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.

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-10−6) 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 (k=2) was estimated to, for the SOP and TOP, [(10mPa)2+(10×10−6P)2]1/2 and [(16mPa)2+(28×10−6P)2]1/2, 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 (k=2) for comparative measurements (27 ppm). This verified that the estimated error budget for the uncorrelated errors holds over this extensive period of time.

Gas Modulation Refractometry (GAMOR) has recently been developed to mitigate drifts in the length of the cavities in Dual-Fabry-Perot Cavity (DFPC) based refractometry. By performing repeated reference assessments with the measurement cavity being evacuated while the reference cavity is held at a constant pressure, the methodology can reduce the influence of the long-term drifts, allowing it to benefit from the high precision of DFPCbased refractometry at short time scales. A novel realization of GAMOR, referred to as Gas Equilibration GAMOR (GEq-GAMOR), that outperforms the original realization of GAMOR, here referred to as Single Cavity Modulated GAMOR (SCM-GAMOR), is presented. It is based upon the fact that the reference measurements are carried out by equalizing the pressures in the two cavities. By this, the time it takes to reach adequate 2 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 an improved long-term characteristics of the GAMOR methodology. The system was characterized with respect to a dead weight piston gauge. It was found that for short integration times (up to 10 min) it can provide a response that exceeds that of the original SCM-GAMOR system by a factor of two. For integration times longer than this, and up to 18 hours, the system shows, for a pressure of 4303 Pa, an integration time independent Allan deviation of 1 mPa (corresponding to a precision, defined as twice the Allan deviation, of 0.5 ppm). This implies that the novel system shows a significant improvement with respect to the original realization of GAMOR for all integration times (by a factor of 8 for an integration time of 18 hours).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, up to ca. 40 measurement cycles (ca. 1.5 hours), a white-noise limited noise of 0.7 mPa (cycle) 1/2 , and minimum Allan deviation of 0.15 mPa. Furthermore, over the pressure range investigated, i.e. in the 2.8 -10.1 kPa range, it shows, with respect to a dead weight piston gauge, a purely linear response. This implies that the system can be used for transfer of calibration over large pressure ranges with exceptional low uncertainty.3

A novel procedure for a robust assessment of cavity deformation in Fabry–Pérot (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 N2 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 N2.