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为保证测量系统的长期稳定性和复现性, 真空计量将使用气体密度来表征. 利用法布里-珀罗腔可实现对气体折射率的精密测量、并反演得出气体密度. 这种基于光学方法的真空计量方法是将气体宏观介电常数与原子微观极化参数联系在一起, 由量子标准取代目前基于水银压力计的实物标准. 本文讨论了气体折射率至气体压力的反演过程, 并采用激光锁定法布里-珀罗腔的方法测定稀薄氩气的折射率, 讨论了相关参数对所测得气体压力不确定度的贡献. 在1个大气压范围内, 对氩气压力测量的标准不确定度为
$u = \sqrt {{{(6\;{\rm{mPa}})}^2} + {{(73 \times {{10}^{ - 6}}p)}^2}} $ .With the development of vacuum technology, subject to the influence of directional flow and uneven temperature, the thermodynamic equilibrium state is destroyed. In this case, the pressure reference is not suitable for characterizing the vacuum state. To ensure the long-term stability and reproducibility of the measurement system, vacuum metrology will be characterized by gas density. The precisive measurement of gas refractive index based on a Fabry-Perot cavity can be used to derive the gas density. This kind of an optical measurement of vacuum links macroscopic dielectric constants of gases with microscopic polarization parameters of atoms and molecules. It replaces the physical standard based on the mercury pressure gauge with the quantum standard. In this paper, we discuss the reverse process from refractive index to gas pressure, and use the laser-locked Fabry-Perot cavity method to measure the refractive index of argon gas. The contribution of related parameters to the uncertainty of determined gas pressure is analyzed. The influences of material parameters and experimental parameters such as gas molar susceptibility, molar susceptibility, dielectric second Virial coefficient and temperature on gas pressure accuracy are analyzed. The result shows that the uncertainty in our measurement of argon within 1 atm is$u = \sqrt {{{(6\;{\rm{mPa}})}^2} + {{(73 \times {{10}^{ - 6}}p)}^2}} $ . Currently, the uncertainty mainly comes from the measurement deviation of gas temperature inside the cavity. After repeating the measurement a few times, the results show that the statistical uncertainty of refractive index is within 100 ppm, which is limited by the accuracy of the pressure gauge used here. In addition, we compare the dipole calculated by the ab initio method with that by the DOSD method. The results show that the dynamic polarizability obtained by the ab initio method is consistent with our experimental results. In conclusion, these experimental results show that the measurement of gas pressure based on the gas refractive index has high repeatability and accuracy. If the temperature control and corresponding measurement accuracy of the gas are further improved, this method can also be used to obtain high-precision microscopic parameters such as the polarizabilities of atoms and molecules. In the future work, we will focus on improving the temperature control and the design of the cavity to reduce cavity leakage and deflation. It is possible that the measurement accuracy of the gas pressure will be increased to 10 ppm level, which is the same level as the current standard pressure gauge and will become a new standard for pressure measurement in the future.-
Keywords:
- vacuum metrology /
- gas pressure /
- Virial state equation /
- Fabry-Perot cavity
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Google Scholar
[2] 顾世杰 2004 上海计量测试 31 10
Google Scholar
Gu S J 2004 Shanghai Measurement and Testing 31 10
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Google Scholar
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图 1 实验装置图(LO, 本地振荡器; EOM, 电光调制器; IO, 隔离器)
Fig. 1. Experimental setup (LO, local oscillator; EOM, electro-optic modulator; IO, isolator).
图 2 (a)读出温度随时间的变化(b)及其阿伦偏差
Fig. 2. (a) Temperature readout with time and (b) its Allan deviation.
图 3 (a)腔体示意图; (b) 腔体温度分布
Fig. 3. (a) Cavity diagram; (b) temperature distribution inside the sample cell.
表 1 各参数对氩气在1个大气压下压力测量的相对不确定度贡献
Table 1. Uncertainty budget of determined argon pressures within 1 atm.
参数 不确定度u(p)/ppm ΔP/mPa 温度T 67 频率ν # 0.01 氩气纯度 5 压缩滞后 0.1 ${A_\varepsilon }$ 4.0 ${B_\varepsilon }$ ≤ 0.3* ${A_\mu }$ 0.05 $B(T)$ ≤ 10* 体积模量K 27 漏气率 6 ULE热膨胀 0.6 总计 73 6 注: #表示A类不确定度, 其他为B类不确定度; *表示该项不确定度贡献将随压力增大而增大. 
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[1] Gibney E 2017 Nature 551 18
Google Scholar
[2] 顾世杰 2004 上海计量测试 31 10
Google Scholar
Gu S J 2004 Shanghai Measurement and Testing 31 10
Google Scholar
[3] Tilford C R 1994 Metrologia 30 545
Google Scholar
[4] Hendricks J H, Olson D A 2010 Measurement 43 664
Google Scholar
[5] 李得天, 成永军, 习振华 2018 宇航计测技术 38 1
Google Scholar
Li D T, Cheng Y J, Xi Z H 2018 Journal of Astronautic Metrology and Measurement 38 1
Google Scholar
[6] Egan P, Stone J, Ricker J, Hendricks J 2016 2016 Conference on Precision Electromagnetic Measurements Ottawa, Canada, July 10–15, 2016 p1
[7] Egan P F, Stone J A, Ricker J E, Hendricks J H, Strouse G F 2017 Opt. Lett. 42 2944
Google Scholar
[8] Egan P F, Stone J A, Ricker J E, Hendricks J H 2016 Rev. Sci. Instrum. 87 053113
Google Scholar
[9] Egan P F, Stone J A 2011 Appl. Opt. 50 3076
Google Scholar
[10] Lanzinger E, Jousten K, Kuhne M 1998 Vacuum 51 47
Google Scholar
[11] Víquez P, José G 2005 Ph. D. Dissertation (Berlin: Technische Universität Berlin)
[12] Pachucki K, Puchalski M 2019 Phys. Rev. A 99 041803
Google Scholar
[13] Puchalski M, Piszczatowski K, Komasa J, Jeziorski B, Szalewicz K 2016 Phys. Rev. A 93 032515
Google Scholar
[14] Gaiser C, Fellmuth B 2018 Phys. Rev. Lett. 120 123203
Google Scholar
[15] Thakkar A J, Hettema H, Wormer P E S 1992 J. Chem. Phys. 97 3252
Google Scholar
[16] Kumar A, Meath W J 1985 Can. J. Chem. 63 1616
Google Scholar
[17] Vogel E, Jager B, Hellmann R, Bich E 2010 Mol. Phys. 108 3335
Google Scholar
[18] Glick R E 1961 J. Phys. Chem. 65 1552
Google Scholar
[19] Egan P F, Stone J A, Scherschligt J K, Harvey A H 2019 J. Vac. Sci. Technol. A 37 031603
Google Scholar
[20] Gaiser C, Fellmuth B 2019 J. Chem. Phys. 150 134303
Google Scholar
[21] Buckley T J, Hamelin J, Moldover M R 2000 Rev. Sci. Instrum. 71 2914
Google Scholar
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