Assessments of refractivity in a Fabry-Perot (FP) cavity by refractometry often encompass a step in which the penetration depth of the light into the mirrors is estimated to correct for the fraction of the cavity length into which no gas can penetrate. However, as it is currently carried out, this procedure is not always coherently performed. Here, we discuss a common pitfall that can be a reason for this and provide a recipe on how to perform FP-cavity-based refractometry without any influence of mirror penetration depth. © 2021 Author(s).
An updated version of an Invar-based dual Fabry-Perot cavity refractometer utilizing the gas modulation methodology has been characterized with regard to its ability to assess gas pressure in the low pressure regime, defined as the regime in which the instrumentation is mainly limited by the constant term a in the [ ( a ) 2 + ( b × P ) 2 ] 1 / 2 expression for the uncertainty. It is first concluded that this ability is predominantly limited by three entities, viz., the empty cavity repeatability, the residual gas pressures in the evacuated (measurement) cavity, and the contamination of the gas residing in the measurement cavity that originates from leaks and outgassing. We then present and utilize methods to separately estimate the uncertainty of the updated refractometer from these entities. It was found that, when utilizing gas modulation cycles of 100 s and when addressing nitrogen, the system can assess pressure in the low pressure regime with an expanded uncertainty ( k = 2 ) of 0.75 mPa, mainly limited by the empty cavity repeatability and outgassing of hydrogen. This is more than 1 order of magnitude below the previously assessed low pressure performance of the instrumentation.
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. © 2021 Author(s).
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 1 mPa (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 0.15 mPa. 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. © 2019 Author(s).
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 N 2). 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. © 2020 Author(s).