance is significantly higher than chance (<b>a</b>) and zero (<b>b</b>).</p>
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<p>Statistical comparison of MI at different reduction dimensions. The yellow dot in each violin bar indicates the mean value of the data. Notes: * <span class="html-italic">p</span> &lt; 0.05; ** <span class="html-italic">p</span> &lt; 0.01.</p>
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<p>Correlation of the decoding accuracy. (<b>a</b>,<b>b</b>) represent the correlation results of the MI-computed and corresponding accuracy difference for reduction at the spatial, trial dimension and (<b>c</b>,<b>d</b>) represent the temporal dimension (resampling and sliding window). The ellipses depicted here represent the covariance confidence, and the triangles represent the mean data value at the <span class="html-italic">x</span>- and <span class="html-italic">y</span>-axis. ‘r’ and ‘p’ denote the correlation and corresponding significance results. Notes: Univ., univariate; Resamp., resampling; Slid., Sliding window; Temp., temporal; ACC., accuracy.</p>
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16 pages, 3684 KiB  
Article
Noise Reduction and Localization Accuracy in a Mobile Magnetoencephalography System
by Timothy Bardouille, Vanessa Smith, Elias Vajda, Carson Drake Leslie and Niall Holmes
Sensors 2024, 24(11), 3503; https://doi.org/10.3390/s24113503 - 29 May 2024
Viewed by 1036
Abstract
Magnetoencephalography (MEG) non-invasively provides important information about human brain electrophysiology. The growing use of optically pumped magnetometers (OPM) for MEG, as opposed to fixed arrays of cryogenic sensors, has opened the door for innovation in system design and use cases. For example, cryogenic [...] Read more.
Magnetoencephalography (MEG) non-invasively provides important information about human brain electrophysiology. The growing use of optically pumped magnetometers (OPM) for MEG, as opposed to fixed arrays of cryogenic sensors, has opened the door for innovation in system design and use cases. For example, cryogenic MEG systems are housed in large, shielded rooms to provide sufficient space for the system dewar. Here, we investigate the performance of OPM recordings inside of a cylindrical shield with a 1 × 2 m2 footprint. The efficacy of shielding was measured in terms of field attenuation and isotropy, and the value of post hoc noise reduction algorithms was also investigated. Localization accuracy was quantified for 104 OPM sensors mounted on a fixed helmet array based on simulations and recordings from a bespoke current dipole phantom. Passive shielding attenuated the vector field magnitude to 50.0 nT at direct current (DC), to 16.7 pT/√Hz at power line, and to 71 fT/√Hz (median) in the 10–200 Hz range. Post hoc noise reduction provided an additional 5–15 dB attenuation. Substantial field isotropy remained in the volume encompassing the sensor array. The consistency of the isotropy over months suggests that a field nulling solution could be readily applied. A current dipole phantom generating source activity at an appropriate magnitude for the human brain generated field fluctuations on the order of 0.5–1 pT. Phantom signals were localized with 3 mm localization accuracy, and no significant bias in localization was observed, which is in line with performance for cryogenic and OPM MEG systems. This validation of the performance of a small footprint MEG system opens the door for lower-cost MEG installations in terms of raw materials and facility space, as well as mobile imaging systems (e.g., truck-based). Such implementations are relevant for global adoption of MEG outside of highly resourced research and clinical institutions. Full article
(This article belongs to the Special Issue Quantum Sensors and Their Biomedical Applications)
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<p>System coordinates and phantom design. (<b>a</b>) The 2 passive and 1 active shielding cylinders are shown as semi-transparent blue rectangles. Dimensions for the cylinders and end caps are provided in the cylinder coordinate system. The location of the helmet and the volume for field mapping are shown as overlapping semi-transparent orange rectangles. Points A and B indicate a 24 cm sided cube within which the vector magnetic field will be mapped. Points C and D indicate the volume containing the sensor array (i.e., helmet). (<b>b</b>) Schematic of the phantom with the relevant angles for the coordinate system indicated in blue. (<b>c</b>) Phantom mounted in the OPM helmet. (<b>d</b>) Participant ready to be inserted into the shield. (<b>e</b>) OPM time courses from a single recording. Each line represents the magnetic field recorded at one of sixteen sensors (one colour per sensor) during a phantom recording. A 30 Hz low-pass filter (no high pass) was applied to the data to highlight raw signals in the lower-frequency regime.</p>
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<p>Magnetic field and shielding factor spectra. Magnetic field spectra acquired (top row) outside of the shield and (middle row) at the centre of the helmet are shown, as well as the (bottom row) associated shielding factor, for sensors oriented (<b>a</b>) posterior to anterior, (<b>b</b>) left to right, and (<b>c</b>) superior to inferior. Coordinates are with respect to a human participant in a supine position with their head in the helmet. (<b>d</b>) The vector magnitude spectra and associated shielding factors.</p>
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<p>Vector field within the volume of interest. DC field vector strength along each cardinal axis is provided as a function of location within a volume encompassing the OPM helmet. Field vector amplitudes in the (top row) x, (middle row) y, and (bottom row) z orientations are shown with respect to position in the (<b>a</b>) x, (<b>b</b>) y, and (<b>c</b>) z directions. Data are shown for points on a 4 × 4 × 8 (x-y-z) grid. Each line in each plot represents field vector amplitude along one line.</p>
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<p>A 3-D vector representation of the field map. The arrows represent the field vector at each point in space, with orientation accurately represented and arrow length proportional to field strength. The mean field across the volume is subtracted from each vector to highlight the field gradients across the volume.</p>
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<p>Evoked field data for phantom sources. (<b>a</b>) Evoked field topographies generated by activation of four current sources on the phantom. A schematic of the helmet is superimposed in each topography to clarify the spatial arrangement of sensors. Participant left is on the left and the nose is at the top for each topography. (<b>b</b>) Evoked field as a function of time for all 104 OPM sites and four current sources on the phantom.</p>
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<p>Localization errors (LE) for measured and simulated equivalent current dipoles. LE is shown for each of the 12 sources, along each cardinal axis (x, y, z) and as a vector magnitude (R). LE measured with a phantom in the OPM system is shown on the left. LE measured based on simulations with the same parameters is shown on the right. Each coloured column indicates LE for a different phantom source location.</p>
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<p>Noise reduction in phantom recordings. Magnetic field spectra (<b>a</b>) prior to and (<b>b</b>) following reference array regression and homogenous field correction for all 104 OPM recording sites. (<b>c</b>) The shielding factor spectra associated with these two processes are also shown. Black lines in (<b>a</b>–<b>c</b>) indicate the mean across all sensors. Each coloured lines indicates the spectrum for one recording site in the helmet.</p>
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16 pages, 7422 KiB  
Article
Automatic Estimation of the Interference Subspace Dimension Threshold in the Subspace Projection Algorithms of Magnetoencephalography Based on Evoked State Data
by Ruochen Zhao, Ruonan Wang, Yang Gao and Xiaolin Ning
Bioengineering 2024, 11(5), 428; https://doi.org/10.3390/bioengineering11050428 - 26 Apr 2024
Viewed by 1376
Abstract
A class of algorithms based on subspace projection is widely used in the denoising of magnetoencephalography (MEG) signals. Setting the dimension of the interference (external) subspace matrix of these algorithms is the key to balancing the denoising effect and the degree of signal [...] Read more.
A class of algorithms based on subspace projection is widely used in the denoising of magnetoencephalography (MEG) signals. Setting the dimension of the interference (external) subspace matrix of these algorithms is the key to balancing the denoising effect and the degree of signal distortion. However, most current methods for estimating the dimension threshold rely on experience, such as observing the signal waveforms and spectrum, which may render the results too subjective and lacking in quantitative accuracy. Therefore, this study proposes a method to automatically estimate a suitable threshold. Time–frequency transformations are performed on the evoked state data to obtain the neural signal of interest and the noise signal in a specific time–frequency band, which are then used to construct the objective function describing the degree of noise suppression and signal distortion. The optimal value of the threshold in the selected range is obtained using the weighted-sum method. Our method was tested on two classical subspace projection algorithms using simulation and two sensory stimulation experiments. The thresholds estimated by the proposed method enabled the algorithms to achieve the best waveform recovery and source location error. Therefore, the threshold selected in this method enables subspace projection algorithms to achieve the best balance between noise removal and neural signal preservation in subsequent MEG analyses. Full article
(This article belongs to the Special Issue 10th Anniversary of Bioengineering: Biosignal Processing)
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<p>Flowchart of the threshold estimation method.</p>
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<p>(<b>a</b>) Simulation experiment system. (<b>b</b>) Top view of the 31 channel sensors relative to the head position. (<b>c</b>) Location of simulation neural source. (<b>d</b>) Amplitude of the simulation neural source.</p>
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<p>(<b>a</b>) System for somatosensory- and auditory-evoked experiments. (<b>b</b>) Sensor locations for somatosensory-evoked experiment. (<b>c</b>) Sensor locations for auditory-evoked experiment.</p>
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<p>Threshold results in the simulation experiment. (<b>a</b>) SSP. (<b>b</b>) S3P.</p>
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<p>Average waveforms in the simulation experiment with different thresholds. (<b>a</b>) Internal simulated signal. (<b>b</b>) Bandpass filtering only. (<b>c</b>) SSP, <span class="html-italic">x</span> = 4. (<b>d</b>) SSP, <span class="html-italic">x</span> = 7. (<b>e</b>) S3P, <span class="html-italic">x</span> = 4. (<b>f</b>) S3P, <span class="html-italic">x</span> = 6.</p>
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<p>Average results of all channels of time–frequency analysis in the simulation experiment. (<b>a</b>) Internal simulated signal. (<b>b</b>) Bandpass filtering only. (<b>c</b>) SSP, <span class="html-italic">x</span> = 4. (<b>d</b>) SSP, <span class="html-italic">x</span> = 7.</p>
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<p>(<b>a</b>) Time–frequency analysis results of different channels in the simulation experiment. (<b>b</b>–<b>e</b>): “17” Channel results. (<b>b</b>) Internal simulated signal. (<b>c</b>) Bandpass filtering only. (<b>d</b>) SSP, <span class="html-italic">x</span> = 4. (<b>e</b>) SSP, <span class="html-italic">x</span> = 7. (<b>f</b>–<b>i</b>): “21” Channel results. (<b>f</b>) Internal simulated signal. (<b>g</b>) Bandpass filtering only. (<b>h</b>) SSP, <span class="html-italic">x</span> = 4. (<b>i</b>) SSP, <span class="html-italic">x</span> = 7.</p>
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<p>Threshold results in somatosensory-evoked experiment. (<b>a</b>) SSP. (<b>b</b>) S3P.</p>
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<p>Comparison of results with different thresholds in somatosensory-evoked experiment. (<b>a</b>) Results for the inferior threshold, <span class="html-italic">x</span> = 3. (<b>b</b>) Results for the optimal threshold, <span class="html-italic">x</span> = 6. The left row is the result of averaging the superimposed waveforms, the middle row is the result of time–frequency analysis, and the right row is the result of source localization.</p>
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<p>Threshold results in auditory-evoked experiment. (<b>a</b>) SSP. (<b>b</b>) S3P.</p>
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<p>Comparison of results with different thresholds in auditory-evoked experiment. (<b>a</b>) Results for the inferior threshold, <span class="html-italic">x</span> = 6. (<b>b</b>) Results for the optimal threshold, <span class="html-italic">x</span> = 3. The left row is the result of averaging the superimposed waveforms, the middle row is the result of time–frequency analysis, and the right row is the result of source localization.</p>
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16 pages, 7951 KiB  
Article
Compact and Fully Integrated LED Quantum Sensor Based on NV Centers in Diamond
by Jens Pogorzelski, Ludwig Horsthemke, Jonas Homrighausen, Dennis Stiegekötter, Markus Gregor and Peter Glösekötter
Sensors 2024, 24(3), 743; https://doi.org/10.3390/s24030743 - 24 Jan 2024
Cited by 8 | Viewed by 4880
Abstract
Quantum magnetometry based on optically detected magnetic resonance (ODMR) of nitrogen vacancy centers in diamond nano or microcrystals is a promising technology for sensitive, integrated magnetic-field sensors. Currently, this technology is still cost-intensive and mainly found in research. Here we propose one of [...] Read more.
Quantum magnetometry based on optically detected magnetic resonance (ODMR) of nitrogen vacancy centers in diamond nano or microcrystals is a promising technology for sensitive, integrated magnetic-field sensors. Currently, this technology is still cost-intensive and mainly found in research. Here we propose one of the smallest fully integrated quantum sensors to date based on nitrogen vacancy (NV) centers in diamond microcrystals. It is an extremely cost-effective device that integrates a pump light source, photodiode, microwave antenna, filtering and fluorescence detection. Thus, the sensor offers an all-electric interface without the need to adjust or connect optical components. A sensitivity of 28.32nT/Hz and a theoretical shot noise limited sensitivity of 2.87 nT/Hz is reached. Since only generally available parts were used, the sensor can be easily produced in a small series. The form factor of (6.9 × 3.9 × 15.9) mm3 combined with the integration level is the smallest fully integrated NV-based sensor proposed so far. With a power consumption of around 0.1W, this sensor becomes interesting for a wide range of stationary and handheld systems. This development paves the way for the wide usage of quantum magnetometers in non-laboratory environments and technical applications. Full article
(This article belongs to the Special Issue Quantum Sensors and Quantum Sensing)
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<p>(<b>a</b>) Diamond crystal structure formed by carbon atoms (grey) with nitrogen atom (red) and adjacent vacancy forming a nitrogen vacancy (NV) center. NV centers are formed in all axes of the diamond lattice (indicated by yellow-colored carbon atoms). Green arrow indicates an external magnetic field <math display="inline"><semantics> <msub> <mi>B</mi> <mi>z</mi> </msub> </semantics></math> whereas the blue arrow indicates the vectorial projection on one of the NV-axis <math display="inline"><semantics> <msub> <mi>B</mi> <mrow> <mo>|</mo> <mo>|</mo> </mrow> </msub> </semantics></math> (<b>b</b>) simplified energy diagram of the NV center. (<b>c</b>) Example spectrum measured by multimeter (upper curve—related to right axis) and lock-in amplifier (lower curve—related to left axis). Contrast of the resonance <math display="inline"><semantics> <msub> <mi>C</mi> <mrow> <mi>N</mi> <mi>V</mi> </mrow> </msub> </semantics></math> and full width at half maximum <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>ν</mi> </mrow> </semantics></math> are extracted from fit function. The slope of the resonance is extracted from a fit to the demodulated signal of the LIA.</p>
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<p>(<b>a</b>) Sensor setup containing LED-PCB, microwave (MW) antenna structure (MW-PCB) and the PCB to mount the photodiode (PD-PCB), as well as the <math display="inline"><semantics> <mrow> <mn>100</mn> <mspace width="3.33333pt"/> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> thick filterfoil between MW-PCB and PD-PCB. The overall size is <math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <mn>6.9</mn> <mo>×</mo> <mn>3.65</mn> <mo>×</mo> <mn>15.9</mn> <mo>)</mo> </mrow> <mspace width="3.33333pt"/> <msup> <mi>mm</mi> <mn>3</mn> </msup> </mrow> </semantics></math>. (<b>b</b>) Simulation of the field distribution inside the sensor at <math display="inline"><semantics> <mrow> <mn>10</mn> <mspace width="3.33333pt"/> <mi>dBm</mi> </mrow> </semantics></math> microwave power. (<b>c</b>) Electronic block diagram. A 9V battery feeds a lab-built constant current source for <math display="inline"><semantics> <mrow> <mn>30</mn> <mspace width="3.33333pt"/> <mi>mA</mi> </mrow> </semantics></math> LED current. The microwave source generates a frequency-modulated microwave whose LF frequency is used as the demodulation frequency for the lock-in amplifier (LIA). The photocurrent is fed to a lab-built TIA which provides input voltage for the LIA and a multimeter.</p>
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<p>(<b>a</b>) Emission spectra for the LED (green) only, fluorescence spectra LED with diamond microcrystal after passing through long pass filter with cut-on wavelength at <math display="inline"><semantics> <mrow> <mn>600</mn> <mspace width="3.33333pt"/> <mi>nm</mi> </mrow> </semantics></math> (blue) and <math display="inline"><semantics> <mrow> <mn>622</mn> <mspace width="3.33333pt"/> <mi>nm</mi> </mrow> </semantics></math> (orange). The spectra are recorded by fiber-coupled spectrometer (Ocean HDX, Ocean Insight, Orlando, FL, USA) whereas PD-PCB is replaced by a focusing lens to couple into the fiber. Integration time is set to <math display="inline"><semantics> <mrow> <mn>1</mn> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. (<b>b</b>) Model of light paths showing the light path of the fluorescence emitted by the diamond.</p>
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<p>(<b>a</b>) Temperature drifts with different microwave power. Saturation is reached at temperature of the diamond <math display="inline"><semantics> <mrow> <msub> <mi>T</mi> <mrow> <mi>N</mi> <mi>V</mi> </mrow> </msub> <mo>≈</mo> <mn>306</mn> <mspace width="3.33333pt"/> <mi mathvariant="normal">K</mi> <mrow> <mo>(</mo> <mn>32.85</mn> <mspace width="3.33333pt"/> <mo>°</mo> <mi mathvariant="normal">C</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <mn>10</mn> <mspace width="3.33333pt"/> <mi>dBm</mi> </mrow> </semantics></math> microwave power with reference to the ambient temperature of <math display="inline"><semantics> <mrow> <mn>296.2</mn> <mspace width="3.33333pt"/> <mi mathvariant="normal">K</mi> <mspace width="3.33333pt"/> <mo>(</mo> <mn>23.05</mn> <mspace width="3.33333pt"/> <mo>°</mo> <mi mathvariant="normal">C</mi> <mo>)</mo> </mrow> </semantics></math>. (<b>b</b>,<b>c</b>) Measurement of the surface temperature of the sensor at an ambient temperature of <math display="inline"><semantics> <mrow> <mn>296.9</mn> <mspace width="3.33333pt"/> <mi mathvariant="normal">K</mi> <mspace width="3.33333pt"/> <mo>(</mo> <mn>23.76</mn> <mspace width="3.33333pt"/> <mo>°</mo> <mi mathvariant="normal">C</mi> <mo>)</mo> </mrow> </semantics></math> and with <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mi>M</mi> <mi>W</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> <mspace width="3.33333pt"/> <mi>dBm</mi> </mrow> </semantics></math>. Top view refers to the view of the LED-PCB and bottom view refers to the view of the PD-PCB. The largest temperature increase of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>T</mi> <mrow> <mi>s</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mn>8.1</mn> <mspace width="3.33333pt"/> <mi mathvariant="normal">K</mi> </mrow> </semantics></math> is measured at a contact of the LED.</p>
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<p>Shot noise limited sensitivity for different FM parameters. (<b>a</b>) Sweep of the microwave power from <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mi>M</mi> <mi>W</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mn>10</mn> <mspace width="3.33333pt"/> <mi>dBm</mi> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mi>M</mi> <mi>W</mi> </mrow> </msub> <mo>=</mo> <mn>19</mn> <mspace width="3.33333pt"/> <mi>dBm</mi> </mrow> </semantics></math>. Almost consistently good results were achieved between <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mi>M</mi> <mi>W</mi> </mrow> </msub> <mo>=</mo> <mn>4</mn> <mspace width="3.33333pt"/> <mi>dBm</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mi>M</mi> <mi>W</mi> </mrow> </msub> <mo>=</mo> <mn>11</mn> <mspace width="3.33333pt"/> <mi>dBm</mi> </mrow> </semantics></math>. (<b>b</b>) The local oscillator frequency of the FM is swept between <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>L</mi> <mi>F</mi> </mrow> </msub> <mo>=</mo> <mn>250</mn> <mspace width="3.33333pt"/> <mi>Hz</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>L</mi> <mi>F</mi> </mrow> </msub> <mo>=</mo> <mn>20</mn> <mspace width="3.33333pt"/> <mi>kHz</mi> </mrow> </semantics></math>. The measured values correlate with the measured noise power density spectrum in <a href="#sensors-24-00743-f006" class="html-fig">Figure 6</a>, which shows a similar decay and constant good values from leaving the 1/f noise at above approximately 1 kHz. (<b>c</b>) Sweep of the deviation used in the frequency modulation. <math display="inline"><semantics> <msub> <mi>f</mi> <mrow> <mi>d</mi> <mi>e</mi> <mi>v</mi> <mi>i</mi> </mrow> </msub> </semantics></math> is changed between <math display="inline"><semantics> <mrow> <mn>50</mn> <mspace width="3.33333pt"/> <mi>kHz</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>4</mn> <mspace width="3.33333pt"/> <mi>MHz</mi> </mrow> </semantics></math>. The best values are reached between <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>d</mi> <mi>e</mi> <mi>v</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mn>1.75</mn> <mspace width="3.33333pt"/> <mi>MHz</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>d</mi> <mi>e</mi> <mi>v</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mn>3</mn> <mspace width="3.33333pt"/> <mi>MHz</mi> </mrow> </semantics></math>.</p>
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<p>Measured voltage spectral density for different cases. Purple spectra: A simulated spectral density according to Equation (<a href="#FD7-sensors-24-00743" class="html-disp-formula">7</a>) is shown whereas the amplitude is chosen arbitrarily. Blue spectra: the noise floor measured without any signal cable attached. Orange spectra: all devices running. LED is turned off. Red spectra: The LED is then turned on and the microwave is kept in a non-sensitive regime of <math display="inline"><semantics> <mrow> <mn>2.4</mn> <mspace width="3.33333pt"/> <mi>GHz</mi> </mrow> </semantics></math>. Green spectra: the carrier frequency <math display="inline"><semantics> <msub> <mi>f</mi> <mi>c</mi> </msub> </semantics></math> of the microwave is tuned to resonance. The frequency peaks follow the simulated frequency comb (purple).</p>
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<p>(<b>a</b>) The Allan deviation is measured for different cut-off frequencies of the LIA. The minimum detectable magnetic field change is the average minimum of all curves <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>B</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mn>15.44</mn> <mspace width="3.33333pt"/> <mi>nT</mi> </mrow> </semantics></math> (<b>b</b>) Sensitivity in relation to averaging time. Between <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.1</mn> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>3</mn> <mspace width="3.33333pt"/> <mi mathvariant="normal">s</mi> </mrow> </semantics></math> the mean sensitivity is <math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mn>28.32</mn> <mspace width="3.33333pt"/> <mi>nT</mi> <mo>/</mo> <msqrt> <mi>Hz</mi> </msqrt> </mrow> </semantics></math>.</p>
Full article ">Figure 8
<p>Measurement of a <math display="inline"><semantics> <mrow> <mn>0.5</mn> <mspace width="3.33333pt"/> <mi>Hz</mi> </mrow> </semantics></math> square wave signal with <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>L</mi> <mi>F</mi> </mrow> </msub> <mo>=</mo> <mn>3</mn> <mspace width="3.33333pt"/> <mi>kHz</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>d</mi> <mi>e</mi> <mi>v</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mspace width="3.33333pt"/> <mi>MHz</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mi>M</mi> <mi>W</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> <mspace width="3.33333pt"/> <mi>dBm</mi> </mrow> </semantics></math>. <math display="inline"><semantics> <msub> <mi>f</mi> <mi>c</mi> </msub> </semantics></math> is tuned to resonance. The LIA filter is set to 8th order and <math display="inline"><semantics> <mrow> <mi>BWNEP</mi> <mo>=</mo> <mn>19.69</mn> <mspace width="3.33333pt"/> <mi>Hz</mi> </mrow> </semantics></math>. The sample rate used is 6.67<math display="inline"><semantics> <mrow> <mspace width="3.33333pt"/> <mi mathvariant="normal">k</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. (<b>a</b>) Measured magnetic field component by the quantum sensor <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>B</mi> <mrow> <mi>N</mi> <mi>V</mi> </mrow> </msub> </mrow> </semantics></math> corrected by the angle <math display="inline"><semantics> <mi>θ</mi> </semantics></math> between NV-axis and direction of the applied magnetic field <math display="inline"><semantics> <msub> <mi>B</mi> <mi>Z</mi> </msub> </semantics></math>. (<b>b</b>) Histogram of the difference between <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>B</mi> <mi>Z</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>B</mi> <mrow> <mi>N</mi> <mi>V</mi> </mrow> </msub> </mrow> </semantics></math>. From the standard deviation <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>654.4</mn> <mspace width="3.33333pt"/> <mi>nT</mi> </mrow> </semantics></math> and the <math display="inline"><semantics> <mrow> <mi>BWNEP</mi> <mo>=</mo> <mn>19.69</mn> <mspace width="3.33333pt"/> <mi>Hz</mi> </mrow> </semantics></math> the sensitivity is calculated as <math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mn>147.48</mn> <mspace width="3.33333pt"/> <mi>nT</mi> </mrow> </semantics></math>. (<b>c</b>) Difference between <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>B</mi> <mi>Z</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>B</mi> <mrow> <mi>N</mi> <mi>V</mi> </mrow> </msub> </mrow> </semantics></math> over time. Peaks at the switching edges result from the time constant of the filter.</p>
Full article ">Figure 9
<p>Measurement of a <math display="inline"><semantics> <mrow> <mn>200</mn> <mspace width="3.33333pt"/> <mi>Hz</mi> </mrow> </semantics></math> sinusoidal signal. LIA sample rate and BWNEP were changed to 26.8<math display="inline"><semantics> <mrow> <mspace width="3.33333pt"/> <mi mathvariant="normal">k</mi> <mo>/</mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>BWNEP</mi> <mo>=</mo> <mn>359</mn> <mspace width="3.33333pt"/> <mi>Hz</mi> </mrow> </semantics></math>. (<b>a</b>) Measured magnetic field component by the quantum sensor <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>B</mi> <mrow> <mi>N</mi> <mi>V</mi> </mrow> </msub> </mrow> </semantics></math> corrected with the angle <math display="inline"><semantics> <mi>θ</mi> </semantics></math> between NV-axis and direction of the applied magnetic field <math display="inline"><semantics> <msub> <mi>B</mi> <mi>Z</mi> </msub> </semantics></math>. (<b>b</b>) Histogram of the difference between <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>B</mi> <mi>Z</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>B</mi> <mrow> <mi>N</mi> <mi>V</mi> </mrow> </msub> </mrow> </semantics></math>. Resulting standard deviation <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>3.55</mn> <mspace width="3.33333pt"/> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">T</mi> </mrow> </semantics></math> and with <math display="inline"><semantics> <mrow> <mi>BWNEP</mi> <mo>=</mo> <mn>359</mn> <mspace width="3.33333pt"/> <mi>Hz</mi> </mrow> </semantics></math> the sensitivity is calculated as <math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mn>187.44</mn> <mspace width="3.33333pt"/> <mi>nT</mi> </mrow> </semantics></math>. (<b>c</b>) Difference between <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>B</mi> <mi>Z</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>B</mi> <mrow> <mi>N</mi> <mi>V</mi> </mrow> </msub> </mrow> </semantics></math> over time.</p>
Full article ">Figure 10
<p>Selection of published sensors in terms of size and sensitivity. Only publications that have integrated a photodiode were considered. Also, publications using additional flux concentrators to improve sensitivity are not included. Furthermore, a distinction is made between fully integrated sensors (LED [<a href="#B32-sensors-24-00743" class="html-bibr">32</a>] or integrated laser [<a href="#B28-sensors-24-00743" class="html-bibr">28</a>,<a href="#B29-sensors-24-00743" class="html-bibr">29</a>,<a href="#B30-sensors-24-00743" class="html-bibr">30</a>,<a href="#B31-sensors-24-00743" class="html-bibr">31</a>]) and partial fiber-based sensors with external laser [<a href="#B1-sensors-24-00743" class="html-bibr">1</a>,<a href="#B24-sensors-24-00743" class="html-bibr">24</a>,<a href="#B26-sensors-24-00743" class="html-bibr">26</a>,<a href="#B27-sensors-24-00743" class="html-bibr">27</a>]. It can be seen that fully integrated LED-based sensors can currently be manufactured with smaller form factor.</p>
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