Objective With the development of vacuum technology, subject to directional flow and uneven temperature, the thermodynamic equilibrium has been destroyed. In this case, the pressure standard has become unsuitable for characterizing the vacuum state. To improve the accuracy of vacuum measurement and the stability of 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 type of vacuum metrology based on the optical method can transform vacuum metrology from physical standards based on the mercury pressure gauge to quantum standard. In recent years, quantum vacuum metrology technology based on the Fabry-Perot cavity has been widely studied; however, the laser resonance frequency at a high vacuum reference point is generally used as the reference frequency to measure the refractive index of a gas. Therefore, the measurement period of the system will be longer in the high vacuum reference point, and the cavity length will change due to gas pressure and gas penetration, which has a considerable effect on the accuracy of refractive index measurement. In this study, we report a method to measure the refractive index of gas, i.e., using a Fabry-Perot resonator for measuring the refractive index of a gas at a low vacuum constant pressure reference point. This method can shorten the measurement period and improve the measurement accuracy. We hope that our basic strategy and findings will aid in reducing the effect of cavity length change caused by gas pressure and gas permeation on gas refractive index measurement.
Methods Firstly, based on the first principles, we calculate the theoretical refractive index values at constant pressure and temperature through ab initio calculation. Then, the refractive index measurement expression of the constant pressure reference point is derived by varying the laser longitudinal mode frequency before and after inflation. In the next step, at 10 -5 Pa high vacuum reference point and 10 3 Pa constant pressure reference point, using the quantum vacuum measurement device based on Fabry-Perot cavity, the laser frequency change in the cavity is accurately measured using PDH(Pound-Drever-Hall) frequency locking technology and beat frequency technology, respectively, and the helium refractive index is obtained.
Results and Discussions The refractive index measurement method of low vacuum constant pressure reference point was used for measurement, and the refractive index measurement value of constant pressure reference point was found to be closer to the theoretical value of the refractive index compared with the high vacuum reference point at the pressure level of 10 2 Pa and 10 3 Pa. At the same pressure point, the deviation between the measured and theoretical values at the constant pressure reference point is smaller than that at the high vacuum reference point (Fig. 2 and Fig. 3) because the change in cavity length caused by gas pressure and penetration is effectively shielded, the reduction of helium in the cavity caused by helium penetration is reduced, and the measurement period is shortened in the pressure range from high vacuum to the constant pressure reference point using the theoretical refractive index of the constant pressure reference point as the refractive index measurement coefficient. In general, this method can improve the accuracy of gas refractive index measurement. In addition, the contribution of related parameters to the uncertainty of refractive index measurement is analyzed. The relative uncertainty of the theoretical value of the refractive index at the constant pressure reference point is 6.74×10 -14, and the measurement uncertainty of refractive index parameters is 1.28×10 -8 and 1.22×10 -8 when the cavity pressure is lower or higher than the constant pressure reference point, respectively.
Conclusions In researching quantum vacuum metrology standards, this paper proposes a method to measure the refractive index of gas and obtains the refractive index measurement expression of the constant pressure reference point. Using 10 3 Pa constant pressure as the reference pressure to measure the refractive index, the measurement error caused by the cavity length change in the pressure range from high vacuum to constant pressure reference point is effectively shielded. Consequently, the uncertainty of refractive index measurement caused by the decrease of helium present in the cavity caused by helium penetration is reduced. The refractive index measurement of the constant pressure reference point is compared with that of a high vacuum. We found that this method can effectively improve the measurement accuracy. During the actual measurement process, we discovered that this method could shorten the measurement cycle and reduce the effect of system thermal noise. Our research shows that using appropriate pressure reference points to reduce the effect of cavity length change caused by gas pressure and gas penetration can improve the accuracy of refractive index measurement.
