High spatial resolution multi-channel optically pumped atomic magnetometer based on a spatial light modulator

Xiujie Fang; Kai Wei; Tian Zhao; Yueyang Zhai; Yueyang Zhai; Danyue Ma; Bozheng Xing; Ying Liu; Zhisong Xiao; Zhisong Xiao

doi:10.1364/OE.398540

1. Introduction

Precise multi-channel magnetic detection methods can be used in many different spatial scales. On a large spatial scale, these detection methods can be used for applications such as archaeological and geological explorations [1] and nondestructive testing (NDT) of components. They are important for electric dipole moment (EDM) measurements [2], magnetic resonance imaging (MRI) [3], and magnetoencephalography (MEG) and magnetocardiography (MCG) measurements on a small spatial scale. Furthermore, on an even smaller spatial scale, these detection methods find use in magnetic microscopy applications, such as bacterial magnetic image generation [4] and cell protein analysis [5], wherein the magnetic sensor can be considerably close to the magnetic source. Nitrogen-Vacancy Diamond technology can measure the magnetic field distribution on the micro scale. In 2013, Harvard University successfully applied Nitrogen-Vacancy Diamond technology to the measurement of cell biological magnetic field and achieved a spatial resolution of 400 nm and a magnetic field sensitivity of 1µT/Hz^1/2 [4]. However, the theoretical limit sensitivity of the NV-diamond magnetometers is pT/Hz^1/2, which precludes many envisioned applications [6]. To realize higher sensitivity magnetic field measurement on such a small spatial scale, superconductive quantum interference devices (SQUIDs) are primarily used [7,8]. However, because SQUID magnetometers require cryogenic cooling for operation, their installation and operational costs are extremely high [9]. Recently, optically pumped magnetometers (OPMs) with ultra-high sensitivity have been reported that have the potential to replace currently used SQUID magnetometers [10–12]. These OPMs operate at or above room temperature without the need for liquid helium dewars; furthermore, their compact size enables more flexible positioning of the OPM sensor compared with their SQUID counterparts. Thus, it is expected that miniaturization of OPMs and multi-channel detection using OPMs would also be relatively easy to implement.

With further advances in the fields of medicine, biology, and material sciences, it has become increasingly important to understand the microscopic characteristics of biological structures and materials. This trend has prompted the need for magnetic field detectors with ultra-high sensitivity and spatial resolution. In 2003, the Romalis Group of Princeton University first realized the magnetic field sensitivity of 0.54fT/Hz^1/2 and the spatial resolution of 2 mm based on spin-exchange relaxation-free (SERF) effect [13]. Subsequently they used SERF OPMS to detect MEG signals using a large vapor cell during auditory stimulation [14,15]. Since then, multi-channel SERF magnetometer systems have continued to receive increasing attention from researchers around the world [16–18]. It is beneficial to magnetic imaging and magnetic microscopy to ensure the high sensitivity of multi-channel magnetometer and improve the spatial resolution.

At present, the smallest commercially available OPM detector QUSPIN can operate in a multi-channel configuration by utilizing common elements [19], the dimensions of this detector are 12.4×16.6×24.4mm³. Using multiple SQUID devices will increase costs, such as the 37-channel Siemens Krenikon system [20]. To construct a multi-channel SERF system for magnetic field distribution detection, one method involves arranging together multiple independent detection modules wherein each module contains a vapor cell and lasers [21,22]. However, it is difficult to fabricate vapor cells with identical characteristics and structural differences between vapor cells could affect the uniformity of a sensor. To address this issue and improve measurement consistency of such magnetometers, improvements such as retro-reflected single vapor cell design have been suggested [23,24]. Furthermore, detection methods based on the use of photodiode arrays with large vapor cells and broad beams have also been proposed [25,26]. Another method of detection involves dividing the pump beam in the SERF magnetometer into sections and moving the slit in order to scan a two-dimensional magnetic field distribution [10]. Furthermore, temporal segmentation based on pump-beam modulation or longitudinal parametric modulation can be used to accomplish multi-position measurements in the probe-beam direction [27]. Moreover, by applying a deconvolution or multifactorial algorithm, successive pump layers can be used to enable three-dimensional magnetic field measurements [15]. Nevertheless, using such a multi-channel system not only requires a large number of optical components and amplifiers, but also reduces the flexibility of the system for different applications. In addition, many optical components and amplifiers in such multi-channel systems also increase the electrical noise, system complexity, and inter-channel crosstalk. Most importantly, the spatial resolution of such systems is low because of the limited recognition accuracy of photodiode arrays. While the use of a charge-coupled device (CCD) sensor can increase the resolution of multi-channel magnetic field detection systems, the received intensity from the CCD sensor is still too small for practical applications; moreover, both smear and blooming effects are difficult to eliminate even with the use of the CCD sensor [28].

Accordingly, in this study, to simultaneously obtain ultra-high spatial resolution and ultra-high magnetic field sensitivity from SERF magnetometers, we developed a high-resolution (sub-millimeter) multi-channel SERF atomic magnetometer for two-dimensional magnetic field measurements using a digital micro-mirror device (DMD) as a spatial light modulator. DMDs have previously been used in quantum sensing measurement applications, such as obtaining a spin image smaller than the corresponding diffusion crosstalk free distance [29], capturing AC magnetic field images [30], and measuring the spin spatial frequency response [31]. To simultaneously achieve ultra-high spatial resolution and ultra-high magnetic field sensitivity using our proposed magnetometer, we experimentally determined the appropriate temperature and pump power densities for it. In addition, we evaluated the performance a 25-channel magnetometer designed using our approach by measuring the magnetic field generated by a coil. Our proposed multi-channel magnetometer can also be flexibly altered using grayscale images for channel design, which also ensures strong consistency between the different channels. Furthermore, we demonstrated the use of iterative algorithms for accurate magnetic positioning using measurements made using our proposed magnetometer.

2. Principle

In the SERF regime, a circularly polarized light with a central wavelength at the D1 resonance line of an alkali metal atom is passed through a vapor cell with alkali metal gas. A pump laser field passing through the vapor cell transfers its angular momentum to the alkali atoms in the cell in the form of average spin polarization. The angular momentum can be transferred via the hyperfine interaction between the electron and the nucleus in the atom. In the presence of an external magnetic field, these polarized atoms undergo Larmor precession. The probe light accordingly changes in their polarization axis occur due to the optical rotation. The precession signal of the atomic spin can be detected based on this optical rotation. If the atomic spin exchange rate is significantly higher than its Larmor precession frequency, the spin exchange relaxation effectively vanishes [32]. The density matrix obeys the spin temperature distribution; in particular, the Bloch equation given below can be used to describe the evolution of electron spin polarization [33]:

(1)$$\frac{d}{{dt}}{\boldsymbol P} = \frac{1}{q}[{\boldsymbol {\gamma P} \times {\boldsymbol B} + {R_{\textrm{OP}}}({s\overrightarrow {\textbf{z}} - {\boldsymbol P}} )- {R_{\textrm{rel}}}{\boldsymbol P}} ], $$

where P is the electron spin polarization, q is the nuclear slowing-down factor ranging from 4 to 6 for ⁸⁷Rb with a nuclear spin of 3/2, and B is the perceived external magnetic field. The first term in Eq. (1) represents the Larmor precession, where γ is the electron’s gyromagnetic ratio, while the second term describes the effect of optical pumping. The pumping rate R_OP is the average rate at which an unpolarized atom absorbs a photon from the pump beam, and s$\textrm{ = }$+1 is the average photon spin for ${\sigma ^ + }$ light. Furthermore, the third term describes the depolarization effect of the spin relaxation, while R_rel represents the total spin-relaxation rate. For optical pumping along the z-axis, the probe light direction must be along the x-axis. To describe the frequency response situation, we define the applied magnetic field as B = B₀+B(t), where B₀ is a nanotesla-range static magnetic field and its direction is not completely consistent with the z-axis due to the presence of residual magnetic fields. In the spherical coordinate system, $\theta$ is the polar angle while $\phi$ is the azimuth angle. B(t) represents the time-dependent magnetic field only along y-axis and its Fourier transform is referred to as B(f). Thus, the Bloch equation given by Eq. (1) can now be solved in the frequency domain using the following expression [34]:

(2)$${P^x}(f) ={-} \frac{{\gamma {R_{\textrm{op}}}B(f)}}{{4{\pi ^2}{q^2}\Delta f}}\frac{{\Delta f + if}}{{{f_0}^2 + {{(\Delta f + if)}^2}}}({1 - {f_0}^2\xi {{\sin }^2}\theta } ), $$

where the Larmor frequency ${f_0} = \gamma {B_0}$ and the half width at half maximum (HWHM) Δf=(R_OP+ R_rel)/(2πq) with the modifying factor ξ, which is given by:

(3)$$\xi = \frac{{(2\Delta f + if)[\sin \phi (\Delta f\sin \phi - {f_0}\cos \theta \cos \phi ) + if]}}{{{{(\Delta f + if)}^2}({\Delta {f^2} + {f_0}^2} )}}, $$

Optically pumped atoms exhibit a birefringence effect and thus a nearly resonant light can be used to detect both the atomic spin direction and atomic Larmor precession. After the D2 linearly polarized probe light passes through the polarized atomic cell, the polarization plane rotates by an angle leading to the occurrence of phase retardation [35]. When the hyperfine splitting structure in the ground state is not resolved or when the probe light is considerably detuned compared with the hyperfine splitting in the ground state, the rotation angle θ_pr can be calculated as follows:

(4)$${\theta _{\textrm{pr}}}\textrm{(}f\textrm{) = }\frac{1}{\textrm{2}}l{r_e}cnP_x^{}(f){f_{\textrm{D2}}}\frac{{(v - {v_{\textrm{D2}}})}}{{{{(v - {v_{\textrm{D2}}})}^2} + {{({\Gamma _\textrm{L}}/2)}^2}}}.$$

Where r_e is the classical electron radius; c is the speed of light; f_D2≈0.668 is the oscillator strength, which is the fraction of the total classical integrated cross-section associated with the respective resonance; and Γ_L is the pressure broadening parameter for the D2 resonance line of the alkali metal. According to Eq. (4), the optical rotation angle is proportional to the projection of the electron spin polarization in the direction of the probe light.

For P^x(f) $\; \ll $1, the sensor output voltage V(f) is proportional to θ_pr with the correlation coefficient between them being a. Thus, V(f) can be calculated as follows:

(5)$$V\textrm{(}f\textrm{) = }a{\theta _{\textrm{pr}}} ={-} \frac{{a\gamma {R_{\textrm{op}}}B(f)l{r_e}cn{f_{\textrm{D2}}}}}{{8{\pi ^2}{q^2}\Delta f}}\frac{{\Delta f + if}}{{{f_0}^2 + {{(\Delta f + if)}^2}}}({1 - {f_0}^2\xi {\theta^2}} )\frac{{(v - {v_{\textrm{D2}}})}}{{{{(v - {v_{\textrm{D2}}})}^2} + {{({\Gamma _\textrm{L}}/2)}^2}}}.$$

In our experiment, the rotation angle is detected using the polarization modulation of a photo elastic modulator (PEM) because it has low noise, high modulation purity, and a large reception angle [36]. Because the probe beam is reflected via a micro-mirror, its incident angle slightly changes; therefore, a large range for the reception angle of the PEM is necessary for our experiment. Here, we use the Jones matrix to predict the evolution of the polarized light; the Jones vector of the electric field from the second analyzer can be obtained as follows:

(6)$$\begin{array}{c} E = {\textrm{G}_{\textrm{p2}}} \cdot {\textrm{G}_{\textrm{PEM}}} \cdot {\textrm{G}_{\mathrm{\lambda }\textrm{/4}}} \cdot {\textrm{G}_{\textrm{cell}}} \cdot {\textrm{G}_{\textrm{p1}}}\\ \\ \textrm{ = }\left[ \begin{array}{l} \textrm{0 0}\\ \textrm{0 1} \end{array} \right] \cdot \left[ \begin{array}{l} \cos \frac{{\delta (t)}}{2}\textrm{ }i\sin \frac{{\delta (t)}}{2}\\ i\sin \frac{{\delta (t)}}{2}\textrm{ }\cos \frac{{\delta (t)}}{2} \end{array} \right] \cdot {e^{i\pi /4}}\left[ \begin{array}{l} 1\textrm{ }0\\ 0\textrm{ } - i \end{array} \right] \cdot \left[ \begin{array}{l} \cos {\theta_{pr}}\textrm{ } - \sin {\theta_{pr}}\\ \sin {\theta_{pr}}\textrm{ }\cos {\theta_{pr}} \end{array} \right] \cdot {E_0}\left[ \begin{array}{l} 1\\ 0 \end{array} \right]. \end{array}$$

Where E₀ is the electric-field amplitude of the incident light, and G_p1, G_cell, G_λ/4, G_PEM, and G_p2 are the Jones matrices of the probe laser as it passes through the first polarizer becoming linearly polarized light, then through a sensitive cell with a half or quarter waveplate rotating by an angle θ_pr then a quarter waveplate. The PEM is modeled like a time-dependent quarter waveplate with a time-varying phase retardation δ(t)=δ_msin(w_mt), and finally through the second analyzer with a transmission axis at 90° compared with that of the first polarizer, respectively. Because θ_pr is extremely small and δ_m ${\ll} $1, after applying the Bessel function, the intensity detected by the photodetector changes with the frequency of the detected magnetic field according to the following equation [37]:

(7)$$I = \frac{{{I_0}{\delta _\textrm{m}}^2}}{8} + {I_0}{\theta _{\textrm{pr}}}{\mathrm{\delta }_\textrm{m}}\sin ({w_\textrm{m}}t) - \frac{{{I_0}{\delta _\textrm{m}}^2}}{8}\cos (2{w_\textrm{m}}t).$$

The first harmonic includes the optical rotation angle that can be used to measure the magnetic field. In addition, the light intensity is derived using real-time feedback of the second harmonic. Both these components can be extracted using a lock-in amplifier. Considering the attenuation of the probe light by the cell, G is the conversion coefficient between the input light intensity and the output voltage of the photodetector and η is the attenuation coefficient of the cell for the probe light. The output in the frequency domain can then be determined as follows:

(8)$$V\textrm{(}f\textrm{) = G}\eta {I_0}{\theta _{pr}}{\mathrm{\delta }_\textrm{m}} = K\textrm{(}f\textrm{)}B\textrm{(}f\textrm{)}, $$

here, K(f) is a transfer function, which includes five parameters that are determined by the response for the magnetic fields with different frequencies:

(9)$$\begin{array}{l} K(f;{f_0},\Delta f,\theta ,\phi ,{R_{\textrm{op}}})\\ ={-} G\eta {I_\textrm{0}}{\mathrm{\delta }_m}\frac{{\gamma {R_{\textrm{op}}}l{r_e}cn{f_{\textrm{D2}}}}}{{8{\pi ^2}{q^2}\Delta f}}\frac{{\Delta f + if}}{{{f_0}^2 + {{(\Delta f + if)}^2}}}({1 - {f_0}^2\xi {{\sin }^2}\theta } )\frac{{(v - {v_{\textrm{D2}}})}}{{{{(v - {v_{\textrm{D2}}})}^2} + {{({\Gamma _\textrm{L}}/2)}^2}}}. \end{array}$$

When circularly polarized light propagates through the vapor cell, it can be absorbed by the alkali vapor thereby causing light intensity attenuation and leading to non-uniform polarization within the cell. The optical depth OD describes this attenuation, OD = nσ(v)l, where n is the density of the alkali vapor, σ(v) is the absorption cross-section as a function of the laser frequency, and l is the distance that light propagated in the cell. Assuming that the light pumping rate at point l is R_OP(l), the spin polarization is P(l). According to the Lambert-Beer absorption law, the equation for the pumping rate as a function of distance can be given as follows:

(10)$${R_{\textrm{OP}}}(l) = {R_{\textrm{rel}}}W[\frac{{{R_{\textrm{OP}}}(0)}}{{{R_{\textrm{rel}}}}}exp\left( { - OD\textrm{ + }\frac{{{R_{\textrm{OP}}}(0)}}{{{R_{\textrm{rel}}}}}} \right)].$$

Assuming sufficient collisional mixing in the SERF state, the electron spin polarization P(l) can be written as follows:

(11)$$P(l) = \frac{{{R_{\textrm{OP}}}(l)}}{{{R_{\textrm{OP}}}(l) + {R_{\textrm{rel}}}}}.$$

For magnetic field measurements, inhomogeneity of the spin polarization caused by the attenuation of the pump beam [33] could pose a problem. Using Eqs. (10) and (11), the distribution of polarization is calculated within an optically thick cell where OD=1.16 and the cross-section σ(v) =2.67×10⁻¹³cm², as shown in Fig. 1(a). Furthermore, the polarization uniformity at low pump rates is significantly worse than that at high pump rates. However, although there is a smaller polarization gradient at high pump rates, to obtain the strongest output signal, in our experiment, we set R_OP nearly equal to R_rel. Under this condition, the non-uniformity of the polarization can be as high as 98% when the probe light covers the entire cell. The nonuniformity of polarization destroys the consistency of multi-channel. The consistency between channels is very important for multi-channel measurement. Using our high-spatial-resolution 25-channel sensor, the center of the cell is detected to within 1 mm with the non-uniformity of the polarization being 21% (see Fig. 1(b)). Within this range, the error caused by the non-uniformity of the polarization in the gradient magnetic field measurement can be ignored.

Fig. 1. Distribution of spin polarization as a function of the distance traversed by an incident pump light within an optically thick cell. (a) Distribution at different pump rates. The change in the polarization throughout the cell increases with increasing pumping rate. (b) Polarization distribution at the center of the cell (experimental measurement range) for R_OP=R_rel.

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The internal pressure of the vapor cell is 2.7atm when the atomic vapor cell is at the experimental temperature. At this high pressure, alkali atoms diffuse slowly and are confined to small regions in the cell during a single coherence lifetime. Thus, the magnetic field gradients cause atoms in the different regions to process at different frequencies thereby enabling the use of these different volumes of atoms in the vapor cell as independent local magnetic sensors. Thus, detection using different parts of the DMD split probe beam makes it possible to measure the magnetic field distribution.

DMD is an array, which consists of multiple high-speed digital aluminum light reflectors. It is a micro-electromechanical system (MEMS) with an electronic input and optical output. A small reflector corresponding to one pixel is located on the corresponding CMOS storage unit, and the number of lenses used is determined based on the display resolution required for an image. Using the pixel-level controllability of the DMD device and its high-speed flip frequency (in the microsecond range), each image point can or cannot be scanned onto the detector. The DMD controller loads “1” or “0” for each basic storage unit, which produces a mirror reset pulse that, in turn, produces the corresponding micro-mirror orientations as ±12° flips: the +12° state corresponds to an “on” pixel, while the −12° state corresponds to an “off” pixel as shown in Fig. 2). A DMD (Texas Instruments V-9501) with a pixel size of 10.8×10.8µm² was used to modulate the probe light in our experiment. The probe light reflected off the DMD based on the grayscale [38] control image loaded onto it. According to the principle described earlier, a pixel gray value is 0 in grayscale image indicates on-state, while it is 256 when it is in the off-state. The probe light beam is divided into several units by DMD, each of which contains 20 pixels with an area of 216×216µm². The highest switching frequency is 17.9 kHz. 5×5 units can be used to construct a two-dimensional multi-channel magnetometer that can be used for magnetic field distribution detection.

Fig. 2. Propagation of a light beam under different orientations of the DMD micro-mirrors.

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The cross-talk between adjacent channels caused by atomic diffusion must be considered. If rubidium atoms do not diffuse from one channel to another in spin coherence time, the cross-talk between adjacent channels will not occur. The spatial resolution is limited by the diffusion length of atoms. The diffusion distance l_D is given as follows:

(12)$${l_D} = \sqrt {\frac{{D_{}^0{{\left( {\frac{T}{{273K}}} \right)}^{3/2}}\frac{{1atm}}{p}}}{\Gamma }} , $$

where Γ is the total transverse spin relaxation rate, p is the gas pressure, and D⁰ is the diffusion coefficient under standard condition [39]. In our experiment, there are ⁴He and N₂ in the cell. The diffusion distance is 103µm calculated by Eq. (12). The diffusion distance is smaller than the spacing between the adjacent channels. The diffusion phenomenon can be further reduced by increasing the gas pressure.

3. Experimental setup

The experimental setup used in our study is shown in Fig. 3. The sensor head of our proposed multi-channel SERF atomic magnetometer was a 20×20×20mm³ cubic cell made of GE180 aluminosilicate glass. In the liquid nitrogen environment, the cubic vapor cell was filled with Rb atoms, 10Torr of N₂ as a quenching gas, and 513Torr of ⁴He as a buffer gas. Pressure spread of alkali metals was measured as 42.37 GHz by Raoul's law using alkali metal absorption spectroscopy. The cubic cell was placed in a boron nitride ceramic oven, which, in turn, was placed in a nonmagnetic poly-ether-ether-ketone vacuum chamber because the vacuum conditions reduce thermal diffusion and improve thermal stability. Twisted-pair wires with AC currents of 300kHz were used to heat the cubic cell. The vacuum chamber was further enclosed by four cylindrical high-permeability µ-metal magnetic shields with a shielding factor of 10⁵ and saddle-compensating magnetic coils. The magnetic shields were used to create a low magnetic field environment below 2nT to ensure that the alkali atoms remain in the SERF region.

Fig. 3. Experimental setup of the proposed high-resolution multi-channel SERF atomic magnetometer. A cubic cell with Rb was placed inside four layers of magnetic shields. The magnetic field distribution was measured along the y-axis. The inset image depicts the single-channel beam quality measured using a beam quality analyzer (Thorlabs Beam 7.0).

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The Rb atoms were polarized using a distributed Bragg reflector (DBR) diode laser along the z-axis and centered on the Rb D1 resonance line. The pump light was circularly polarized by passing it through a polarizer and a quarter waveplate. This circularly polarized pump light was then expanded to a width of 20 mm using a set of beam expanders in order to cover the entire cell.

In contrast, the probe light was produced using a DBR diode laser with a tapered laser amplifier; the maximum light intensity of this probe light was up to 2W and it was detuned by 1.08 nm from the Rb D2 resonance line. Subsequently, this probe light was linearly polarized by passing it through a polarizer in the horizontal direction along the x-axis. The linearly polarized probe light was then expanded to a 3×3mm² square by the beam expander and rectangular aperture into the DMD. To ensure appropriate orientation of the DMD micro-mirror, the positions of both the DMD and the cubic cell had to be well-defined. First, we aligned the center of the DMD with the center of the vapor cell. We generated a grayscale image of the same size as the probe light beam with a gray level of 0 at the center of the DMD. Then, the light intensity reflected towards the cell by the DMD was detected by a photodetector. If the reflected light intensity of the generated grayscale image was different from that of the probe light incident on the DMD, a left or right ordered binary search was performed to detect the center of the cell. Based on the difference in the reflected beam intensity compared with the incident beam intensity, it was determined whether to continue searching in the left half or right half of the image. Based on this determination, the iterative binary search was continued in a similar manner until the intensities of the incident and reflected light beams were the same. The resulting DMD beam of the generated grayscale image corresponds to the incident light beam, which is intended for a specific position of the gas cell. After finding the range, small-scale multi-channel gray-scale image design is carried out in this large range. Based on this iterative algorithm, every image generates one probe channel; therefore, to generate a scanning light field of 25 channels, 25 such grayscale images are required. Each of these channels consist of 20 pixels (216µm) with no interval between two adjacent channels; thus, the total size of all 25 channels was 1080×1080µm². We used a beam quality analyzer (Thorlabs Beam 7.0) to measure the light width when the light entered the vapor cell. The width of each channel in the transverse direction was 225 ± 5µm, while the width in the longitudinal direction was 207 ± 5µm. Thus, the size of probe light beam met requirements. The light power of each channel was uniform (2.3 mW). After DMD loading an image, the probe light passed through the cell and its polarization was detected using the PEM (Hinds Instruments).

Polarization is an important characteristic in an atomic magnetometer. Under certain conditions, the higher the polarization is, the higher the signal-to-noise ratio of the magnetometer is, the better its performance is [32]. According to Eq. (7), polarization in an atomic magnetometer is determined by its pumping rate and the longitudinal relaxation time of the atoms used in the magnetometer. Furthermore, increasing the pump light intensity can increase the polarization; however, this would also lead to a decrease in the transverse relaxation time. Because the signal-to-noise ratio of the magnetometer is proportional to the product of the total transverse relaxation time and polarization for a given noise, the larger the signal-to-noise ratio is, the higher the sensitivity of the magnetometer will be; therefore, the sensitivity of the magnetometer can be improved by increasing the pump light intensity and there is an optimal pump light intensity. To obtain the optimal operating conditions for our proposed 25-channel magnetometer, first, we optimized the ambient temperature. As shown in Fig. 4(a), we used channel Ch1 to find the pump light intensity with the highest signal response at different temperatures. Then, we fixed the pump light intensity to the obtained value corresponding to the maximum signal response for different temperatures and compared the magnetic field responses obtained by applying a magnetic field along the y-axis using the magnetic coils. As shown in Fig. 4(b), the slope of the magnetic field response increased with increasing temperature. Moreover, owing to the SERF effect, the relaxation rate decreases with increasing temperature. Based on these observations, the operating temperature and pump light intensity were set at 160°C and 21.1 mW, respectively, to optimize the performance of the magnetometer for 25-channel high-spatial-resolution magnetic field measurements.

Fig. 4. (a) Signal response of channel Ch1 at different temperatures and pump light intensities. The pump light intensity was calibrated to obtain the highest signal response. (b) Based on the signal response (shown in (a)), the pump light intensity was fixed to the value associated with the highest signal response at different temperature conditions. We obtained the magnetic field response by applying a magnetic field along the sensitive y-axis using the reference coil; the slope of the magnetic field response increased with increasing temperature. The shadow error bars represent the maximum and minimum values in the repeated experiments.

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4. Results and discussion

Multi-channel frequency responses of the magnetometer for the five channels in the first row are shown in Fig. 5. Before performing the frequency response test, a DC field was used for magnetic compensation in the shielding barrel. For the frequency response test, this compensating DC field was maintained and AC magnetic fields of known amplitude but different frequencies (below 100 Hz) were applied in the direction of the sensitive axis. The bandwidth of frequency response increased with increasing pump light intensity and decreasing temperature. Figure 6 shows the magnetic field sensitivities of five channels (Ch1–Ch5). The absolute field sensitivity of the magnetometer was acquired by applying a small sinewave calibrating magnetic field of 30 Hz with an amplitude of 100pT, processed it using the fast Fourier transform (FFT), and then fit the processed response into a normalized frequency-response function as in Eq. (8). The red dotted line is the probe noise. The peak of probe noise is caused by DMD vibration.

Fig. 5. Multi-channel frequency response of the magnetometer for the five channels in the first row. The frequency responses for channels Ch1–Ch5 are considerably similar, i.e., they are highly consistent with respect to the response per channel.

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Fig. 6. Magnetic field sensitivities for the five channels were 22.5, 20.1, 20.8, 23.5, and 24.7fT/Hz^1/2, respectively, for the frequency range of 30–40 Hz. The sensitivities of the five channels were almost identical. The red dotted line is the probe noise.

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The average sensitivity of the proposed multi-channel magnetometer was found to be 22.3fT/Hz^1/2 at 30 Hz for the five channels of the first line. Furthermore, its spatial resolution was 216µm, which, to the best of our knowledge, is higher than the highest spatial resolution for SERF multi-channel magnetometers thus far. The differences in the sensitivities between the channels are attributed to the uneven distribution of the probe light (as indicated by Eqs. (8) and (9)) and manufacturing defects in the glass cell. The noise in a single channel was dominated by the magnetic noise from the shield, the detection noise which including the vibration noise of DMD, electronic 1/f noise at low frequency, and laser disturbance noise. The magnetic noise attributed to Johnson noise due to the magnetic shielding material used in our system was about 10fT/Hz^1/2. Furthermore, noise below 10 Hz was caused by changes in temperature and laser frequency power drifts. It should be noted that the atom shot noise represents the fundamental limit for the sensitivity of a magnetometer [32]. Nevertheless, the sensitivity of a magnetometer can be improved further by using a differential detection scheme between two channels.

To verify the feasibility of the proposed multi-channel magnetic field distribution measurement method under optimal conditions, we measured the two-dimensional magnetic field distribution of a saddle gradient coil. The gradient coil was placed on a vacuum skeleton using two flexible coils. The diameter of the skeleton was 96 mm and the distance between the two coils was 66.5 mm. Currents in opposite directions were passed through the two coils to form a saddle gradient magnetic field. The magnetic field generated from the coil can be calculated using the Biot–Savart law:

(13)$$\delta {\boldsymbol B} = \frac{{{\mu _0}}}{{4\pi }}\frac{{I\mathrm{\delta }s \times {\boldsymbol r}}}{{{{|{\boldsymbol r} |}^3}}}$$

where µ₀ is the permeability of the vacuum, Iδs is the current element in the gradient coil, and r is the position vector.

The experimental principle for our two-dimensional magnetic field distribution measurement is illustrated in Fig. 7. After the first measurement was completed, the lock-in amplifier sent a TTL signal to the cascade synch port of the DMD using a multi-purpose I/O connector to replace the current grayscale image with the next one for magnetic field detection using the next channel. The signals were recorded using the LabVIEW data acquisition program and the magnetic field distributions were obtained in the z-direction between each row and in the y-direction between each column. We used the g value to assess the accuracy of our measurements [16,27], which can be described as follows:

(14)$$g = \left( {1 - \frac{{B_e^2}}{{\sum\limits_i {B_i^{^{\prime}2}} }}} \right) \times 100\%$$

(15)$$B_e^2 = \sum\limits_i {{{({B_i^{\prime} - {B_i}} )}^2}}$$

where B_i^’ is the experimentally measured value of the gradient magnetic field, while B_i is the theoretical value obtained via finite element simulation. Figures 8(a) and 8(b) show the simulated and experimental values for the magnetic field distributions, respectively. The distortion in the color map showing the experimentally measured magnetic field values can be attributed to manufacturing errors in the production of the flexible coils and the non-orthogonality during the installation of the coils. The calculated g value was 99.2%, which confirms that the magnetic field distribution measured using our proposed multi-channel high-spatial-resolution magnetometer was accurate.

Fig. 7. Schematic depiction of the measurement principle used to detect the magnetic field distribution using a single Rb vapor cell filled with buffer gas. The broad probe beam is incident on the DMD and the vapor cell is continuously scanned by the reflection in the micro-mirror.

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Fig. 8. Magnetic field distribution of a saddle gradient coil within the experimental measurement range. The resolution of each channel was 216µm. (a) Theoretically calculated results. (b) Experimentally measured results. The solid black points indicate the measurement positions in our experiment.

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5. Conclusion

In this study, we proposed and evaluated a new type of high-resolution 25-channel magnetometer based on a DMD; to the best of our knowledge, the spatial resolution of our proposed magnetometer was higher than that of the state-of-the-art SERF magnetometer attaining a resolution on the sub-millimeter scale. At an operating temperature of 160°C and with a pump light intensity of 21.09 mW, the average sensitivity of our proposed magnetometer reached approximately 25fT/Hz^1/2 at 30 Hz and was primarily limited by magnetic noise and mechanical vibration. The proposed multi-channel magnetometer included a large cubic cell, which ensured consistency among the channels used for magnetic field measurements. The 25-channel magnetometer also reduced device costs and eliminated any crosstalk between the different channels. Furthermore, we used iterative algorithms in combination with a DMD to improve the positioning accuracy. As the channels were controlled using computer-generated grayscale images, the number and shapes of these channels can be changed as per experimental needs; thus, our proposed magnetometer is practically flexible. It is noteworthy, however, that if the number of measurement channels are increased, the pressure inside the vapor cell would have to be changed accordingly. The g value for two-dimensional magnetic field measurements performed using our magnetometer was 99.2%, which confirms the excellent measurement performance of our proposed SERF magnetometer. The sensitivity of our proposed magnetometer could perhaps be further improved by further suppression of the magnetic noise, stabilization of the laser, and use of differential detection methods. A sufficiently high spatial resolution can potentially open avenues for use of SERF magnetometers in magnetic microscopy techniques and for observing micro-characteristics of materials.

Funding

Major Scientific Research Project of Zhejiang Lab (2019MB0AE03); National Key Research and Development Program of China (2016YFB0501600, 2017YFB0503100); National Natural Science Foundation of China (61703025, 61975005); Foundation from Beijing Academy of Quantum Information Sciences (Y18G28).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

References

1. C. Zimmer, K. K. Khurana, and M. G. Kivelson, “Subsurface Oceans on Europa and Callisto: Constraints from Galileo Magnetometer Observations,” Icarus 147(2), 329–347 (2000). [CrossRef]

2. 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]

3. I. M. Savukov, V. S. Zotev, P. L. Volegov, M. A. Matlashov, A. N. Gomez, and R. H. Kraus, “MRI with an atomic magnetometer suitable for practical imaging applications,” J. Magn. Reson. 199(2), 188–191 (2009). [CrossRef]

4. D. L. Sage, K. Arai, D. R. Glenn, S. J. DeVience, L. M. Pham, L. Rahn-Lee, M. D. Lukin, A. Yacoby, A. Komeili, and R. L. Walsworth, “Optical magnetic imaging of living cells,” Nature 496(7446), 486–489 (2013). [CrossRef]

5. S. Qin, H. Yin, C. Yang, Y. Dou, Z. Liu, P. Zhang, H. Yu, Y. Huang, J. Feng, J. Hao, J. Hao, L. Deng, X. Yan, X. Dong, Z. Zhao, T. Jiang, H. Wang, S. Luo, and C. Xie, “A magnetic protein biocompass,” Nat. Mater. 15(2), 217–226 (2016). [CrossRef]

6. E. V. Levine, M. J. Turner, P. Kehayias, C. A. Hart, N. Langellier, R. Trubko, D. R. Glenn, R. R. Fu, and R. L. Walsworth, “Principles and techniques of the quantum diamond microscope,” Nanophotonics 8(11), 1945–1973 (2019). [CrossRef]

7. C. Denis, “Magnetoencephalography: Detection of the Brain’s Electrical Activity with a Superconducting Magnetometer,” Science 175(4022), 664–666 (1972). [CrossRef]

8. S. Chatraphorn, E. F. Fleet, and F. C. Wellstood, “Scanning SQUID microscopy of integrated circuits,” Appl. phys. lett. 76(16), 2304–2306 (2000). [CrossRef]

9. M. Hämäläinen, R. Hari, R. J. Ilmoniemi, J. Knuutila, and O. V. Lounasmaa, “Magnetoencephalography theory, instrumentation, and applications to noninvasive studies of the working human brain,” Rev. Mod. Phys. 65(2), 413–497 (1993). [CrossRef]

10. A. P. Colombo, T. R. Carter, A. Borna, Y. Y. Jau, C. N. Johnson, and A. L. Dagel, “Four-channel optically pumped atomic magnetometer for magnetoencephalography,” Opt. Express 24(14), 15403 (2016). [CrossRef]

11. V. Venkatraman, S. Kang, C. Affolderbach, H. Shea, and G. Mileti, “Optical pumping in a microfabricated Rb vapor cell using a microfabricated Rb discharge light source,” Appl. Phys. Lett. 104(5), 054104 (2014). [CrossRef]

12. E. Boto, S. S. Meyer, V. Shah, O. Alem, S. Knappe, P. Kruger, T. M. Fromhold, P. Glover, P. G. Morris, R. Barnes, and M. J. Brookes, “A new generation of magnetoencephalography: Room temperature measurements using optically-pumped magnetometers,” Neuroimage 149, 404–414 (2017). [CrossRef]

13. I. K. Kominis, T. W. Kornack, and J. C. Allred, “A subfemtotesla multichannel atomic magnetometer,” Nature 422(6932), 596 (2003). [CrossRef]

14. H. Xia, A. Baranga, D. Hoffman, and M. V. Romalis, “Magnetoencephalography with an atomic magnetometer,” Appl. Phys. Lett. 89(21), 211104 (2006). [CrossRef]

15. K. Kim, S. Beguš, H. Xia, S. Lee, V. Jazbinsek, Z. Trontelj, and M. V. Romalis, “Multi-channel atomic magnetometer for magnetoencephalography: A configuration study,” Neuroimage 89, 143–151 (2014). [CrossRef]

16. K. Nishi, Y. Ito, and T. Kobayashi, “High-sensitivity multi-channel probe beam detector towards MEG measurements of small animals with an optically pumped K-Rb hybrid magnetometer,” Opt. Express 26(2), 1988–1996 (2018). [CrossRef]

17. G. Zhang, S. Huang, F. Xu, Z. Hu, and Q. Lin, “Multi-channel spin exchange relaxation free magnetometer towards two-dimensional vector magnetoencephalography,” Opt. Express 27(2), 597–607 (2019). [CrossRef]

18. 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 (2015). [CrossRef]

19. http://www.quspin.com for detailed information of a commercial QuSpin single-channel OPM

20. S. Schneider, E. M. Hoenig, H. Reichenberger, K. Fuchs, W. E. Moshage, A. Oppelt, H. Stefan, and A. Weikl, “Multichannel biomagnetic system for study of electrical activity in the brain and heart,” Radiology 176(3), 825–830 (1990). [CrossRef]

21. W. R. Wyllie, M. Kauer, R. T. Wakai, and T. G. Walker, “Optical magnetometer array for fetal magnetocardiography,” Opt. Lett. 37(12), 2247 (2012). [CrossRef]

22. G. Bison, N. Castagna, A. P. Hofer, P. E. Knowles, J. Schenker, M. Kasprzak, H. Saudan, and A. Weis, “A room temperature 19-channel magnetic field mapping device for cardiac signals,” Appl. Phys. Lett. 95(17), 173701 (2009). [CrossRef]

23. Y. J. Kim and I. Savukov, “Highly sensitive multi-channel atomic magnetometer,” IEEE Sensors Applications Symposium (SAS), 1–4 (2018).

24. Y. J. Kim, I. Savukov, and S. Newman, “Magnetocardiography with a 16-channel fiber-coupled single-cell Rb optically pumped magnetometer,” Appl. Phys. Lett. 114(14), 143702 (2019). [CrossRef]

25. 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]

26. A. V. Gusarov, D. Levron, E. Paperno, R. Shuker, and A. Baranga, “Three-Dimensional Magnetic Field Measurements in a Single SERF Atomic-Magnetometer Cell,” IEEE Trans. Magn. 45(10), 4478–4481 (2009). [CrossRef]

27. Y. Mamishin, Y. Ito, and T. Kobayashi, “A novel method to accomplish simultaneous multilocation magnetic field measurements based on pump-beam modulation of an atomic magnetometer,” IEEE Trans. Magn. 53(5), 1–6 (2017). [CrossRef]

28. Y. Ito, D. Sato, K. Kamada, and T. Kobayashi, “Measurements of Magnetic Field Distributions With an Optically Pumped K-Rb Hybrid Atomic Magnetometer,” IEEE Trans. Magn. 50(11), 1–3 (2014). [CrossRef]

29. H. Dong, J. Chen, J. Li, C. Liu, A. Li, N. Zhao, and F. Guo, “Spin image of an atomic vapor cell with a resolution smaller than the diffusion crosstalk free distance,” J. Appl. Phys. 125(24), 243904 (2019). [CrossRef]

30. S. Taue, Y. Toyota, K. Fujimori, and H. Fukano, “AC magnetic field imaging by using digital micro-mirror device,” Microoptics Conference (MOC), 212–213(2017).

31. L. X. Yin and J. Chen, “Spin Spatial Frequency Response of Atomic Magnetometer,” Key Eng. Mater. 787, 81–86 (2018). [CrossRef]

32. J. C. Allred, R. N. Lyman, T. W. Kornak, and M. V. Romalis, “High sensitivity atomic magnetometer unaffected by spin-exchange relaxation,” Phys. Rev. Lett. 89(13), 130801 (2002). [CrossRef]

33. M. P. Micah, I. M. Savukov, V. M. Acosta, D. Budker, and M. V. Romalis, “Spin-exchange-relaxation-free magnetometry with Cs vapor,” Phys. Rev. A 77(3), 033408 (2008). [CrossRef]

34. 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]

35. S. J. Seltzer and M. V. Romalis, “High-temperature alkali vapor cells with antirelaxation surface coatings,” J. Appl. Phys. 106(11), 114905 (2009). [CrossRef]

36. A. J. Zeng, F. Y. Li, and L. L. Zhu, “Simultaneous measurement of retardance and fast axis angle of a quarter-wave plate using one photoelastic modulator,” Appl. Opt. 50(22), 4347 (2011). [CrossRef]

37. L. Duan, J. Fang, R. Li, L. Jiang, M. Ding, and W. Wang, “Light intensity stabilization based on the second harmonic of the photoelastic modulator detection in the atomic magnetometer,” Opt. Express 23(25), 32481 (2015). [CrossRef]

38. T. Welsh, M. Ashikhmin, and K. Mueller, “Transferring color to greyscale images,” ACM Trans. Graph. 21(3), 277–280 (2002). [CrossRef]

39. F. A. Franz and C. Volk, “Spin relaxation of rubidium atoms in sudden and quasimolecular collisions with light-noble-gas atoms,” Phys. Rev. A 14(5), 1711–1728 (1976). [CrossRef]

High spatial resolution multi-channel optically pumped atomic magnetometer based on a spatial light modulator

Abstract

1. Introduction

2. Principle

3. Experimental setup

4. Results and discussion

5. Conclusion

Funding

Disclosures

References

Cited By

Figures (8)

Equations (15)

Optics Express