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.

Gas modulation refractometry is a technique for assessment of gas refractivity, density, and pressure that, by a rapid modulation of the gas, provides a means to significantly reduce the pickup of fluctuations. Although its unique feature has previously been demonstrated, no detailed explication or analysis of this ability has yet been given. This work provides a theoretical explanation, in terms of the length of the modulation cycle, of the extent to which gas modulation can reduce the pickup of fluctuations. It is indicated that a rapid modulation can significantly reduce the influence of fluctuations with Fourier frequencies lower than the inverse of the modulation cycle length, which often are those that dominate. The predictions are confirmed experimentally.

Gas modulation refractometry (GAMOR) is a methodology that can mitigate fluctuations and drifts in refractometry. This can open up for the use of non-conventional cavity spacer materials. In this paper, we report a dual-cavity system based on Invar that shows better precision for assessment of pressure than a similar system based on Zerodur. This refractometer shows for empty cavity measurements, up to 10(4) s, a white noise response (for N-2) of 3 mPa s(1/2). At 4303 Pa, the system has a minimum Allan deviation of 0.34 mPa (0.08 ppm) and a long-term stability (24 h) of 0.7 mPa. This shows that the GAMOR methodology allows for the use of alternative cavity materials.

A transportable refractometer for assessment of kPa pressures with ppm level precision is presented. It is based on the GAs MOdulation Refractometry (GAMOR) methodology, making it resistant to fluctuations and drifts. At the National Metrology Institute at RISE, Sweden, the system assessed pressures in the 4.3 - 8.7 kPa range with sub-ppm precision (0.5 - 0.9 ppm). The system was thereafter disassembled, packed, and transported 1040 km to Umeå University, where it, after unpacking and reassembling, demonstrated a similar precision (0.8 - 2.1 ppm). This shows that the system can be disassembled, packed, transported, unpacked, and reassembled with virtually unchanged performance.

Gas modulation refractometry (GAMOR) is a methodology that, by performing repeated reference assessments with the measurement cavity being evacuated while the reference cavity is held at a constant pressure, can mitigate drifts in dual Fabry-Perot cavity based refractometry. A novel realization of GAMOR, referred to as gas equilibration GAMOR, that outperforms the original realization of GAMOR, here referred to as single cavity modulated GAMOR (SCM-GAMOR), is presented. In this, the reference measurements are carried out by equalizing the pressures in the two cavities, whereby the time it takes to reach adequate conditions for the reference measurements has been reduced. This implies that a larger fraction of the measurement cycle can be devoted to data acquisition, which reduces white noise and improves on its short-term characteristics. The presented realization also encompasses a new cavity design with improved temperature stabilization and assessment. This has contributed to improved long-term characteristics of the GAMOR methodology. The system was characterized with respect to a dead weight pressure balance. It was found that the system shows a significantly improved precision with respect to SCM-GAMOR for all integration times. For a pressure of 4303 Pa, it can provide a response for short integration times (up to 10 min) of 1.5 mPa (cycle)1/2, while for longer integration times (up to 18 h), it shows an integration time-independent Allan deviation of 1mPa (corresponding to a precision, defined as twice the Allan deviation, of 0.5 ppm), exceeding the original SCM-GAMOR system by a factor of 2 and 8, respectively. When used for low pressures, it can provide a precision in the sub-mPa region; for the case with an evacuated measurement cavity, the system provided, for up to 40 measurement cycles (ca. 1.5 h), a white noise of 0.7 mPa (cycle)1/2, and a minimum Allan deviation of 0.15mPa. It shows a purely linear response in the 2.8-10.1 kPa range. This implies that the system can be used for the transfer of calibration over large pressure ranges with exceptional low uncertainty.

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.

An Invar-based Fabry-Perot cavity refractometer equipped with an automated, miniaturized gallium fixed-point cell for assessment of pressure is presented. The use of an Invar cavity spacer has previously demonstrated pressure assessments with sub-0.1 ppm precision. The fixed-point cell, whose design and implementation are presented here, provides a reference for temperature assessment of the gas inside the cavity with an uncertainty of 4 ppm. This opens up for a self-contained system for realization of the Pascal with an accuracy in the low ppm range. This is an important step towards disseminating the Pascal through fundamental principles.

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.

A novel procedure for a robust assessment of cavity deformation in Fabry-Perot (FP) refractometers is presented. It is based on scrutinizing the difference between two pressures: one assessed by the uncharacterized refractometer and the other provided by an external pressure reference system, at a series of set pressures for two gases with dissimilar refractivity (here, He and N2). By fitting linear functions to these responses and extracting their slopes, it is possible to construct two physical entities of importance: one representing the cavity deformation and the other comprising a combination of the systematic errors of a multitude of physical entities, viz., those of the assessed temperature, the assessed or estimated penetration depth of the mirror, the molar polarizabilities, and the set pressure. This provides a robust assessment of cavity deformation with small amounts of uncertainties. A thorough mathematical description of the procedure is presented that serves as a basis for the evaluation of the basic properties and features of the procedure. The analysis indicates that the cavity deformation assessments are independent of systematic errors in both the reference pressure and the assessment of gas temperature and when the gas modulation refractometry methodology is used that they are insensitive to gas leakages and outgassing into the system. It also shows that when a high-precision (sub-ppm) refractometer is characterized according to the procedure, when high purity gases are used, the uncertainty in the deformation contributes to the uncertainty in the assessment of pressure of N-2 with solely a fraction (13%) of the uncertainty of its molar polarizability, presently to a level of a few ppm. This implies, in practice, that cavity deformation is no longer a limiting factor in FP-based refractometer assessments of pressure of N-2.

The 18SIB04 QuantumPascal EMPIR project aims for development of photon-based standards that can replace primary standards of the SI unit of pressure, the Pascal. In this project, four partners simulated the pressure-induced deformation of a given Fabry-Pérot cavity, using various versions of two types of software, COMSOL Multiphysics® and ANSYS Workbench. It was demonstrated that, for a given geometry and set of material parameters, simulations of the deformation could be performed by the various partners with such small discrepancies that methodological mistakes of the simulation procedures will solely contribute to a sub-ppm uncertainty in the assessments of refractivity of N₂.

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 calculated from fundamental principles. The most sensitive instruments are currently based on Fabry-Perot cavities where a laser is used to probe the frequency of a cavity mode. However, for best accuracy, the realization of such systems requires exceptional mechanical stability. Gas modulation refractometry (GAMOR) has previously demonstrated an impressive ability to mitigate the influence of fluctuations and drifts whereby it can provide high-precision (sub-ppm, i.e., sub-parts-per-million or sub-) assessment of gas refractivity and pressure. In this work, two independent GAMOR-based refractometers are individually characterized, compared to each other, and finally compared to a calibrated dead weight piston gauge with respect to their abilities to assess pressure in the 4-25 kPa range. The first system, referred to as the stationary optical pascal (SOP), uses a miniature fixed point gallium cell to measure the temperature. The second system, denoted the transportable optical pascal (TOP), relies on calibrated Pt-100 sensors. The expanded uncertainty for assessment of pressure () was estimated to, for the SOP and TOP, and , respectively. While the uncertainty of the SOP is mainly limited by the uncertainty in the molar polarizability of nitrogen (8 ppm), the uncertainty of the TOP is dominated by the temperature assessment (26 ppm). To verify the long-term stability, the systems were compared to each other over a period of 5 months. It was found that all measurements fell within the estimated expanded uncertainty () for comparative measurements (27 ppm). This verified that the estimated error budget for the uncorrelated errors holds over this extensive period of time.

Refractometry is a powerful technique for pressure assessments that, due to the recent redefinition of the SI system, also offers a new route to realizing the SI unit of pressure, the Pascal. Gas modulation refractometry (GAMOR) is a methodology that has demonstrated an outstanding ability to mitigate the influences of drifts and fluctuations, leading to long-term precision in the 10−7 region. However, its short-term performance, which is of importance for a variety of applications, has not yet been scrutinized. To assess this, we investigated the short-term performance (in terms of precision) of two similar, but independent, dual Fabry–Perot cavity refractometers utilizing the GAMOR methodology. Both systems assessed the same pressure produced by a dead weight piston gauge. That way, their short-term responses were assessed without being compromised by any pressure fluctuations produced by the piston gauge or the gas delivery system. We found that the two refractometer systems have a significantly higher degree of concordance (in the 10−8 range at 1 s) than what either of them has with the piston gauge. This shows that the refractometry systems under scrutiny are capable of assessing rapidly varying pressures (with bandwidths up to 2 Hz) with precision in the 10−8 range.

Using a transportable Fabry-Pérot cavity refractometer, a circular comparison of existing primary standards at several national metrology institutes is currently underway. This paper provides information about the refractometer, the preparation for the comparison, and the transportation procedure.

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.