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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.

A unified description of physical phenomena through measurement science is one of the foundational pillars in a global society. The International System of Units (SI) is the most widely used system of units and since its redefinition in 2019, all units encompassed by it are based on fundamental physical constants. The units of the SI, such as the second, metre, and kilogram, are realized by the use of primary standards which are used, through calibration chains, to certify the accuracy of measuring devices in our society. Its redefinition enabled the realization of the SI-unit for pressure (pascal) in a novel way; instead of force per area (N/m²), it can alternatively be defined as an energy density (J/m³). Subsequently, this opened up for the use of optical realizations of the pascal (Pa). It has been prophesied that a possible means to do this is by assessing refractivity through the use of Fabry-Pérot (FP) refractometry. Although such instrumentation indeed can assess refractivity, it has unfortunately been found that they in practice are affected by various types of disturbances that aggravate assessments with the required uncertainty.

This thesis describes the development of FP-based refractometers utilizing a novel measurement methodology, denoted gas modulation refractometry (GAMOR). By the use of rapid gas modulation and baseline interpolation, GAMOR has the ability to significantly reduce the influence of various types of disturbances, not least drifts and fluctuations. From this, two FP-based refractometers have been developed; one stationary, denoted the SOP, capable of assessing pressure with an uncertainty of [(10 mPa)² + (10 × 10⁻⁶·P)²]^1/2, and one transportable, denoted the TOP, with an uncertainty of [(16 mPa)² + (28 × 10⁻⁶·P)2]^1/2. Furthermore, it was shown that their mutual short-term precision is excellent, with a deviation of only 0.04 ppm when simultaneously assessing a pressure of 16 kPa.

A major part of this thesis was devoted to the construction of the TOP and an investigation of its transportability and performance. It was used in a ring comparison with various pressure standards at four European national metrology institutes. It was concluded that, despite being transported, the performance remained virtually unchanged, and that, in the 10 – 90 kPa range, all the standards agreed within their uncertainties.

These results indicate that FP-based refractometers utilizing the GAMOR methodology have the potential to act as transportable standards based on fundamental physical constants and paves the way for future research within the field.

En av grundpelarna i ett globalt samhälle är en enad syn på fysikaliska fenomen med förankring i vetenskap. Det Internationella måttenhetssystemet (SI) är det mest använda enhetssystemet och sedan dess omdefiniering 2019 är alla dess enheter baserade på grundläggande fysikaliska konstanter. SI-enheterna, som exempelvis sekund, meter och kilogram, realiseras genom primära standarder. Dessa standarder används, via kalibreringskedjor, för att certifiera noggrannheten av mätinstrument runtom vårt samhälle. Omdefiniering ledde till möjligheten att realisera enheten för tryck (pascal) på ett nytt sätt; i stället för kraft per area (N/m²) går det numera att definiera tryck som energidensitet (J/m³). Detta ledde i sin tur till att optiska realiseringar av pascal (Pa) för gastryck blev en möjlighet. Det har påvisats att detta kan uppnås genom att mäta refraktivitet med hjälp av Fabry-Pérot (FP)-refraktometri. Även om denna teknik kan användas för att bestämma refraktivitet, påverkas den i praktiken av diverse störningar vilket försvårar den nogrannhet som krävs för att ersätta dagens mekaniska tryckstandarder.

I denna avhandling beskrivs utvecklingen av FP-baserade refraktometrar som använder sig av en av oss nyutvecklad mätteknik; gasmodulationsrefraktometri (GAMOR). Tekniken bygger på en snabb modulering av gas och baslinje-interpolering, vilket reducerar effekten av snabba likaväl som långsamma störningar. Baserat på detta har två refraktometrar utvecklats; en stationär, SOP, som kan mäta tryck med en osäkerhet på [(10 mPa)² + (10 × 10⁻⁶·P)²]^1/2, samt en transportabel, TOP, med en osäkerhet på [(16 mPa)² + (28 × 10⁻⁶·P)²]^1/2. Vidare har det visats att deras inbördes korttidsprecision är utmärkt, med en avvikelse på endast 0.04 ppm när de samtidigt mätte ett tryck på 16 kPa.

En signifikant del av denna avhandling har ägnats till att konstruera TOP:en, samt att undersöka dess transporterbarhet och prestanda. Den användes i en serie jämförelsemätningar av olika tryckstandarder där fyra europeiska nationella metrologiska institut deltog. Från dessa mätningar konstaterades det att TOP:ens prestanda inte påverkades av transporten och att tryckstandarderna, inom det spann som undersöktes, 10 – 90 kPa, överensstämde inom deras osäkerheter.

Resultaten som presenteras tyder på att FP-baserade refraktometrar som använder sig av GAMOR-metodiken har potentialen att kunna agera som transportabla standarder baserade på grundläggande fysikaliska konstanter, något som banar vägen för framtida forskning inom området.

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.

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.

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).

The QuantumPascal (QP) project combines the capabilities of 12 European institutions to enable traceable pressure measurements utilizing quantum-based methods that evaluate the number density instead of force per area to target the wide pressure range between 1 Pa and 3 MPa. This article summarizes the goals and results since the project start in June 2019.

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.

An Invar-based dual Fabry-Pérot cavity refractometer used for assessments of pressure by the gas modulation refractometry (GAMOR) methodology has been scrutinized with respect to the influence of thermodynamic effects (pV-work) that originates from the gas exchange process when 100 kPa of nitrogen is addressed. It is shown that the actual temperature variation of the cavity spacer solely is a fraction of the previously assessed upper limits (0.5 mK/100 kPa), limited to sub-parts-per-million (ppm) levels. This finding additionally supports the conclusion that the thermodynamic effects will not be a limiting factor when the system is used for assessments of pressure.

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.

A technique for high-precision and high-accuracy assessment of both gas molar (and number) density and pressure, Gas Modulation Refractometry (GAMOR), is presented. The technique achieves its properties by assessing refractivity as a shift of a directly measurable beat frequency by use of Fabry-Perot cavity (FPC) based refractometry utilizing the Pound-Drever-Hall laser locking technique. Conventional FPC-based refractometry is, however, often limited by fluctuations and drifts of the FPC. GAMOR remedies this by an additional utilization of a gas modulation methodology, built upon a repeated filling and evacuation of the measurement cavity together with an interpolation of the empty cavity responses. The procedure has demonstrated an ability to reduce the influence of drifts in a non-temperature stabilized dual-FPC (DFPC)-based refractometry system, when assessing pressure, by more than three orders of magnitude. When applied to a DFPC system with active temperature stabilization, it has demonstrated, for assessment of pressure of N2 at 4304 Pa at room temperature, which corresponds to a gas molar density of 1.7 × 10−6 mol/cm3, a sub-0.1 ppm precision (i.e. a resolution of 0.34 mPa). It is claimed that the ability to assess gas molar density is at least as good as so far has been demonstrated for pressure (i.e. for the molar density addressed, a resolution of at least 1.2 × 10−13 mol/cm3). It has recently been argued that the methodology should be capable of providing an accuracy that is in the low ppm range. These levels of precision and accuracy are unprecedented among laser-based techniques for detection of atomic and molecular species. Since the molar polarizability of He can be calculated by ab initio quantum mechanical calculations with sub-ppm accuracy, it can also be used as a primary or semi-primary standard of both gas molar (and number) density and pressure.