QuantumPascal Report A143 Gas modulated Fabry-Perot-cavity-based refractometry (GAMOR) — Guide to its basic features, performance, and implementation

Although Fabry-Perot-cavity (FPC) based refractometry has demonstrated an extraordinary potential for assessment of refractivity and pressure, such systems are often adversely affected by various type of disturbances (drifts, fluctuations, and noise). The realization of high-performance systems therefore requires an exceptional mechanical stability, a low noise electrical environment, and temperature stabilized conditions. The gas modulation refractometry (GAMOR) methodology has been developed to automatically mitigate the influence of various types of disturbances on assessments of refractivity. It is based on two principles: (i) an assessment of the refractivity of the gas in the measurement cavity by a frequent referencing of filled measurement cavity beat frequencies to evacuated cavity beat frequencies; and (ii) an estimate of the empty measurement cavity beat frequency by an interpolation between two evacuated beat frequency assessments performed just before and after the filled cavity assessments. By this, the methodology can swiftly mitigate the influence of various types of disturbances in refractometry systems, e.g. changes in length of the cavity caused by relaxations or drifts in the temperature of the spacer and drifts from gas leakages and outgassing. The methodology has demonstrated an outstanding performance regarding precision; it has repeatedly demonstrated assessments with sub parts-per-million precision. This guide provides a compilation of the principles, properties, and performance of the GAMOR methodology applied to dual FPC (DFPC) refractometry. First, a short introduction to ordinary FPC-based refractometry is given, where its susceptibility to various types of disturbances is highlighted. The guide then provides general expressions for how to assess refractivity from measurements of shifts of the beat frequency and mode hops that serve as the basis for FPC-based refractometry in general as well as for GAMOR based instrumentation. Pressure is then assessed by the use of the Lorentz-Lorenz expression and an equation of state. This is followed by explanations and descriptions of the ability of the GAMOR methodology to mitigate the influence of fluctuations and drifts. Next, a short description of the most commonly used experimental set-up, viz. an Invar-based DFPC system, is given. This is followed by an illustration of the operation and performance of the methodology. A summary of the most important achievements of the GAMOR methodology is given. After an experimental verification of the ability of the GAMOR methodology to mitigate the influence of fluctuations and drifts, its precision is illustrated under various conditions. It is shown that an Invar-based FPC system can provide a sub-0.1 ppm precision when addressing vacuum pressures and that two GAMOR based refractomomters coupled to the same pressure gauge can provide a short-term correlation that is well into the 10−8 range. It is also shown that these properties have allowed for the development of disturbance-resistant methodologies for assessment of cavity deformation and mirrors penetration depth. To assess its uncertainty, also the influence of pV-work and its ability to assess the gas temperature have been addressed. It has been concluded that GAMOR-based instrumentation can provide an expanded uncertainty (k=2) of [(10 mPa)2 + (10 × 10−6P)2]1/2. It is also shown that its extraordinary properties allows for realization of transportable set-ups. Finally, to facilitate the dissemination of the GAMOR methodology, this guide provides a recipe on how to implement GAMOR in a DFPC-system.Acknowledgement: This project '18SIB04 QuantumPascal' has received funding from the EMPIR programme co-financed by the Participating States and from the European Union's Horizon 2020 research and innovation programme. More information can be found on the website: https://www.ptb.de/empir2019/quantumpascal