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Abstract

Absolute gravimeter has played an important role in geophysics, metrology, geological exploration, etc. It is an instrument applying laser interferometry or atom interferometry to the measurement of gravitational acceleration g(approximately 9.8 m/s ²). To achieve a high accuracy, a vibration correction method is often employed to reduce the influence of the vibration of the reference object (a retro-reflector or a mirror) on the measurement result of absolute gravimeter. Specifically, in an atomic-interferometry absolute gravimeter, the phase noise caused by the vibration of the reference mirror, namely the vibration phase, can be calculated from the output signal of a sensor, either a seismometer or an accelerometer, placed below or next to the mirror. Considering this vibration phase, the fringe signal of the atomic interferometer as a function of the phase shift set by the control system of the gravimeter can be corrected to approach to an ideal sinusoidal curve, thus reducing the fitting residual. Currently, the parameters in the algorithm of most vibration correction methods used in atomic-interferometry absolute gravimeters are set to be constant. As a result, the performances of these methods may be limited when the practical transfer function between the real vibration of the reference mirror and the signal of the sensor has a variation due to the change of measurement environments. In this paper, based on a simplified model of the practical transfer function previously proposed in an algorithm used in laser-interferometry absolute gravimeter, a new vibration correction method for atomic-interferometry absolute gravimeter is presented. Firstly, a detailed description of its principle is introduced. With a searching algorithm, the time delay and the proportional element in the simplified model can be obtained from the fringe signal of the atomic interferometer and the output of the vibration sensor. In this way, the parameters used to calculate the vibration phase can be adjusted to approach to their true values in different environments, causing the fitting residual of the corrected fringe to decrease as much as possible. Then the measurement results of the homemade NIM-AGRb-1 atomic-interferometry absolute gravimeters using this method is analyzed. It is indicated that with the vibration correction algorithm, the standard deviation of the fitting residual of the measured fringe signal can be reduced by 58% at the best level in a quiet environment. In the future, the performance of this vibration correction algorithm will be further improved in other atomic-interferometry absolute gravimeters during their measurements in hostile environments.

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Authors and contacts

Corresponding author:Yao Jia-Min,yaojm@nim.ac.cn

Funds:Project supported by the National Key Research and Development Program of China (Grant No. 2021YFB3900204) and the Research Funds for National Institute of Metrology, China (Grant Nos. 29-AKY1922-21, AKYZD2002)

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符号	含义	说明
P(ΔФ_th)	原始干涉条纹	横坐标为理论原子相位ΔФ_th, 纵坐标为跃迁概率的实测值P
P_fit(ΔФ_th)	理论干涉条纹	横坐标仍为ΔФ_th, 纵坐标为对P进行余弦拟合得到的拟合值P_fit
U_s,v_m	地震计输出电压, 参考镜真实速度	—
τ,K	延时系数, 增益系数	从U_s到v_m的传递函数H的简化模型中的系数
τ_opt,K_opt	最优延时系数, 最优增益系数	振动补偿算法搜索出的最优值
Δφ_vib	推算出的振动相位噪声	从U_s根据搜索出的τ_opt和K_opt以及重力仪灵敏度函数S(t)计算得到
ΔФ_v	推算出的仅受振动影响的原子相位	—
P(ΔФ_v)	修正干涉条纹	与原始干涉条纹相比, 横坐标由ΔФ_th变为ΔФ_v

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序号		1	2	3	4
输入参数		\|Δφ_vib\| ≤ 400 mrad, Δφ_others= 0,N= 30	\|Δφ_vib\| ≤ 400 mrad, \|Δφ_others\| ≤ 10 mrad,N= 30	\|Δφ_vib\| ≤ 4000 mrad, \|Δφ_others\| ≤ 10 mrad,N= 30	\|Δφ_vib\| ≤ 400 mrad, \|Δφ_others\| ≤ 10 mrad,N= 60
设定值τ_set/ms		5
计算值τ_opt/ms		5.0	2.7	4.1	6.8
设定值K_set		0.9
计算值K_opt		0.900	0.957	0.919	0.876
条纹拟合RMSE值	补偿前/10^–3	13.1	18.3	30.9	15.2
	补偿后/10^–3	0.02	8.3	7.2	6.7
	衰减比/%	99.8	54.6	76.7	55.9
条纹残差标准差	补偿前σ_m/10^–3	12.39	17.32	29.28	14.80
	补偿后σ_c/10^–3	0.02	7.82	6.78	6.50
	衰减比/%	99.8	54.8	76.8	55.7

DownLoad: CSV

组号	延时系数τ_opt/ms	增益系数K_opt	条纹拟合RMSE值		条纹残差标准差
组号	延时系数τ_opt/ms	增益系数K_opt	补偿前/10^–3	补偿后/10^–3	补偿前σ_m/10^–3	补偿后σ_c/10^–3	衰减比/%
1	1.79	0.970	11.2	4.8	10.62	4.58	56.9
2	1.17	1.210	17.3	7.2	16.33	6.83	58.2
3	5.06	1.109	11.4	7.0	10.82	6.67	38.3
4	5.42	1.357	13.8	8.5	13.08	8.05	38.5
5	4.23	1.037	9.1	5.6	8.59	5.30	38.3
6	7.29	1.025	11.7	5.8	11.03	5.52	50.0
7	1.43	1.223	15.1	9.9	14.31	9.34	34.7
8	4.53	1.118	13.6	7.3	12.86	6.94	46.0
9	-0.62	1.057	14.0	8.0	13.19	7.54	42.8
10	5.25	1.079	10.9	6.5	10.31	6.14	40.4
均值	3.56	1.119	—	—	—	—	44.4

DownLoad: CSV

序号	输入参数	设定值 τ_set/ms	延时系数τ_opt/ms		相关系数 C_R的极大值
序号	输入参数	设定值 τ_set/ms	以RMSE值为优化目标	以C_R为优化目标	相关系数 C_R的极大值
1	\|Δφ_vib\| ≤ 400 mrad, Δφ_others= 0,N= 30	5	5.0	5.0	0.999
2	\|Δφ_vib\| ≤ 400 mrad, Δφ_others≤ 10 mrad,N= 30		2.7	2.7	0.892
3	\|Δφ_vib\| ≤ 4000 mrad, Δφ_others≤ 10 mrad,N= 30		4.1	4.2	0.972
4	\|Δφ_vib\| ≤ 400 mrad, Δφ_others≤ 10 mrad,N= 60		6.8	8.6	0.896

DownLoad: CSV

组号	计算值τ_opt/ms		相关系数C_R 的最大值
组号	以RMSE值为优化目标	以C_R为优化目标	相关系数C_R 的最大值
1	1.79	1.84	0.902
2	1.17	–4.38	0.909
3	5.06	5.05	0.785
4	5.42	5.27	0.785
5	4.23	4.24	0.787
6	7.29	7.29	0.866
7	1.43	1.42	0.757
8	4.53	4.70	0.841
9	–0.62	–0.83	0.821
10	5.25	5.25	0.802

DownLoad: CSV

类型	设定值τ_set/ms	计算值τ_opt/ms		设定值K_set	计算值K_opt
类型	设定值τ_set/ms	以RMSE值为优化目标	以σ_c为优化目标	设定值K_set	以RMSE值为优化目标	以σ_c为优化目标
仿真数据第3种情况	5	4.1	4.2	0.9	0.919	0.918
仿真数据第4种情况	5	6.8	8.6	0.9	0.876	0.865
实测数据第9组	—	–0.62	1.32	—	1.057	1.033

DownLoad: CSV

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Vol. 71, Issue 11 - 2022-06-05

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