Measurement of the refractive index of air in a low-pressure regime and the applicability of traditional empirical formulae

Abstract

The refractive index of air is a major limiting factor in length measurements by interferometry, which are mostly performed under atmospheric conditions. Therefore, especially in the last century, measurement and description of the air refractive index was a key point in order to achieve accuracy in the realisation of the length by interferometry. Nevertheless, interferometric length measurements performed in vacuum are much more accurate since the wavelength of the light is not affected by the air refractive index. However, compared with thermal conditions in air, in high vacuum heat conduction is missing. In such a situation, dependent on the radiative thermal equilibrium, a temperature distribution can be very inhomogeneous. Using a so-called contact gas instead of high vacuum is a very effective way to enable heat conduction on nearly the same level as under atmospheric pressure conditions whereby keeping the effect of the air refractive index on a small level. As physics predicts, and as we have demonstrated previously, helium seems like the optimal contact gas because of its large heat conduction and its refractive index that can be calculated from precisely known parameters. On the other hand, helium gas situated in a vacuum chamber could easily be contaminated, e.g. by air leakage from outside. Above the boiling point of oxygen (−183 °C) it is therefore beneficial to use dry air as a contact gas. In such an approach, the air refractive index could be calculated based on measured quantities for pressure and temperature. However, existing formulas for the air refractive index are not valid in the low-pressure regime. Although it seems reasonable that the refractivity (n − 1) of dry air simply downscales with the pressure, to our knowledge there is no experimental evidence for the applicability of any empirical formula. This evidence is given in the present paper which reports on highly accurate measurements of the air refractive index n for the wavelengths 532 nm, 633 nm and 780 nm in the low-pressure regime from 0 Pa to 1300 Pa. In our approach, using a vacuum cell, n − 1 is obtained from the comparison of optical path lengths in vacuum and air along the same path by imaging interferometry. These measured values are compared with the ones obtained from Bönsch's formula. An agreement of ±10 −9 is found in the low-pressure regime. Accordingly, this formula could be applied for the accurate determination of the refractive index of dry air even at low pressures, provided that the pressure is measured with high accuracy.

Optimization of Au:CuO Nanocomposite Thin Films for Gas Sensing with High-Resolution Localized Surface Plasmon Resonance Spectroscopy

“…Pure He was considered as the working medium for all the sensitivity tests, thus, the atmosphere surrounding the film was switched between He and either Ar, N 2 , O 2 or a mixture of N 2 +O 2 every 120 s. The partial pressure of each gas was possible to be adjusted to about 1 / 4 of the atmospheric pressure so that the RI difference between He and test gas was even lower. In fact, according to some authors, , the RIs of these gases are scaled linearly with pressure, which means that the RIs of pure He, Ar, N 2 , and O 2, at low pressure of about 2.6 × 10 4 Pa, are 1.000009, 1.000070, 1.000075, and 1.000068 RIU, respectively, and the RI of the mixture is 1.000073, considering its composition. Several He/ (Ar, N 2 , N 2 +O 2 , O 2 ) cycles were employed at room temperature and the LSPR peak position was monitored in real time.…”

Precision measurement of the refractive index of air using a phase modulated homodyne interferometer with a variable length vacuum cavity

“…The standard deviation of the measurement discrepancy of RIA between the proposed method and the Edlén equations is 2.8 parts in 10 7 [18]. Schödel et al realized RIA measurement under a low-pressure regime by imaging interferometry using PTB's ultra-precision interferometer and one vacuum cell, and an agreement of 10 −9 was achieved by comparing the measured values with the ones obtained from Bönsch's formula [19]. In our previous study, by combining the laser synthetic wavelength interferometry with the Edlén equations' estimation, we adopted two vacuum cavities and realized the measurement accuracies of better than 2.5 × 10 −8 in 2 h and 6.2 × 10 −8 in 18 h without ambiguity [20].…”

“…In order to solve this problem, the second kind adopts one or more permanent evacuated chambers [16][17][18][19][20]. Based on laser heterodyne interferometry, Huang et al realized the measurement range of 3.1 × 10 −4 and the uncertainty of 2.3 × 10 −8 by synthesizing a set of synthetic pseudo-wavelengths with three specific length vacuum cells [16].…”

Influence of the environment on the effect of super resonance in mesoscale dielectric spheres

“…The refractive index of air depends on many parameters, such as humidity, pressure, temperature, etc. [28][29][30][31]. In our studies, to demonstrate the effect of environmental refractive index on super resonance properties, we used the value of n=1.000241307 as example.…”