When Fabry-Perot (FP) refractometry is used to assess the refractivity of gases, it has so far been assumed that the Gouy phase is independent of the presence of gas in the cavity. Here we show, by both theory and experiments, that this is only correct for a non-deformable cavity. For a deformable one, the pressure can affect the radius of curvature of the mirrors. This gives the Gouy phase a component that is proportional to gas pressure. Although being a small effect (1.6 nrad/Pa), since it affects the Gouy phase only when the cavity contains gas, it affects the refractivity on a 10−6 level. 

This work models and experimentally assesses the influence of absorption of laser light in mirrors in Fabry-Pérot based refractometers used for realization of pressure. Model parameters are assessed by experimental characterizations. Characterizations of two refractometers agree well with the predictions of the model. It is shown that, when pressures are assessed in the viscous region, the absorption of laser light in mirrors will give rise to a small alteration in the proportional response and a pressure-independent offset, where the latter is significant for He but considerably smaller for Ar and N2

A procedure for automated low uncertainty assessment of empty cavity mode frequencies in Fabry-Pérot cavity based refractometry that does not require access to laser frequency measuring instrumentation is presented. It requires a previously well-characterized system regarding mirror phase shifts, Gouy phase, and mode number, and is based on the fact that the assessed refractivity should not change when mode jumps take place. It is demonstrated that the procedure is capable of assessing mode frequencies with an uncertainty of 30 MHz, which, when assessing pressure of nitrogen, corresponds to an uncertainty of 0.3 mPa. 

Based on a recent experimental determination of the static polarizability and a first-principle calculation of the frequency-dependent dipole polarizability of argon, this work presents, by using a Fabry–Perot refractometer operated at 1550 nm, a realization of the SI unit of pressure, the pascal, for pressures up to 100 kPa, with an uncertainty of [(1.0 mPa)2 + (5.8 × 10−6 P)2 + (26 × 10−12P2)2]1/2. The work also presents a value of the molar polarizability of N2 at 1550 nm and 302.9146 K of 4.396572(26) × 10−6 m3/mol, which agrees well with previously determined ones. 

An updated version of an Invar-based dual Fabry-Perot cavity refractometer utilizing the gas modulation methodology has been characterized with regard to its ability to assess gas pressure in the low pressure regime, defined as the regime in which the instrumentation is mainly limited by the constant term a in the [ ( a ) 2 + ( b × P ) 2 ] 1 / 2 expression for the uncertainty. It is first concluded that this ability is predominantly limited by three entities, viz., the empty cavity repeatability, the residual gas pressures in the evacuated (measurement) cavity, and the contamination of the gas residing in the measurement cavity that originates from leaks and outgassing. We then present and utilize methods to separately estimate the uncertainty of the updated refractometer from these entities. It was found that, when utilizing gas modulation cycles of 100 s and when addressing nitrogen, the system can assess pressure in the low pressure regime with an expanded uncertainty ( k = 2 ) of 0.75 mPa, mainly limited by the empty cavity repeatability and outgassing of hydrogen. This is more than 1 order of magnitude below the previously assessed low pressure performance of the instrumentation.

Fabry–Pérot-based refractometry has demonstrated the ability to assess gas pressure with high accuracy and has been prophesized to be able to realize the SI unit for pressure, the pascal, based on quantum calculations of the molar polarizabilities of gases. So far, the technology has mostly been limited to well-controlled laboratories. However, recently, an easy-to-use transportable refractometer has been constructed. Although its performance has previously been assessed under well-controlled laboratory conditions, to assess its ability to serve as an actually transportable system, a ring-type comparison addressing various well-characterized pressure balances in the 10–90 kPa range at several European national metrology institutes is presented in this work. It was found that the transportable refractometer is capable of being transported and swiftly set up to be operational with retained performance in a variety of environments. The system could also verify that the pressure balances used within the ring-type comparison agree with each other. These results constitute an important step toward broadening the application areas of FP-based refractometry technology and bringing it within reach of various types of stakeholders, not least within industry.

By measuring the refractivity and the temperature of a gas, its pressure can be assessed from fundamental principles. The highest performing instruments are based on Fabry-Perot cavities where a laser is used to probe the frequency of a cavity mode, which is shifted in relation to the refractivity of the gas in the cavity. Recent activities have indicated that such systems can demonstrate an extended uncertainty in the 10 ppm (parts-per-million or 10-6) range. As a means to reduce the influence of various types of disturbances (primarily drifts and fluctuations) a methodology based on modulation, denoted gas modulation refractometry (GAMOR), has recently been developed. Systems based on this methodology are in general high-performance, e.g. they have demonstrated precision in the sub-ppm range, and they are sturdy. They can also be made autonomous, allowing for automated and unattended operation for virtually infinite periods of time. To a large degree, the development of such instruments depends on the access to modern photonic components, e.g. narrow line-width lasers, electro-and acousto-optic components, and various types of fiber components. This work highlights the role of such modern devices in GAMOR-based instrumentation and provides a review on the recent development of such instruments in Sweden that has been carried out in a close collaboration between a research institute and the Academy. It is shown that the use of state-of-the-art photonic devices allows sturdy, automated and miniaturized instrumentation that, for the benefit of industry, can serve as standards for pressure and provide fast, unattended, and calibration-free pressure assessments at a fraction of the present cost. © 2022 The Author(s).

A procedure is presented for in situ determination of the frequency penetration depth of coated mirrors in Fabry-Perot (FP) based refractometers and its influence on the assessment of refractivity and pressure. It is based on assessments of the absolute frequency of the laser and the free spectral range of the cavity. The procedure is demonstrated on an Invar-based FP cavity system with high-reflection mirrors working at 1.55 µm. The influence was assessed with such a low uncertainty that it does not significantly contribute to the uncertainties (k = 2) in the assessment of refractivity (<8 × 10−13) or pressure of nitrogen (<0.3 mPa).

By measuring the refractivity and the temperature of a gas, its pressure can be assessed from fundamental principles. The highest performing instruments are based on Fabry-Perot cavities (FPC). Gas modulation refractometry (GAMOR) is a methodology that has the ability to reduce the influence of disturbances to such an extent that high-precision (sub-parts-per-million) assessments of pressure can be made by the use of FPCs of Invar. To allow for high accuracy assessments, it is of importance to assess the uncertainty contribution from the thermodynamic effects that are associated with the gas filling and emptying of the cavity (pV-work). This paper presents a detailed scrutiny of the influence of the gas exchange process on the assessment of gas temperature on an Invar-based dual-FPC (DFPC) instrumentation. It is shown that by virtue of a combination of a number of carefully selected design entities (a small cavity volume with a bore radius of 3 mm, a spacer material with high heat capacitance, large thermal conductivity, and no regions that are connected with low thermal conductance, i.e. no heat islands, and a continuous assessment of temperature of the cavity spacer) the system is not significantly affected by pV-work. Simulations show that 10 s after the filling all temperature gradients in the system are well into the sub-mK range. Experiments support that refractivity assessments initiated after 40 s are not significantly affected by the pV-work. The analysis given in this work indicates that an upper limit for the influence of pV-work on the Invar-based DFPC system using 100 s long gas modulation cycles is 0.5 mK/100 kPa (or 1.8 ppm/100 kPa). Consequently, thermodynamic effects will not be a limiting factor when the Invar-based DFPC GAMOR system is used for assessments of pressure or as a primary pressure standard up to atmospheric pressures. 

Gas modulation refractometry (GAMOR) is a methodology for assessment of gas refractivity, molar density, and pressure that, by a rapid gas modulation, exhibits a reduced susceptibility to various types of disturbances. Although previously demonstrated experimentally, no detailed analysis of its ability to reduce the pickup of drifts has yet been given. This work provides an explication of to what extent modulated refractometry in general, and GAMOR in particular, can reduce drifts, predominantly those of the cavity lengths, gas leakages, and outgassing. It is indicated that the methodology is insensitive to the linear parts of so-called campaign-persistent drifts and that it has a significantly reduced susceptibility to others. This makes the methodology suitable for high-accuracy assessments and out-of-laboratory applications