Measurement of Raman beam inclination changes in a cold atom gravimeter based on Raman beam interference

Jingsheng Tan; Bin Wu; Bing Cheng; Peishuang Ding; Kanxing Weng; Dong Zhu; Kainan Wang; Xiaolong Wang; Qiang Lin

doi:10.3788/COL202523.111104

1. Introduction

The cold atom gravimeter, which is a crucial tool for exploring and perceiving the Earth^[1–5], offers high accuracy and a rapid sampling rate for continuous gravity measurements. The cold atom gravimeter can be deployed in various settings, including static environments^[6,7], vehicle-mounted platforms^[8], shipboard installations^[9,10], airborne systems^[11], and microgravity conditions^[12–15]. Additionally, cold atom gravimeters play a significant role in fundamental physics, such as determining the Newtonian gravitational constant^[16] and verifying the weak equivalence principle^[17,18].

The Raman beam sequence splits, reflects, and recombines the atomic wave packet for interferometry^[19], playing a critical role in gravity measurements. The Raman beams should be strictly parallel to the direction of gravity; otherwise, the deviation of the measured gravity is proportional to the square of the inclination deviation. To correct the systematic error caused by the inclination error, scholars have proposed numerous approaches^[7,20–26]. In all cases, tiltmeters are required to monitor inclination change. In general, tiltmeters use MEMS devices or electrolytes to locate the direction of gravity and obtain the inclination variation. These devices are mounted on the frame of the Raman beam correlation optics to continuously monitor inclination change.

However, these conventional tiltmeters have some problems in use, such as the nonlinearity may not be good enough, which can lead to deviations from the measured optimum inclination, the presence of sensitive components within the sensor, stress relief, component aging, charge leakage, and changes in ambient temperature^[27,28], leading to deviations from the compensated gravity value. This affects the precision and accuracy of the gravimeter^[7,26]. For example, for a typical micro electro mechanical system (MEMS) tiltmeter (MT) used for a year of long-term measurements, the deviation may be up to 170 µrad, resulting in a change in the gravity value of more than 58 µGal. Electrolyte-based tiltmeters (ET) with better performance also have uncertainties in extinguishing the drift, and have questionable nonlinearity performance. In addition, the conventional tiltmeter measures the frame rather than the Raman beam. There are numerous angle measurement technologies such as optical, capacitive, Hall effect, inductive, and magneto-resistive technologies; most are used to measure the roll angle rather than the pitch angle and are sensitive to environmental influences^[29,30]. This makes them unsuitable for cold atom gravimeters. A method borrowed from optical gravimetry was used to determine the verticality and measure the inclination change of Raman light using a position-sensing detector (PSD); the vertical calibration deviation of this method is less than 200 µrad, which corresponds to a systematic error of 20 µGal in gravity measurements, and an accuracy of 30 µrad for inclination change measurements^[31]. This may not be sufficient for high-precision gravity measurements. Optical interferometry, which offers resolution and nonlinearity in the nano-radian scale^[32], is one of the most accurate angular measurement methods. In this study, we present a novel Raman beam inclination change measurement method based on Raman beam interference for cold atom gravimeters.

The rest of this paper is organized as follows. In Sec. 2, we discuss how to construct an optical interference for an atom gravimeter without disturbing the gravity measurements and describe the principle of our method. In Sec. 3, we present the experimental procedure and results, including the field, nonlinearity, and drift tests, and the relationship between the gravimeter’s inclination and the measured gravity. Finally, in Sec. 4, we summarize our work.

2. Theoretical Background and the Proposed Method

In the following, we provide a brief review of the gravity measurement bias caused by inclination measurement errors. The Raman beams of a typical cold atom gravimeter, which contain two frequency components ( $k_{1}$ , $k_{2}$ ), are collimated by the collimator, pass through the vacuum chamber and the quarter-wave plate in turn, and are then reflected by a retro-reflection mirror to form a wave vector in the opposite direction ( $- k_{1}$ , $- k_{2}$ ). The counter-propagating beams act on the atoms in the vacuum chamber to realize the interference of the atom wave packet. Together, $k_{1}$ and $k_{2}$ construct the effective wave vector of the Raman beam, denoted as $k_{eff}$ . The relation between gravity and the Raman beam is given as $g = Δ Φ / k_{eff} T^{2}$ , where $Δ Φ$ is the phase shift of the interferometer and $T$ is the interrogation time between the Raman pulses.

If the two counter-propagating Raman beams always remain strictly overlapping, considering two Raman beams as a single unit, the measured gravity is a quadratic function of the inclination deviation of the gravimeter in an arbitrary one-direction space^[25,26]: $g_{θ} = g_{0} - A {(θ_{0} - θ_{C})}^{2},$ (1)where $g_{θ}$ is the actual measured gravity, $g_{0}$ is the measured gravity without a tilt effect, i.e., measured gravity at optimum inclination, $θ_{0}$ is the optimum inclination, $A$ is a constant factor, and $θ_{C}$ is the actual inclination. According to Eq. (1), we can measure $g_{θ}$ for different $θ_{C}$ to determine $θ_{0}$ and $A$ , and ensure that the Raman beam is strictly parallel to the direction of gravity. After setting the inclination to $θ_{0}$ , the inclination of the Raman beams may drift due to the deformation, and thus, we need to compensate for the bias caused by the drift. Inclination measurement errors can lead to incorrect compensation. According to Eq. (1), if there is a measurement error $θ_{error}$ in the measured value, i.e., the measured value is $θ_{C} + θ_{error}$ , the gravity compensation error ( $g_{error}$ ) caused by the inclination error ( $θ_{error}$ ) can be expressed as $g_{error} = A [2 (θ_{0} - θ_{C}) θ_{error} + θ_{error}^{2}] .$ (2)

In the case where the two Raman beams do not overlap, the gravity compensation error ( $g_{error}$ ) caused by the inclination error of the retro-reflection mirror ( $θ_{error}$ ) can be expressed as $g_{error} = 2 A [2 (θ_{0} - θ_{C}) θ_{error} + θ_{error}^{2}] .$ (3)The term $(θ_{0} - θ_{C})$ , which can be regarded as the drift or the inclination deviating from the optimum inclination, is usually in the tens of µrad range. The reason for multiplying by a factor of two is that the change in the angle of the reflected beam is twice the change in the angle of the mirror. The more tilt drift there is, the greater the gravity measurement error caused by the tilt measurement error.

2.1. Optical interference path setup inside an atom gravimeter

Introducing a beam splitter (BS) in the Raman beam path can easily construct an optical coherence system. However, to ensure that the gravity measurement process is not disturbed, careful consideration must be given to the placement of the BS. The addition of a BS alters the wavefront, polarization, and power of the Raman beam, and cold atom interferometers are highly sensitive to these three factors^[33–36]. A polarizing beam splitter (PBS) can provide a polarized beam with sufficient quality. If the PBS is located between the vacuum chamber and the collimator, the wavefront aberrations present in both counter-propagating Raman beams will cancel and only aberrations present in one of the beams contribute to the phase error^[33]. If the counter-propagating Raman beams do not strictly overlap, or the transmission wavefront of the PBS leads to diffusion or convergence, aberration may still exist. Placing a PBS between the vacuum chamber and the collimator appears to be a practical solution to fulfill our purpose and has been successfully applied in previous work^[37]. However, PBS will obstruct the retro beam from entering the collimator since the polarizations of the counter-propagating Raman beams are mutually orthogonal. This prevents us from using the light reflected back into the fiber to optimize the inclination of the retro Raman beam^[22]. Moreover, constructing such an optical interference path in a compact and portable gravimeter, which is already in use, presents significant practical challenges.

The clear aperture of our Raman collimator is 24 mm, and approximately $10^{8}$ atoms are captured; the temperature of the atoms is about 3 µK, and the interrogation time between the Raman pulses is 90 ms in our cold atom gravimeter. The diameter of the atom cloud may expand to about 1.3 cm when the final Raman pulse acts on the atoms. This indicates that only a portion of the Raman beam can interact with the atoms. We designed a hollow beam splitter plate based on this. As shown in Fig. 1, the hollow beam splitter utilizes the margin component of the Raman beam for optical interference and does not influence the middle component, which interacts with the atoms. Theoretically, the hollow BS can be placed anywhere along the Raman beam optical path. We place the BS between the quarter-wave plate and the retro-reflection mirror as it can quickly be disassembled and assembled in our system, and it is easier to match the optical path difference between the two optical interference arms.

Figure 1.Schematic diagram of the optical interference optical path inside the cold atom gravimeter. (a) Overall schematic and the setup for the whole gravimeter inclination measurement. (b) Specific schematic: the setup for retro-reflection Raman beam inclination measurements.

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2.2. Measurement principle

The reference beam $E_{1}$ and the sample beam $E_{2}$ can be expressed as ${\begin{matrix} E_{1} (x, y) = a_{1} e^{j 2 π (f x_{1} \cdot x + f y_{1} \cdot y)} \\ E_{2} (x, y) = a_{2} e^{j 2 π (f x_{2} \cdot x + f y_{2} \cdot y)} \end{matrix},$ (4)and the interference equation can be written as $I (x, y) = | E_{2} + E_{1} |^{2} = {a_{2}^{2} + a_{1}^{2} + a_{2} a_{1} e^{j 2 π [(f x_{2} - f x_{1}) \cdot x + (f y_{2} - f y_{1}) \cdot y]} + a_{2} a_{1} e^{- j 2 π [(f x_{2} - f x_{1}) \cdot x + (f y_{2} - f y_{1}) \cdot y]}} \cdot S (x, y),$ (5)where $a_{1}$ and $a_{2}$ are the amplifications of $E_{1}$ and $E_{2}$ , respectively, and $f x_{1}$ , $f x_{2}$ , $f y_{1}$ , and $f y_{2}$ are the space-frequencies of $E_{1}$ and $E_{2}$ , respectively. As the interference fringes may have an irregular shape, $S (x, y)$ is taken as the function of the interferogram shape, with values of zero or one. If the tilt angle of the sample beam changes, the interference equation can be written as $I^{'} (x, y) = {| E_{2}^{'} + E_{1} |}^{2} = {a_{2}^{2} + a_{1}^{2} + a_{2} a_{1} e^{j 2 π [(f x_{2}^{'} - f x_{1}) \cdot x + (f y_{2}^{'} - f y_{1}) \cdot y]} + a_{2} a_{1} e^{- j 2 π [(f x_{2}^{'} - f x_{1}) \cdot x + (f y_{2}^{'} - f y_{1}) \cdot y]}} \cdot S (x, y) .$ (6)

Taking $I (x, y)$ as an example, as shown in Fig. 2, we now introduce the angle extracting process.

Figure 2.Schematic diagram of the calculation process.

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The pixels in the $i$ row along the $x$ -direction of the interferogram are taken out and subjected to a one-dimensional Fourier transform, and band-pass filtering is performed to get $B (x, y_{i}) = a_{2} a_{1} e^{j 2 π [(f x_{2} - f x_{1}) \cdot x]} \cdot S (x, y_{i}) .$ (7)

We retain the pixels that meet $| B (x, y_{i}) | > Q$ , where $Q$ is the threshold value. This process filters out the domains without interference fringes and extracts $n_{i}$ pixels with interference fringes in row $i$ . The phase angles are then extracted, unwrapping is performed to recover the continuous phase, and the resulting continuous phase is fitted using least-squares fitting to derive the spatial frequency $ν_{i}$ of row $i$ . The total spatial frequency along the $x$ -direction is $f x_{1} + f x_{2} = \sum_{i} ν_{i} n_{i} / \sum_{i} n_{i} = k_{x},$ (8)which can be expressed as $\frac{\cos α_{1}}{λ} + \frac{\cos α_{2}}{λ} = k_{x},$ (9)where $α_{1}$ is the angle between the reference beam and CCD, and $α_{2}$ is the angle between the sample beam and CCD. If the reference beam is perpendicularly incident to the CCD, the measurement angles can be written as $α_{2} = \arccos (k_{x} λ) / 2, β_{2} = \arccos (k_{y} λ) / 2 .$ (10)

Using the same method, we can obtain the angle after changing in the $x$ - and $y$ -directions, denoted as $α_{2}^{'}$ and $β_{2}^{'}$ , respectively. The variation of the inclination is $d α = α_{2} - α_{2}^{'}, d β = β_{2} - β_{2}^{'},$ (11)where $d α$ and $d β$ are the angle variations along the $x$ - and $y$ -directions of the CCD, respectively.

If the reference beam is non-perpendicular to the CCD, the measurement angle in a single direction can be written as $α_{2} = \arccos [k_{x} λ + \cos (α_{1})] / 2$ , and the angle variation between $I (x, y)$ and $I^{'} (x, y)$ is $d α = [\arccos (k_{x} λ + \cos α_{1}) - \arccos (k_{x}^{'} λ + \cos α_{1})] / 2, d β = [\arccos (k_{x} λ + \cos β_{1}) - \arccos (k_{x}^{'} λ + \cos β_{1})] / 2,$ (12)where $k_{x}, k_{y}, k_{x}^{'}$ , and $k_{y}^{'}$ are the measurement space-frequencies of the $x$ - and $y$ -directions of $I (x, y)$ and $I^{'} (x, y)$ .

Although we can obtain the angle variation over Eq. (11), we now discuss the impact of the non-perpendicular situation to make our approach more universal. We simulate the relationship among the measured angle variation, the actual angle variation, and $α_{1}$ based on Eq. (12).

As shown in Fig. 3, the less perpendicular the reference beam is to the CCD, the more the ratio varies with the measurement angle variation. However, the ratio variation is about 0.1% under a measurement range of 8 mrad even if the reference beam has an angular deviation of 0.45 rad. This indicates that the non-perpendicular situation has minimal impact on the cold atom gravimeter measurements. Therefore, the ratio can be treated as a constant and Eq. (12) can be rewritten as $d α = f_{a} \cdot d α_{A}, d β = f_{b} \cdot d β_{A},$ (13)where $d α_{A}$ and $d β_{A}$ are the actual angle variations along the $x$ - and $y$ -directions, respectively, and $f_{a}$ and $f_{b}$ are the corresponding ratios.

Figure 3.Simulation of the relationship among the measured angle variation, the actual angle variation, and α₁. The ratio is the measured angle deviation divided by the true angle variation.

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3. Experiment

3.1. Field angle variation measurements compared with the commercial tiltmeter

We assembled our OT in the field and compared its performance to that of a commercial ET to verify the feasibility of the OT. The setup for this experiment is shown in Fig. 1(b). Specifically, we employed a Schäfter + Kirchhoff 60FC-Q780-4-M100S-37 collimator, a Jing Hang JHUM2000Bs-E CCD, and a Jewell 755 tiltmeter. The reference mirror, BS, and CCD were all fixed with the gravimeter. We adjusted the angle of the retro-reflection beam by adjusting the frame pitch of the Raman mirror. We obtained nine interferograms at different tilt angles and the corresponding outputs from the ET. A fluctuation of a few micro-radians in each direction was observed, which may be attributed to tiny vibrations. We confirmed that the gravity measurement remains unchanged before and after assembling our OT.

To illustrate that interferograms are highly contrasting and the shape of the interferogram is part of a ring that is difficult to process using conventional methods, one of the nine interferograms is depicted in Fig. 4. We process the interferograms using the method described in Sec. 2.2 and recombine all the rows together (bottom in Fig. 4). The fringes are much sharper after being processed by our method and retain the same shape as the raw interferogram. Comparisons between the top and bottom sides of Fig. 4 demonstrate that our method can effectively process the irregularly shaped interferogram.

Figure 4.A raw interferogram versus the image after filtering using our method. Top: original interferogram. Bottom: filtering with our method.

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Calculating the difference between each measured inclinations and the starting inclination gives us nine values for the angle change in each direction. We denote $d α_{O}$ as the angle variation measured by our OT in the $x$ -direction and $d β_{O}$ as the angle variation in the $y$ -direction. Moreover, the angle variation measured by the ET is denoted by $d α_{E}$ and $d β_{E}$ . The total angle variations are given as $d θ_{E} = \sqrt{d α_{E}^{2} + d β_{E}^{2}},$ (14) $d θ_{O} = \sqrt{d α_{O}^{2} + d β_{O}^{2}},$ (15)where $d θ_{E}$ and $d θ_{O}$ are the total inclination variation measured by the ET and OT, respectively. For the non-perpendicular case, based on Eq. (15), we have $d θ_{c} = \sqrt{{(d α_{O} / f_{a})}^{2} + {(d β_{O} / f_{b})}^{2}},$ (16)where $d θ_{c}$ is the corrected angle variation and $f_{a}$ and $f_{b}$ are the ratios described in Sec. 2.2. We assume that the measured inclination by the ET is precise and denote $d θ_{A}$ as the actual angle variation; $d θ_{A}$ , $d θ_{E}$ , and $d θ_{O}$ satisfy the following relationship: $d θ_{A} = d θ_{O} = d θ_{E},$ (17)which can be expressed as $\sqrt{{(d α_{O} / f_{a})}^{2} + {(d β_{O} / f_{b})}^{2}} = \sqrt{d α_{E}^{2} + d β_{E}^{2}} .$ (18)

Fitting the data with Eq. (18) yields $f_{a}$ and $f_{b}$ . To compare the measurement results from our OT with those of the ET, the residuals of the angular variation between the two measurements are calculated. The results are shown in Fig. 5. The trend of our OT measurements is consistent with that of the ET. This verifies that our OT is feasible even if we temporarily assemble it in the field, i.e., it is easy to implement and is robust. This experiment also provides a method for measuring the inclination of a retro-reflection Raman beam. However, an outlier residual datum of 19 µrad is significantly larger than the noise and other data. The error may originate from one of the tiltmeters or from operational mistakes.

Figure 5.Results of angular variation measurement in the field.

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3.2. Nonlinearity and drift

In this section, we compare the nonlinearity and drift of our OT with the ET and the MT to investigate the causes of the outlier datum mentioned in Sec. 3.1 and the performance of the OT. The ET and MT models are Jewell 755 and Ruifen ACA826T. The experimental setup is shown in Fig. 6. We fix the sample mirror, the conventional tiltmeters, and a small collimator on a rigid metal rod. The light from the small collimator hits the beam analyzer at a distance of about 1.8 m. We modulate the inclination by adjusting the height of a fulcrum. The variation in angle is determined by monitoring the displacement of the spot on the beam analyzer. We consider that the accuracy of the beam analyzer is within a pixel, which is equivalent to about 1.9 µrad.

Figure 6.Apparatus of the nonlinearity test.

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Considering the consistency of the tiltmeter’s sensitive axis with the modulation direction, we calculated the coupling coefficient in the $x$ - and $y$ -directions for each tiltmeter and compensated for it. Linearly fitting the data provides us with the slope $K$ of each tiltmeter. The residual is defined as $R = d θ_{tiltmeter} - K d θ_{B A}$ , where $R$ is the residual, $d θ_{tiltmeter}$ is the angle variation measured by the tiltmeters, $d θ_{B A}$ is the reference angle variation measured by the beam analyzer, and $θ_{B A}$ is the angular variation measured by the beam analyzer. This residual $R$ is used to characterize the nonlinearity. We perform the experiment three times to eliminate the possibility of random factors, and the results are shown in Fig. 7. The residual curves of our OT appear to be random noise, while the residual curves of the conventional tiltmeters exhibit higher-order terms. The nonlinearity of our OT is approximately 0.4% within a measurement range of 2 mrad. In contrast, the data from the ET show a characteristic peak in all three experiments, with an amplitude of approximately 28 µrad and a range of 700 µrad. This characteristic peak can reasonably explain the outlier observed in Sec. 3.1. Therefore, within a measurement range of 2 mrad, the nonlinearity of the ET is approximately 1.4%, while the nonlinearity increases to around 4% if the measurement ranges within the interval of the characteristic peak.

Figure 7.Nonlinearity test results. O.O.I. is the output of our optical interference method; O.E.T. is the output of the ET; O.M.T. is the output of the MT; and O.B.A. is the output of the beam analyzer. The blue circles represent the measured data. The red solid lines are the linearly fitted results of the output of the tiltmeters and the beam analyzer. The orange curves represent the residual. The first set of results [(a), (d), and (g)] has been averaged over 20 s. The second and third sets of results [(b), (e), and (h); (c), (f), and (i)] have been averaged over 50 s to reduce the effect of small vibrations on the results.

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We then placed the three tiltmeters statically for about 100 h to investigate their drift in a single direction. Due to the presence of tiny vibrations, we applied low-pass filtering with the same bandwidth to the data in order to better reveal the drift behavior. The results are presented in Fig. 8.

Figure 8.Long-term test results. Storage issues resulted in the loss of some data.

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Figure 8 reveals that the measurement fluctuation of our OT remains below 7 µrad. In contrast, in the first 10 h, the ET measurements exhibit a drastic unidirectional change up to approximately 30 µrad, and subsequently stabilize. A notable drift of up to about 50 µrad is observed for the MT measurements. This cannot be attributed to long-term creep of the tiltmeter installation, as the long-term test was immediately followed by the nonlinear test of over a week’s duration, during which the fixed tiltmeter was not reinstalled.

In summary, although the limitations of the measurement methodology prevent precise testing, our synchronous comparison of three tiltmeters demonstrates that our OT outperforms the conventional tiltmeter in both nonlinearity and drift. The relative nonlinearity of our OT is approximately 0.4% when the angle change range is under 2 mrad, while the relative nonlinearity of the ET is around 4.3% under a specific measurement range of 0.7 mrad. During over 90 h of measurements, the drift of our OT method remains below 7 µrad, which is at least 23 µrad lower than that of the conventional tiltmeters. According to Eq. (3), if the actual inclination drifts by 50 µrad in each direction or exhibits equivalent deviations from the optimum inclination, the combined effects of nonlinearity error and the 23 µrad drift in the inclination measurement of the retro-reflection mirror could result in a total systematic error of approximately 4 µGal in the atom gravimeter.

3.3. Variation of measured gravity with inclination deviation

In this section, we investigate the relationship between gravity measurements and inclination measurements from our OT and the ET. We modulate the inclination of the whole gravimeter in this experiment. We keep one direction of the whole gravimeter unchanged while altering another orthogonal direction to obtain the $x$ - and $y$ -directions of the tilt measurements as they vary with the gravity measurements. The data are fitted using Eq. (1). The inclination of the unchanged direction is close to the optimum inclination (within 20 µrad), and thus the peak value of the fitted result of the two directions should be identical and close to $g_{0}$ .

To measure the tilt of the entire gravimeter using our OT, the reference mirror should be independent of the gravimeter. The configuration of this experiment is shown in Fig. 1(a). The BS and the CCD are fixed with the gravimeter. Unlike the setup described in Sec. 3.1, we add an additional 45° mirror, also fixed with the gravimeter. The reference mirror is fixed on a frame that is anchored to the ground. It is worth noting that the reference mirror cannot be parallel to the vector of gravity, as this would result in the loss of one measurement direction. We change the inclination of the whole gravimeter by adjusting the height of the feet.

The results are presented in Fig. 9 and Table 1. Although the five-point data ensure the fit, we append two additional points with larger inclinations of the gravimeter to further verify the nonlinearity. Before and after appending these two points, the two fitting curves from our OT nearly overlap, and the errors in the fitting parameters are within tolerance, while in the $y$ -direction. In contrast, the two fitted curves in the $y$ -direction of ET are clearly separated, the fitted data are highly variable, and $g_{0}$ is far from the actual value. This further confirms that our OT outperforms the ET and demonstrates that our OT can measure the inclination variations and determine the optimum inclination for the whole cold atom gravimeter. This experiment is also the calibration of the OT against the gravimeter, and after calibration, our optical interferometer can be used as an absolute tiltmeter.

Table 1. Fitted Data of the Results in Fig. 9

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Table 1. Fitted Data of the Results in Fig. 9

	g₀/μGal	A/a.u.	θ₀/mrad
OI-x blue dash	−92.5 ± 2.5	479.3 ± 3.5	3.6468 ± 0.0025
OI-y blue dash	−91.9 ± 3.1	493.2 ± 4.4	4.3566 ± 0.0030
OI-x red solid	−90.5 ± 2.4	484.2 ± 2.1	3.6434 ± 0.0015
OI-y red solid	−91.1 ± 4.8	493.3 ± 4.8	4.3513 ± 0.0038
ET-x blue dash	−91.8 ± 2.6	507.7 ± 3.9	0.3270 ± 0.0023
ET-y blue dash	−92.5 ± 2.5	613.2 ± 13.2	0.3450 ± 0.0042
ET-x red solid	−83.2 ± 5.2	515.7 ± 5.0	0.3199 ± 0.0033
ET-y red solid	−131.7 ± 12.3	562.2 ± 11.5	0.3509 ± 0.0054

Figure 9.Variation of measured gravity with inclination measurement. The blue triangles and dashed curves represent the five data points and the corresponding fitting results, respectively. The red circles are the appended points and the red solid curves are the fitting results of the seven points.

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4. Conclusion

We utilize the inherent Raman beam to construct an optical interferometer inside the gravimeter to measure the inclination change of the Raman beam. Ensuring no effect on the cold atom interference, a hollow BS is used to realize optical division multiplexing. We propose a method based on one-dimensional Fourier filtering to process the irregular interferogram caused by hollow BS and extract valid information. The nonlinearity of our OT is 0.4%, while the nonlinearity of the commercial tiltmeters is over 4%, and our OT also has at least 23 µrad less drift than commercial tiltmeters in long-term measurements. This could result in a 4 µGal reduction in the systematic error of cold atom gravimeters when the actual tilt angle deviates from the optimal tilt angle by 50 µrad. In conclusion, our proposed optical tiltmeter for gravimeters is robust and has high accuracy, a simple setup process, and small drift, which makes it a reliable method to measure the inclination angle of gravimeters in the laboratory and field. More importantly, Raman beam interference may be a potential tool to study cold atom interferometers and improve their performance.

Category: Imaging Systems and Image Processing

Received: Apr. 3, 2025

Accepted: Jun. 23, 2025

Published Online: Sep. 23, 2025

The Author Email: Bin Wu (wubin@zjut.edu.cn), Qiang Lin (qlin@zjut.edu.cn)

DOI:10.3788/COL202523.111104

CSTR:32184.14.COL202523.111104