Open Access
Add to BibSonomy
Abstract
We propose a miniaturized single-beam optically pumped magnetometer (OPM) with a laser power differential structure, along with a dynamically-adjusted detection circuit. This design enables the suppression of optical fluctuation noise and the enhancement of magnetometer sensitivity. For a single-beam OPM, pump light fluctuation noise is a significant contributor to output noise. To address this, we propose an OPM with a laser differential structure that separates the pump light as a part of the reference signal before it enters the cell. The reference current and OPM output current are then subtracted to suppress the noise introduced by pump light fluctuations. To achieve optimal optical noise suppression, we implement balanced homodyne detection (BHD) with real-time current adjustment, which dynamically adjusts the reference ratio between the two currents according to their amplitude. Ultimately, we can reduce the noise introduced by pump light fluctuations by 47% of the original. The OPM with laser power differential achieves a sensitivity of 17.5 fT/Hz1/2, with the optical fluctuation equivalent noise at 13 fT/Hz1/2.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Ultra-sensitive magnetic measurement devices are extensively utilized in fundamental physics experimental research [1–4]. Their non-contact measurement advantages and high temporal-spatial resolution [5] make them ideal for detecting abnormal bio-magnetic changes, enabling disease diagnosis [6–8]. Currently, superconducting quantum interference devices (SQUIDs) with ultra-high sensitivity are widely used in bio-magnetic research and medical diagnosis [9,10]. However, SQUIDs require superconducting loops containing Josephson junctions to maintain their sensitivity, which necessitates operating them in liquid nitrogen, leading to high maintenance costs.
The development of optically-pumped magnetometers (OPMs) operating at room temperature has enabled the creation of portable bio-magnetic measurement devices [7,11–13]. OPMs have several advantages over SQUIDs, including a smaller size which allows closer proximity to the patient’s scalp, resulting in a stronger magnetic field signal and higher signal-to-noise ratio (SNR). In particular, the SERF-OPM with alkali atoms in the spin-exchange relaxation-free (SERF) region achieves magnetic field measurements with sensitivity comparable to that of SQUIDs, based on the interaction between alkali metal atoms in a vapor and the magnetic field [14–16]. This suggests that OPMs may serve as a potential replacement for SQUIDs.
Unlike dual-beam magnetometers with differential detection of the probe beam [15,17,18], which require larger sensor sizes, single-beam OPMs use only one pump beam to polarize alkali metal atoms and measure the magnetic field based on the intensity of the transmitted light from the cell [19]. However, fluctuations in the pump light and 1/f noise in the detection circuit can reduce the signal-to-noise ratio (SNR) of the magnetic field measurement. A common approach to improve SNR is to apply an oscillating transverse magnetic field to the ambient magnetic field of the cell [19,20], which modulates the measurement signal of the magnetometer to a higher frequency and reduces the effect of low frequency detection noise on sensitivity. However, even with this method, the noise introduced by pumping light fluctuations near the modulation frequency is still significant. To further reduce this noise and improve sensitivity, the magnetic gradiometer is proposed [21–23], which measures the differences in magnetic fields using two magnetometers with the same parameters. This method can achieve a high common mode rejection ratio in the face of large ambient magnetic fields and pump light intensity fluctuations. However, this method cannot measure the ambient magnetic field. According to the analysis of Sulai et al. [24], the SNR of the gradiometer may be lower than that of two separate magnetometers due to baseline length, the magnitude of uncorrelated and correlated noise.
Various methods have been explored to decrease pumped optical noise. Research by Shah et al. [25] and Krzyzewski et al. [26] demonstrate that using a low-noise VCSEL laser or closed-loop control of the pumping intensity can reduce optical noise. However, these methods increase the complexity of the OPM structure, making it challenging to integrate additional sensors into the on-scalp MEG system.
An alternative approach proposed by Chen et al. [27] utilizes the laser power differential method to suppress both background offset and laser power noise. This method involves splitting the beam into two halves using a $\lambda /2$ waveplate and a polarizing beam splitter (PBS), with one beam acting as a reference beam and the other beam passing through the vapor cell for measurement. However, adjusting the neutral density filter (ND) to ensure that the power of the two beams is the same for the array OPMs can be difficult. Additionally, as the measurement beam can fluctuate due to ambient magnetic fields and cell temperature during OPM operation, a fixed ratio may not always provide optimal noise suppression performance.
Therefore, this paper theoretically analyses the noise signal characteristics of single-beam OPM and optimizes the OPM with laser power differential method. A balanced homodyne detection circuit with real-time current adjustment is proposed, which can adjust the ratio of the reference beam in real-time based on the measurement beam power, thus maintaining optimal noise rejection performance for optical noise. Finally, the proposed laser power differential OPM achieves a sensitivity of $17.5\,fT/Hz^{1/2}$, where the optical fluctuation equivalent noise is reduced to $13\,fT/Hz^{1/2}$.
2. Theory
2.1 Output characteristics of OPM with laser power differential
For an atomic magnetometer, when the ambient magnetic field surrounding the alkali metal atoms in the vapor cell is close to zero and the spin exchange rate of the atoms is much higher than the Larmor precession frequency caused by the ambient magnetic field, the electron spins are in the spin exchange relaxation-free regime. For the following explanation, we establish a right-handed coordinate system where the direction of the pump light propagation is along the Z-axis, the direction of the oscillating magnetic field $B_{\mathrm {m}} \cos \left (\omega _{\mathrm {m}} t\right )$ and the magnetic field being measured $B_\mathrm {0}$ are along the X-axis. The electron polarization rate along the direction of the pump light can be separated into a DC component $P_{\mathrm {z-DC}}$ and a first harmonic component $P_{\mathrm {z-1st}}$ associated with the magnetic field being measured.
For the single-beam OPM, the circularly polarized pump beam was also used to detect the polarization rate $P_{\mathrm {z }}$ of electrons along the direction of the pump light. The transmitted light was detected by the photodetector (PD) behind the vapor cell. The polarization rate $P_{\mathrm {z }}$ and the PD output current $I_{\mathrm {OPM}}$ have the following relationship:
Based on studies in Ref. [26–28] regarding the effect of pump light fluctuations on sensitivity, we can consider the noise introduced by pump light power fluctuations as additive noise, whose amplitude is proportional to the transmitted pump light. In this case, we assume that the laser intensity noise near the modulation frequency is white noise with an RMS value of $p_{\mathrm {n}}$. A polarizing beam splitter (PBS) transmits a portion of the beam onto a photodetector (PD), which serves as the reference signal, while the rest of the beam is detected by the second PD after passing through the vapor cell as the signal (shown in Fig. 3). Assuming the ratio of the pump light power after and before the PBS is $k_{\mathrm {PBS}}$, the currents of the reference PD and signal PD can be expressed as:
The noise component in the $I_{\mathrm {OPM}}$ can be minimized if the magnitude of the $I_{\mathrm {ref}}$ is appropriately scaled so that its DC component is equal to the DC component of the $I_{\mathrm {OPM}}$.
Equation (4) shows that after a gain of $k_{\mathrm {dc}}$ times the amplitude of $I_{\mathrm {ref}}$, the noise component in its differential signal $I_{\mathrm {diff}}$ with the $I_{\mathrm {OPM}}$ is completely eliminated. In practice, we can complete the extraction of the differential signal using analogue circuits with different gain amplitudes, or directly using digital signals. However, according to Eqs. (1)–(3), the gain coefficient $k_{\mathrm {dc}}$ is affected by the cell temperature, the splitting ratio of the PBS, the electron spin polarization, the modulation index and other parameters that may change during the long operation of the OPM. In the case of array OPMs, the gain coefficients $k_{\mathrm {dc}}$ of adjacent channels are more likely to differ significantly. A fixed gain coefficient $k_{\mathrm {dc}}$ that does not match the actual output signal of the sensor will result in a lower SNR of the OPM output signal. Therefore, we implement a balanced homodyne detection circuit that can adjust the gain coefficient $k_{\mathrm {dc}}$ in real time according to the DC components of $I_{\mathrm {OPM}}$ and $I_{\mathrm {ref}}$ to ensure that the optical noise of all sensors can be suppressed to the maximum extent during the operation of the array OPMs.
2.2 Balanced homodyne detection with real-time current adjustment
Balanced homodyne detection (BHD) with real-time current adjustment is illustrated in Fig. 1. It comprises a current splitter (CS), a transimpedance amplifier (TIA), and a PI controller. D1 converts the light reflected by the PBS, as it passes through the cell, into the photocurrent signal $I_{\mathrm {OPM}}$, while D2 converts the transmitted light into the reference signal $I_{\mathrm {ref}}$. Q1 and Q2 represent a matched pair of NPN bipolar transistors (BJT), and the differential between their base-emitter voltages, $\delta V_{\mathrm {BE}} = V_{\mathrm {BE2}} - V_{\mathrm {BE1}}$, controls the ratio of their collector currents, $I_{\mathrm {C2}}/I_{\mathrm {C1}}$. Since both emitters are connected and the base and collector of Q1 are grounded, $I_{\mathrm {C2}}/I_{\mathrm {C1}}$ is considered to be controlled by the base voltage $V_{\mathrm {B2}}$ of Q2.
Fig. 1. Schematic diagram of BHD with real-time current adjustment. The circuit is mainly composed of current splitter, transimpedance amplifier and PI controller. $I_{\mathrm {OPM}}$ is the signal including the DC component and noise output from the OPM, while $I_{\mathrm {ref}}$ is the reference signal.
Part of the current output from the OPM is split between the current splitter into $I_{\mathrm {C2}}$ and the TIA into $I_{\mathrm {TIA}}$. The theoretical analysis in the previous section shows that when the noise component of the $I_{\mathrm {OPM}}$ and $I_{\mathrm {ref}}$ outputs is the coherence signal, the differential signal $I_{\mathrm {diff}}$ has the lowest optical noise when the DC component of $I_{\mathrm {TIA}}$ is zero. We adjust the current splitting ratio $I_{\mathrm {C2}}/I_{\mathrm {C1}}$ by varying the base voltage $V_{\mathrm {B2}}$ of Q2 so that the DC component of $I_{\mathrm {TIA}}$ is zero. To achieve automatic adjustment of the current splitting ratio, we introduce a PI controller. This controller integrates the signal $V_{\mathrm {out}}$ to obtain the control voltage $V_{\mathrm {B2}}$, which is used to regulate the current splitting ratio and eliminate the $V_{\mathrm {out}}$ DC component in real time, resulting in a zero DC component of $I_{\mathrm {TIA}}$. As a result, the TIA amplifies and outputs $I_{\mathrm {sig}}$, the component of the photocurrent signal $I_{\mathrm {OPM}}$ related to the magnetic field to be measured, while the noise component, along with the DC component, is eliminated by the reference signal $I_{\mathrm {ref}}$ through CS.
In the circuit shown in Fig. 1, $R_{\mathrm {f}}$ is used to set the gain of the signal component $I_{\mathrm {sig}}$, while $C_{\mathrm {f}}$ is necessary to compensate for the phase shift introduced by the feedback network, eliminate oscillations, and attenuate high-frequency disturbances. $R_{\mathrm {e1}}$ and $R_{\mathrm {e2}}$ form a voltage divider, primarily used to reduce the impact of voltage fluctuations on the base control voltage of the CS Q2 caused by OP-amp noise, thus decreasing the internal electrical noise of the BHD.
The closed-loop control block diagram of BHD is shown in Fig. 2. Where $G_{\mathrm {TIA}}(s)$, $G_{\mathrm {PI}}(s)$, $K_{\mathrm {VD}}$ and $K_{\mathrm {CS}}$ are the transfer functions of TIA, PI controller, voltage divider and CS respectively. The following equations show the transfer functions for each component.
Fig. 2. The closed-loop control block diagram of BHD. Where $G_{\mathrm {TIA}}(s)$, $G_{\mathrm {PI}}(s)$, $K_{\mathrm {VD}}$ and $K_{\mathrm {CS}}$ are the transfer functions of TIA, PI controller, voltage divider and current splitter respectively.
According to Eq. (5), the relationship between the Q2 base voltage $V_{\mathrm {B2}}$ and the current flowing through the collector $I_{\mathrm {C2}}$ can be obtained as follows.
Since the collector current $I_{\mathrm {C2}}$ is not linearly related to the base voltage $V_{\mathrm {B2}}$, for ease of analysis it is assumed that the currents flowing through the collector of the NPN-matched BJT pair $I_{\mathrm {C1}}$ and $I_{\mathrm {C2}}$ are equal when the BHD is operating, i.e., the base voltage $V_{\mathrm {B2}}$ fluctuates around zero. And assuming that the amplitude of the reference current $I_{\mathrm {ref}}$ is constant, the change in the base voltage $V_{\mathrm {B2}}$ leading to the change in the collector current $I_{\mathrm {C2}}$ can be approximated as the derivative of Eq. (7) around $V_{\mathrm {B2}}=0$.
Then the closed-loop transfer function of BHD is as follows.
The system has two poles and a zero point for a typical bandpass filter model. Where the low frequency cut-off frequency $f_{cl}$ is approximated as:
This low cut-off frequency indicates that signals below this frequency, either common mode or differential mode signals of the $I_{\mathrm {OPM}}$, are treated by the BHD as changes in the DC component of the $I_{\mathrm {OPM}}$ due to cell temperature variations, changes in the ambient magnetic field, etc., so that the current splitting ratio will be adjusted to eliminate the out-of-bandwidth signals. And in the bandwidth range, the differential-mode signal is amplified by the TIA, while the common-mode (noise) signal is eliminated by the CS, suppressing the optical noise component in the output $V_{\mathrm {out}}$ of the BHD.
3. Experimental setup and regulation procedure
3.1 Experimental setup
Figure 3 shows the experimental setup. To eliminate the impact of geomagnetic variations on the experimental results, the OPM was placed in a four-layer $\mu$-metal cylindrical magnetic shielding. To reduce the OPM’s volume, we used a $\mathrm {3 \times 3 \times 3mm}$ cubic atomic vapor cell containing a drop of $^{\mathrm {87}} \mathrm {Rb}$, 50 torr of $\mathrm {N_2}$ for quenching, and 700 torr of He as a buffer gas. A heater attached to the cell’s side was designed to overlap the top and bottom wires and to pass a 400 kHz current through the heater to minimize additional magnetic field noise. The PT1000 for measuring the cell temperature is attached to the other side of the cell, and the cell temperature is controlled at $140^{\circ } \mathrm {C}$ by the heater driver.
Fig. 3. Schematic of the experimental apparatus. PMF: polarization maintaining fiber, FC: fiber collimator, PBS: polarizing beam splitter, $\lambda /4$: 1/4 waveplate. The pump light enters the sensor via the PMF and is split by the PBS into a reference beam and a measurement beam. PD2 detects the reference beam and outputs the reference current $I_{\mathrm {ref}}$. The measurement beam passes through the cell and is detected by PD1, which outputs the signal current $I_{\mathrm {OPM}}$.
DBR lasers tuned to the D1 line of $^{\mathrm {87}} \mathrm {Rb}$ emit a beam that is coupled into a polarization maintaining fiber (PMF) and delivered to the sensor. At the sensor’s entrance, a fiber collimator (FC) focuses the light from the PMF into a spatially parallel beam. A PBS divides the beam into a reference beam and a measurement beam. The reference beam is converted to the reference signal $I_{\mathrm {ref}}$ by PD2, while the measurement beam passes through the cell after the 1/4 waveplate. After the $^{\mathrm {87}} \mathrm {Rb}$ interacts with the resonant circularly polarized light, the laser transmitted from the cell is detected by PD1 and converted to the OPM signal $I_{\mathrm {OPM}}$. By adjusting the angle between the fast axis of the half-wave plate and the principal axis of the PBS, we can control the ratio of the light intensities received by PD1 and PD2.
To shift the detected signal to the modulation frequency and avoid low frequency detection noise, a modulated magnetic field is generated by a function generator (Keysight 33500B) and applied in the X-direction of the OPM. The photocurrents $I_{\mathrm {ref}}$ and $I_{\mathrm {OPM}}$ from PD1 and PD2 are differentiated by the BHD and converted into an AC voltage signal at the same frequency as the modulation frequency. The AC voltage signal is processed by a lock-in amplifier (LIA) (Zurich Instrument MFLI) to produce a voltage signal proportional to the magnetic field to be measured. And together with the feedback voltage $V_{\mathrm {B2}}$ from the BHD, is acquired by the DAQ.
3.2 Optical noise analysis of OPM
To test the hypothesis proposed in the previous section about the relationship between optical noise and the amplitude of the pump light, we set the cell temperature to $140^{\circ } \mathrm {C}$. After completing magnetic field compensation, we adjusted the angle between the fast axis of the half-wave plate and the principal axis of the PBS so that the photocurrents from PD1 and PD2 are approximately equal in magnitude. Then, we varied the amplitude of the laser power and simultaneously recorded the amplitude and waveform of both using two commercial TIAs (Thorlabs PDA200C) and a DAQ (NI PXIe-4499). We estimated the noise power spectral density (NSD) of the above signal using MATLAB’s periodgram function. Using the amplitude of the DC component of both as the differential scale, we obtained the differential signal $I_{\mathrm {diff}}$ referred to in Eq. (4), and analyzed the NSD of this signal.
The NSD results for the three near the modulation frequency (1kHz) are shown in Fig. 4. The plus and cross signs represent the measured results of $I_{\mathrm {OPM}}$ and $I_{\mathrm {ref}}$ noise at different photocurrents, respectively. The solid black line is the fitted curve based on the results of both ${i_n} = {K_{pump}}{I_{DC}} + NF$, where $K_{\mathrm {pump}}$ is the coefficient between the DC current $I_{\mathrm {DC}}$ and the current noise due to pump light fluctuation. $NF$ is the noise floor introduced by the dark current of the PD, thermal noise of the circuit, etc. Both the reference signal $I_{\mathrm {ref}}$ and the OPM output signal $I_{\mathrm {OPM}}$, generated by the same laser, have noise amplitudes proportional to the DC component of the photocurrent and can be fitted with the same noise versus current curve.
Fig. 4. Relationship between the noise floor of $I_{\mathrm {OPM}}$, $I_{\mathrm {ref}}$ and $I_{\mathrm {diff}}$ near the modulation frequency and photocurrent amplitude. The black and red solid lines are the noise fitting curves for the original and differential signals respectively.
The red triangle shows the measured results for $I_{\mathrm {diff}}$ noise, and the solid red line uses the same equation as $I_{\mathrm {OPM}}$ and $I_{\mathrm {ref}}$ to obtain the fitted results. The results for all three are shown in Table 1. In terms of the coefficient $K_{\mathrm {pump}}$, the differential current $I_{\mathrm {diff}}$ noise is approximately 48.9% of the current $I_{\mathrm {OPM}}$ and $I_{\mathrm {ref}}$ noise, i.e., the differential photocurrent for the OPM shown in Fig. 3 reduces the noise caused by the fluctuation of the pump light.
Table 1. The fitting result of the amplitude of photocurrent and the noise floor.
Next, we held the DC amplitude of the OPM output current $I_{\mathrm {OPM}}$ constant and set three different DC values of the reference current $I_{\mathrm {ref}}$ to analyze the relationship between the amplitude scaling of $I_{\mathrm {ref}}$ and the noise floor of the differential current $I_{\mathrm {diff}}$. The results are presented in Fig. 5, where the black cross sign indicates the $I_{\mathrm {diff}}$ noise floor obtained by scaling the DC component. Notably, the noise floor at the lowest point of the curve is approximately the same for all three sets of experiments, as the DC amplitude of the OPM output current $I_{\mathrm {OPM}}$ remains constant. The presence of the black cross sign at the lowest point of the respective curves demonstrates that the optical noise of the reference beam and the measurement beam after PBS separation is a coherent signal. By differentiating according to the proportion of the DC component, we were able to suppress almost all of the optical noise.
Fig. 5. The relationship between the $I_{\mathrm {diff}}$ noise floor and the differential ratio. The black crosses indicate the noise floor of the signal according to the differential ratio of the $I_{\mathrm {OPM}}$ to the $I_{\mathrm {ref}}$ DC component.
3.3 Noise suppression capability analysis of BHD
In order to verify the bandwidth and noise suppression capability of the BHD circuit proposed in this paper, we design the following experimental setup (Fig. 6).
The single-pole, double-throw switch is used to change the measurement mode when the pole of the switch is connected to the upper terminal and the instrument is operating in the common mode noise rejection test mode. The function generator generates a sinusoidal signal, which is divided into two coherent voltage signals by a potentiometer. The two coherent signals are then converted into coherent current signals by two home-made Howland voltage control current sources (VCCS) with the same parameters. VCCS-1 produces the larger signal, considered to be $I_{\mathrm {ref}}^{\mathrm {sim}}$, and the other is considered to be $I_{\mathrm {OPM}}^{\mathrm {sim}}$. Adjusting the potentiometer changes the ratio of $I_{\mathrm {OPM}}^{\mathrm {sim}}$ and $I_{\mathrm {ref}}^{\mathrm {sim}}$. We set the ratio of $I_{\mathrm {OPM}}^{\mathrm {sim}}$ and $I_{\mathrm {ref}}^{\mathrm {sim}}$ to 1/2, fix the offset of the function generator output voltage so that $I_{\mathrm {ref}}^{\mathrm {sim}} \approx 300\mu A$, and change the frequency of the test signal. The results are shown in the blue solid line in Fig. 7.
Fig. 7. Frequency response curves for the gain of the BHD to the common-mode and differential-mode signals. Where the black dashed line is the result of the fit obtained from Eq. (9).
To verify the ability of this BHD circuit to suppress common mode noise, we measured the common mode rejection ratio (CMRR) of this BHD at different reference currents. We vary both the amplitude of the function generator output signal and the ratio of $I_{\mathrm {OPM}}^{\mathrm {sim}}$ and $I_{\mathrm {ref}}^{\mathrm {sim}}$. Here, we set the common mode signal to be a sine wave at 1 kHz (also the modulation frequency). By measuring the root mean square (RMS) value of the noise signal $I_{\mathrm {ref}}^{\mathrm {sim}}$ before passing through the BHD and the RMS value of the equivalent current signal $V_{\mathrm {out}}$ after passing through the BHD, we can obtain the CMRR of the BHD circuit in the frequency band of interest. The CMRR can be written as:
Figure 8 shows the results, where colors represent the CMRR of the BHD circuit in different scenarios. The outcomes are influenced by both the ratio of $I_{\mathrm {OPM}}^{\mathrm {sim}}$ and $I_{\mathrm {ref}}^{\mathrm {sim}}$, and the amplitude of the input noise. The BHD exhibits the best CMRR when the ratio of $I_{\mathrm {OPM}}^{\mathrm {sim}}$ and $I_{\mathrm {ref}}^{\mathrm {sim}}$ is close to 1/2. Additionally, the CMRR reduces significantly when the input noise amplitude is low due to the impact of VCCS and DAQ background noise. Based on the optical noise test outcomes from the previous section, the noise coefficient of $I_{\mathrm {diff}}$, $K_{\mathrm {pump}}$, is roughly half the noise coefficient of the original signal. Hence, the noise rejection ability of the BHD satisfies the requirements of OPM optical current differentiation, even when $I_{\mathrm {OPM}}^{\mathrm {sim}}$ is small, and the CMRR is less than 20dB.
Fig. 8. Relationship between CMRR and the reference signal $I_{ref}^{sim}$ and the ratio of $I_{\mathrm {OPM}}^{\mathrm {sim}}$ and $I_{\mathrm {ref}}^{\mathrm {sim}}$.
4. Result
The experimental equipment, as depicted in Fig. 3, processed the OPM outputs $I_{\mathrm {OPM}}$ and $I_{\mathrm {ref}}$ using BHD and collected the voltage signal $V_{\mathrm {out}}$ and feedback voltage $V_{\mathrm {B2}}$ of BHD. After the feedback voltage $V_{\mathrm {out}}$ was converted to the equivalent input differential photocurrent by the gain of the TIA, 80 minutes of differential photocurrent and feedback voltage data were recorded (as shown in Fig. 9). The data indicated that the feedback voltage $V_{\mathrm {B2}}$ fluctuates significantly within the first 1200 seconds, which was likely due to the vapor cell’s temperature not being fully equilibrated, causing slight changes in the absorption of the alkali metal for the pump light.
Fig. 9. Long-term drift test results for the equivalent input differential photocurrent and the feedback voltage $V_{\mathrm {B2}}$ from the BHD output when the cell of the OPM is heated to $140^{\circ } \mathrm {C}$.
However, after 1200 seconds, the feedback voltage $V_{\mathrm {B2}}$ became more stable than before. The fluctuations observed thereafter may have resulted from changes in the residual magnetic field in the magnetic shielding, which was influenced by the external magnetic environment, and led to variations in the absorption rate of the alkali metal for the pump light. Nonetheless, despite being influenced by temperature, residual magnetic field, or other factors, the equivalent input differential photocurrent remained stable, demonstrating that the proposed BHD circuit can effectively eliminate the DC components of $I_{\mathrm {OPM}}$.
Next, we collected the NSD of the OPM outputs, $I_{\mathrm {OPM}}$ and $I_{\mathrm {ref}}$, using a low noise transimpedance amplifier (TIA) with $I_{\mathrm {OPM}}\approx 154 \mu A$ and $I_{\mathrm {ref}}\approx 287 \mu A$. We then compared the equivalent NSD, $I_{\mathrm {diff}}^{\mathrm {cal}}$, acquired by digital differential with the NSD obtained by analog differential using BHD, $I_{\mathrm {diff}}^{\mathrm {BHD}}$. The results are shown in Fig. 10. The green and blue lines in the plot represent the NSD of the OPM output currents, $I_{\mathrm {OPM}}$ and $I_{\mathrm {ref}}$, respectively, while the red and cyan lines show the NSD of the digital differential with TIA and BHD output, respectively. The noise of the differential signal, $I_{\mathrm {diff}}^{\mathrm {BHD}}$, after BHD is $9.3 \mathrm {pA/Hz^{1/2}}$, whereas the noise of the OPM output signal, $I_{\mathrm {OPM}}$, is about $19.8\mathrm {pA/Hz^{1/2}}$ around 1kHz. This means that the laser noise of OPM with BHD circuit for laser power differencing would reduce to 47%.
Fig. 10. The NSDs of $I_{\mathrm {OPM}}$, $I_{\mathrm {ref}}$, $I_{\mathrm {diff}}^{\mathrm {cal}}$, $I_{\mathrm {diff}}^{\mathrm {BHD}}$ when the cell of the OPM is heated to $140^{\circ } \mathrm {C}$. The NSDs of $I_{\mathrm {OPM}}$, $I_{\mathrm {diff}}^{\mathrm {BHD}}$, $I_{\mathrm {diff}}$ where $I_{\mathrm {OPM}}$ is the raw current signal from the OPM output, $I_{\mathrm {OPM}}$ is the reference signal. $I_{\mathrm {diff}}^{\mathrm {cal}}$ and $I_{\mathrm {diff}}^{\mathrm {BHD}}$ are the differential signals from the digital differential and BHD outputs respectively.
For low frequency optical noise, there is a significant difference between $I_{\mathrm {diff}}^{\mathrm {cal}}$ and $I_{\mathrm {diff}}^{\mathrm {BHD}}$. Because, for the BHD circuit, the common-mode component of the low-frequency optical noise in $I_{\mathrm {OPM}}$ is eliminated by differential amplification of $I_{\mathrm {ref}}$ according to DC ratio, while the differential-mode component of $I_{\mathrm {OPM}}$ still has a large amplitude after passing through the PI controller due to its low frequency. As a result, this part of the differential-mode component of the $I_{\mathrm {OPM}}$ signal is forced to be part of the current flowing into transistor Q2 when passing through the CS, and is not amplified by the TIA. Therefore, signals outside the BHD bandwidth, both differential-mode and common-mode components will be suppressed.
We also observed that the amplitude of the equivalent current noise obtained after BHD was slightly smaller than the equivalent current noise after digital differencing in the BHD bandwidth range. This suggests that the differential signal extraction method with real-time adjustment of the shunt ratio by BHD has better performance than the differential signal calculated by $I_{\mathrm {OPM}}$ and $I_{\mathrm {ref}}$ DC amplitude in terms of laser noise rejection. Since the absorption capacity of the vapor cell for pump light varies from time to time during the test due to external factors, the latter method cannot ensure optimal optical noise suppression for $I_{\mathrm {OPM}}$ at all times.
We then compared the magnetometer bandwidth performance of the TIA and BHD cases using the same OPM with a modulation field set to 1 kHz and 180 nTpp. The results are presented in Fig. 11 as the blue and green lines, respectively. The black dashed line represents the fitting result obtained based on the OPM frequency response relationship $A(f)=A_0/(1+f^{2}/f_{c}^{2})^{1/2}$ [27], where $A_0$ is the response coefficient of the OPM to the DC magnetic field, and $f_c\approx 342Hz$ is the cut-off frequency of the OPM. The OPM frequency response curves obtained using TIA and BHD are almost identical due to the fact that for a modulated magnetic field of 1 kHz, the frequency range of the OPM output signal $I_{\ mathrm{OPM}}$ processed by TIA and BHD is approximately 600 to 1.4 kHz, while the bandwidth of BHD is 220 Hz to 23.7 kHz, which meets the bandwidth requirements of a reasonable OPM signal.
Finally, we compare the sensitivity of the OPM, as shown in Fig. 3, operating in single-ended mode and laser power differential mode. In single-ended mode, the TIA converts the OPM output signal $I_{\mathrm {OPM}}$ to a voltage signal, while in laser power differential mode, the BHD completes the current-to-voltage conversion. After zeroing the remanence near the cell using the OPM’s internal triaxial coils and applying a modulation field set to 1 kHz 180 nTpp, we apply a calibrated magnetic field of 30 Hz 100 pTrms using external Helmholtz coils. We adjust the phase of the LIA reference signal until it is in phase with the TIA/BHD output signal. At this point, the demodulated magnetic field signal to be measured has the maximum signal-to-noise ratio. We record the LIA output signal using DAQ for 60 s and analyze the recorded signal for power spectral density (PSD). After averaging the noise spectrum in the 1 Hz range, the blue and red lines in Fig. 10 show the spectrum of the OPM output signal in single-ended mode and laser power differential mode, respectively.
Next, we switch off the calibration magnetic field signal and adjust the phase of the LIA reference signal until it is orthogonal to the phase of the TIA/BHD output signal. At this point, we consider the demodulated signal from the LIA output to be independent of the magnetic field to be measured and, in this case, only reflecting the magnitude of the optical and electrical noise of the OPM [26,28]. The LIA output signal is acquired using DAQ for 60 s. The PSD results for both are shown as the cyan and magenta dashed lines in Fig. 12. Then, we switch off the laser and measure the electrical noise introduced by the TIA/BHD, LIA, and DAQ. The test results show that the electrical noise introduced by the TIA and BHD circuits is almost identical in magnitude, mainly because the noise introduced by the BJT is negligible compared to the thermal noise of the gain resistor ($\mathrm {R_f}$). To keep the data simple and intuitive, we have only plotted the equivalent magnetic field noise introduced by the BHD, LIA, and DAQ in Fig. 12. Finally, we used a self-made dual-beam SERF magnetometer [30] to test the magnetic noise inside the shielding cylinder.
At this point, the power density of the pump light transmitted through the cell is approximately $4 \mathrm {mW/cm^2}$, and the OPM operates in single-ended mode with a sensitivity of approximately $25\, \mathrm {fT/Hz}^{1/2}$. Due to the low intensity of the pump light, the output calibration signal of the OPM has a small amplitude, and the equivalent magnetic field noise of the pump light is about $21.5\, \mathrm {fT/Hz}^{1/2}$, which becomes a key factor limiting the sensitivity of the magnetometer. When the OPM is operated in laser power differential mode, the noise of the pump light is significantly suppressed by the BHD, which is about $13\, \mathrm {fT/Hz}^{1/2}$, and the sensitivity of the OPM is about $17.5\, \mathrm {fT/Hz}^{1/2}$. The measurement results using a high-sensitivity dual-beam SERF magnetometer show that the magnetic noise inside the shielding cylinder is less than $7\,\mathrm {fT/Hz}^{1/2}$, and the impact on the sensitivity of the laser power differential OPM can be ignored. In other words, using the laser power differential OPM and the BHD proposed in this paper, the noise of the pump light can be significantly reduced, and the sensitivity of the magnetometer can be improved by significantly reducing the effect of the pump noise on the sensitivity.
5. Discussion
The sensitivity of the OPM proposed in this paper, which uses laser power differential, is obviously somewhat lower than that of the highest level of the current single-beam absorption SERF magnetometer ($7 \,\mathrm {fT/Hz}^{1/2}$) [26]. This is due to the small amplitude of the pump light, resulting in a weak signal at the OPM output. Although the laser power differential method reduces the optical noise amplitude by about 47% around the modulation frequency, there remains some differential mode noise between $I_{\mathrm {OPM}}$ and $I_{\mathrm {ref}}$ that cannot be eliminated due to photon shot noise and possible phase delays caused by the absorption of pump light by the cell. The small signal amplitude at the OPM output causes the equivalent magnetic field noise introduced by this optical noise to be the key factor limiting further improvement in OPM sensitivity, as shown in Fig. 12.
While increasing the intensity of the pump light can help to improve the sensitivity of the magnetometer, it can be challenging to adjust the light intensity of a channel individually in an OPM array for magnetocardiography or magnetoencephalography. In such cases, differential laser power OPMs can suppress the noise introduced by fluctuations in the pump light, ensuring that all OPMs in the array have acceptable sensitivity without the need for additional manual adjustment of pump light intensity for each channel.
Compared to digital differential schemes, the introduction of BHD enables differentiation of $I_{\mathrm {OPM}}$ and $I_{\mathrm {ref}}$ at the analog signal stage, eliminating additional electrical noise introduced by the TIA and DAQ chains and reducing the noise floor of electrical noise introduced by the signal acquisition part. The PI controller of the BHD can keep the differential signal free of DC bias in real-time, and the BHD can be used at higher gain than the TIA for the same pump light intensity, reducing the equivalent input current noise introduced by the circuit system and further improving the SNR of the OPM.
Furthermore, when compared to the gradiometer, the OPM with laser power differential has the ability to measure specific remanence at a particular point in space. This feature enables it to be placed in a magnetically shielded room and combined with a large magnetic field coil to function as a magnetic field sensor in an actively shielded system. This results in lower remanence and magnetic field fluctuations for the scalp MEG system [31].
6. Conclusion
In conclusion, this paper proposes a single-beam laser power-differential OPM that splits a portion of the pump light as a reference signal before entering the cell. This reference signal is subtracted from the OPM output signal by a certain ratio to obtain a differential signal, significantly suppressing the optical noise component. The laser power differential OPM offers the advantage of a small size and high sensitivity.
Theoretical and experimental results show that the OPM has the highest SNR only when the DC component of the differential signal is zero. Therefore, a BHD with a real-time current adjustment circuit is proposed, which dynamically adjusts the differential ratio of the OPM signal to the reference signal according to the magnitude of the reference and signal currents, maintaining the best optical noise rejection performance. In practical tests, the noise introduced by pump light fluctuations of the differential signal is reduced by 47% of the original. As a result, this approach yields lower electrical noise and better optical noise rejection than digital differential solutions.
For the weakly pumped OPM, the sensitivity of the OPM without laser power differential is about $25 \,\mathrm {fT/Hz}^{1/2}$, and the optical noise ($21.5\, \mathrm {fT/Hz}^{1/2}$) becomes the key factor limiting the sensitivity of the OPM. With laser power differential, the optical noise is reduced to $13 \,\mathrm {fT/Hz}^{1/2}$, resulting in a sensitivity of $17.5 \,\mathrm {fT/Hz}^{1/2}$. We hope that the proposed OPM will facilitate the integration of a greater number of highly sensitive sensors into the MEG system, thereby enabling more accurate and precise measurements of biomagnetic fields with higher resolution.
Funding
National Natural Science Foundation of China (51925501).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. K. Wei, W. Ji, C. Fu, A. Wickenbrock, V. V. Flambaum, J. Fang, and D. Budker, “Constraints on exotic spin-velocity-dependent interactions,” Nat. Commun. 13(1), 7387 (2022). [CrossRef]
2. M. Smiciklas, J. M. Brown, L. W. Cheuk, S. J. Smullin, and M. V. Romalis, “New test of local Lorentz invariance using a 21Ne - Rb - K comagnetometer,” Phys. Rev. Lett. 107(17), 171604 (2011). [CrossRef]
3. W. Terrano and M. Romalis, “Comagnetometer probes of dark matter and new physics,” Quantum Sci. Technol. 7(1), 014001 (2022). [CrossRef]
4. M. Rosner, D. Beck, P. Fierlinger, H. Filter, C. Klau, F. Kuchler, P. Rößner, M. Sturm, D. Wurm, and Z. Sun, “A highly drift-stable atomic magnetometer for fundamental physics experiments,” Appl. Phys. Lett. 120(16), 161102 (2022). [CrossRef]
5. N. V. Nardelli, S. P. Krzyzewski, and S. A. Knappe, “Reducing crosstalk in optically-pumped magnetometer arrays,” Phys. Med. Biol. 64(21), 21NT03 (2019). [CrossRef]
6. W. Zheng, S. Su, G. Zhang, X. Bi, and Q. Lin, “Vector magnetocardiography measurement with a compact elliptically polarized laser-pumped magnetometer,” Biomed. Opt. Express 11(2), 649 (2020). [CrossRef]
7. R. A. Seymour, N. Alexander, S. Mellor, G. C. O’Neill, T. M. Tierney, G. R. Barnes, and E. A. Maguire, “Using opms to measure neural activity in standing, mobile participants,” NeuroImage 244, 118604 (2021). [CrossRef]
8. M. Pedersen, D. F. Abbott, and G. D. Jackson, “Wearable opm-meg: A changing landscape for epilepsy,” Epilepsia 63(11), 2745–2753 (2022). [CrossRef]
9. J. Gross, S. Baillet, G. R. Barnes, R. N. Henson, A. Hillebrand, O. Jensen, K. Jerbi, V. Litvak, B. Maess, R. Oostenveld, L. Parkkonen, J. R. Taylor, V. van Wassenhove, M. Wibral, and J.-M. Schoffelen, “Good practice for conducting and reporting meg research,” NeuroImage 65, 349–363 (2013). [CrossRef]
10. J.-H. Storm, P. Hömmen, D. Drung, and R. Körber, “An ultra-sensitive and wideband magnetometer based on a superconducting quantum interference device,” Appl. Phys. Lett. 110(7), 072603 (2017). [CrossRef]
11. E. Boto, N. Holmes, J. Leggett, et al., “Moving magnetoencephalography towards real-world applications with a wearable system,” Nature 555(7698), 657–661 (2018). [CrossRef]
12. E. A. Maguire, “Eleanor a. maguire,” Curr. Biol. 22(24), R1025–R1027 (2012). [CrossRef]
13. R. A. Seymour, N. Alexander, S. Mellor, G. C. O’Neill, T. M. Tierney, G. R. Barnes, and E. A. Maguire, “Interference suppression techniques for opm-based meg: Opportunities and challenges,” NeuroImage 247, 118834 (2022). [CrossRef]
14. J. C. Allred, R. N. Lyman, T. W. Kornack, and M. V. Romalis, “High-sensitivity atomic magnetometer unaffected by spin-exchange relaxation,” Phys. Rev. Lett. 89(13), 130801 (2002). [CrossRef]
15. H. B. Dang, A. C. Maloof, and M. V. Romalis, “Ultrahigh sensitivity magnetic field and magnetization measurements with an atomic magnetometer,” Appl. Phys. Lett. 97(15), 151110 (2010). [CrossRef]
16. I. K. Kominis, T. W. Kornack, J. C. Allred, and M. V. Romalis, “A subfemtotesla multichannel atomic magnetometer,” Nature 422(6932), 596–599 (2003). [CrossRef]
17. Y. Guo, S. Wan, X. Sun, and J. Qin, “Compact, high-sensitivity atomic magnetometer utilizing the light-narrowing effect and in-phase excitation,” Appl. Opt. 58(4), 734–738 (2019). [CrossRef]
18. S. Ichihara, N. Mizutani, Y. Ito, and T. Kobayashi, “Differential measurement with the balanced response of optically pumped atomic magnetometers,” IEEE Trans. Magn. 52(8), 1–9 (2016). [CrossRef]
19. V. Shah, S. Knappe, P. D. D. Schwindt, and J. Kitching, “Subpicotesla atomic magnetometry with a microfabricated vapour cell,” Nat. Photonics 1(11), 649–652 (2007). [CrossRef]
20. J. Wang, W. Fan, K. Yin, Y. Yan, B. Zhou, and X. Song, “Combined effect of pump-light intensity and modulation field on the performance of optically pumped magnetometers under zero-field parametric modulation,” Phys. Rev. A 101(5), 053427 (2020). [CrossRef]
21. K. Kamada, Y. Ito, S. Ichihara, N. Mizutani, and T. Kobayashi, “Noise reduction and signal-to-noise ratio improvement of atomic magnetometers with optical gradiometer configurations,” Opt. Express 23(5), 6976–6987 (2015). [CrossRef]
22. D. Sheng, A. R. Perry, S. P. Krzyzewski, S. Geller, J. Kitching, and S. Knappe, “A microfabricated optically-pumped magnetic gradiometer,” Appl. Phys. Lett. 110(3), 031106 (2017). [CrossRef]
23. Y. Li, Y. Ren, H. Zhai, S. Ai, X. Liu, and S. Zhuang, “Single-beam highly sensitive magnetic field gradiometer based on the atomic spin-exchange relaxation-free effect,” Appl. Opt. 61(1), 149–156 (2022). [CrossRef]
24. I. A. Sulai, Z. J. DeLand, M. D. Bulatowicz, C. P. Wahl, R. T. Wakai, and T. G. Walker, “Characterizing atomic magnetic gradiometers for fetal magnetocardiography,” Rev. Sci. Instrum. 90(8), 085003 (2019). [CrossRef]
25. J. Osborne, J. Orton, O. Alem, and V. Shah, “Fully integrated standalone zero field optically pumped magnetometer for biomagnetism,” Proc. SPIE 10548, 105481G (2018). [CrossRef]
26. S. P. Krzyzewski, A. R. Perry, V. Gerginov, and S. Knappe, “Characterization of noise sources in a microfabricated single-beam zero-field optically-pumped magnetometer,” J. Appl. Phys. 126(4), 044504 (2019). [CrossRef]
27. Y. Chen, L. Zhao, N. Zhang, M. Yu, Y. Ma, X. Han, M. Zhao, Q. Lin, P. Yang, and Z. Jiang, “Single beam cs-ne serf atomic magnetometer with the laser power differential method,” Opt. Express 30(10), 16541 (2022). [CrossRef]
28. Y. Suo, X. Song, L. Jia, T. Long, M. Ye, and B. Zhou, “Analysis and optimization of signal detection noise of single-beam modulated atomic magnetometer array,” IEEE Sens. J. 22(19), 18600–18609 (2022). [CrossRef]
29. K. Yin, B. Zhou, J. Lu, F. Lu, S. Zhang, Y. Yan, and M. Ye, “In-situ relaxation rate measurement in magnetic modulated atomic magnetometers,” IEEE Sens. J. 22(1), 248–255 (2022). [CrossRef]
30. S. Zhang, J. Lu, Y. Zhou, F. Lu, K. Yin, D. Zhan, Y. Zhai, and M. Ye, “Zero field optically pumped magnetometer with independent dual-mode operation,” Chin. Opt. Lett. 20(8), 081202 (2022). [CrossRef]
31. J. Iivanainen, M. Stenroos, and L. Parkkonen, “Measuring meg closer to the brain: Performance of on-scalp sensor arrays,” NeuroImage 147, 542–553 (2017). [CrossRef]
