Gas modulation refractometry (GAMOR) - On its ability to eliminate the influence of drifts

Gas modulation refractometry (GAMOR) is a technique based on a dual-Fabry-Perot (FP) cavity (DFPC) for assessment of gas refractivity, density, and pressure that can alleviate significant limitations of conventional refractometry systems, predominantly those related to drifts. Repeated assessments of the beat frequency when the measurement cavity is evacuated provide conditions under which the methodology is immune to the linear parts of the drifts in the system, both those from length changes of the cavities and those from gas leaks and outgassing. This implies that the technique is solely influenced by the non-linear parts of the drifts. This work provides a description of the principle behind the GAMOR methodology and explicates the background to its unique property. Based on simple models of the drifts of the temperature in the cavity spacer and the residual gas in the reference cavity, this work predicts that a GAMOR system, when used for assessment of refractivity, can sustain significant temperature drifts and leakage rates without being affected by noticeable errors or uncertainties. The cavity spacer can be exposed to temperature fluctuations of 100 mK over 103 s, and the reference cavity can have a leakage that fills it up with gas on a timescale of days, without providing errors or uncertainties in the assessment of refractivity that are 3 x 10^(-12), which, for N2, corresponds to 0.01 ppm (parts per million) of the value under atmospheric pressure conditions, and thereby 1 mPa. Since well-designed systems often have temperature fluctuations and leakage rates that are smaller than these, it is concluded that there will, in practice, not be any appreciable influence from cavity length drifts, gas leaks, and outgassing in the GAMOR methodology

Demonstration of a Transportable Fabry–Pérot Refractometer by a Ring-Type Comparison of Dead-Weight Pressure Balances at Four European National Metrology Institutes

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

Characterization of Multi Plate Field Mill for Lunar Deployment

During the Apollo 10 and 17 missions NASA astronauts reported that they saw streamers emanating from the surface of the moon. They concluded that the streamers were produced by light scattering from dust particles. The particles are believed to be transported by an ambient electric field. This theorized electric field has never been measured directly, although the electric potential on the surface and above it has. The exact behavior and origin of the electric field is unknown, but has been approximated to be between 1 and 12 V/m. To measure this electrical field a new type of instrument, called Multi Plate Field Mills (MPFM) has been developed. This type of instrument is capable of measuring both the amplitude and directionality of the electrical field. Three of these instruments will be mounted on a 1U CubeSat to be lunched with the PTS mission to the moon scheduled to Q4 2019. In this work the MPFM were characterized. The precision of the instrument for electrical fields applied along the z, y and x axis was found to be 0.6, 1.3, 1.4 (V/m)/(Hz)^(1/2) respectively for measurements in air and 0.14, 0.6, 0.6 (V/m)/(Hz)^(1/2) for measurements in vacuum. This sensitivity outperforms the current state of the art Field Mills and, in addition to that, it provides an assessment of the directionality of the electrical field.Umeå Lunar Ventur

Characterization of Multi Plate Field Mill for Lunar Deployment

During the Apollo 10 and 17 missions NASA astronauts reported that they saw streamers emanating from the surface of the moon. They concluded that the streamers were produced by light scattering from dust particles. The particles are believed to be transported by an ambient electric field. This theorized electric field has never been measured directly, although the electric potential on the surface and above it has. The exact behavior and origin of the electric field is unknown, but has been approximated to be between 1 and 12 V/m. To measure this electrical field a new type of instrument, called Multi Plate Field Mills (MPFM) has been developed. This type of instrument is capable of measuring both the amplitude and directionality of the electrical field. Three of these instruments will be mounted on a 1U CubeSat to be lunched with the PTS mission to the moon scheduled to Q4 2019. In this work the MPFM were characterized. The precision of the instrument for electrical fields applied along the z, y and x axis was found to be 0.6, 1.3, 1.4 (V/m)/(Hz)^(1/2) respectively for measurements in air and 0.14, 0.6, 0.6 (V/m)/(Hz)^(1/2) for measurements in vacuum. This sensitivity outperforms the current state of the art Field Mills and, in addition to that, it provides an assessment of the directionality of the electrical field.Umeå Lunar Ventur

Characterization of Multi Plate Field Mill for Lunar Deployment

During the Apollo 10 and 17 missions NASA astronauts reported that they saw streamers emanating from the surface of the moon. They concluded that the streamers were produced by light scattering from dust particles. The particles are believed to be transported by an ambient electric field. This theorized electric field has never been measured directly, although the electric potential on the surface and above it has. The exact behavior and origin of the electric field is unknown, but has been approximated to be between 1 and 12 V/m. To measure this electrical field a new type of instrument, called Multi Plate Field Mills (MPFM) has been developed. This type of instrument is capable of measuring both the amplitude and directionality of the electrical field. Three of these instruments will be mounted on a 1U CubeSat to be lunched with the PTS mission to the moon scheduled to Q4 2019. In this work the MPFM were characterized. The precision of the instrument for electrical fields applied along the z, y and x axis was found to be 0.6, 1.3, 1.4 (V/m)/(Hz)^(1/2) respectively for measurements in air and 0.14, 0.6, 0.6 (V/m)/(Hz)^(1/2) for measurements in vacuum. This sensitivity outperforms the current state of the art Field Mills and, in addition to that, it provides an assessment of the directionality of the electrical field.Umeå Lunar Ventur

Fabry-Pérot-baserad refraktometri : utveckling av en transporterbar refraktometer för mätning av gastryck

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

Fabry-Pérot-baserad refraktometri : utveckling av en transporterbar refraktometer för mätning av gastryck

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

Assessment of gas molar density by gas modulation refractometry: A review of its basic operating principles and extraordinary performance

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

Gas equilibration gas modulation refractometry for assessment of pressure with sub-ppm precision

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