Jacob E. Ricker

Performance of a dual Fabry–Perot cavity refractometer

We have built and characterized a refractometer that utilizes two Fabry-Perot cavities formed on a dimensionally stable spacer. In the typical mode of operation, one cavity is held at vacuum, and the other cavity is filled with nitrogen gas. The differential change in length between the cavities is measured as the difference in frequency between two helium-neon lasers, one locked to the resonance of each cavity. This differential change in optical length is a measure of the gas refractivity. Using the known values for the molar refractivity and virial coefficients of nitrogen, and accounting for cavity length distortions, the device can be used as a high-resolution, multi-decade pressure sensor. We define a reference value for nitrogen refractivity as n-1=(26485.28±0.3)×10(-8) at p=100.0000  kPa, T=302.9190  K, and λ(vac)=632.9908  nm. We compare pressure determinations via the refractometer and the reference value to a mercury manometer.

Comparison measurements of low-pressure between a laser refractometer and ultrasonic manometer

We have developed a new low-pressure sensor which is based on the measurement of (nitrogen) gas refractivity inside a Fabry-Perot cavity. We compare pressure determinations via this laser refractometer to that of well-established ultrasonic manometers throughout the range 100 Pa to 180 000 Pa. The refractometer demonstrates 10(-6) ⋅ p reproducibility for p > 100 Pa, and this precision outperforms a manometer. We also claim the refractometer has an expanded uncertainty of U(pFP) = [(2.0 mPa)(2) + (8.8 × 10(-6) ⋅ p)(2)](1/2), as realized through the properties of nitrogen gas; we argue that a transfer of the pascal to p < 1 kPa using a laser refractometer is more accurate than the current primary realization.

Final report on the key comparison CCM.P-K4.2012 in absolute pressure from 1 Pa to 10 kPa

The report summarizes the Consultative Committee for Mass (CCM) key comparison CCM.P-K4.2012 for absolute pressure spanning the range of 1 Pa to 10 000 Pa. The comparison was carried out at six National Metrology Institutes (NMIs), including National Institute of Standards and Technology (NIST), Physikalisch-Technische Bundesanstalt (PTB), Czech Metrology Institute (CMI), National Metrology Institute of Japan (NMIJ), Centro Nacional de Metrología (CENAM), and DI Mendeleyev Institute for Metrology (VNIIM). The comparison was made via a calibrated transfer standard measured at each of the NMIs facilities using their laboratory standard during the period May 2012 to September 2013. The transfer package constructed for this comparison preformed as designed and provided a stable artifact to compare laboratory standards. Overall the participants were found to be statistically equivalent to the key comparison reference value.

Review Article: Quantum-based vacuum metrology at the National Institute of Standards and Technology

The measurement science in realizing and disseminating the unit for pressure in the International System of Units, the pascal (Pa), has been the subject of much interest at the National Institute of Standards and Technology (NIST). Modern optical-based techniques for pascal metrology have been investigated, including multiphoton ionization and cavity ringdown spectroscopy. Work is ongoing to recast the pascal in terms of quantum properties and fundamental constants and in doing so make vacuum metrology consistent with the global trend toward quantum-based metrology. NIST has ongoing projects that interrogate the index of refraction of a gas using an optical cavity for low vacuum, and count background particles in high vacuum to extreme high vacuum using trapped laser-cooled atoms.The measurement science in realizing and disseminating the unit for pressure in the International System of Units, the pascal (Pa), has been the subject of much interest at the National Institute of Standards and Technology (NIST). Modern optical-based techniques for pascal metrology have been investigated, including multiphoton ionization and cavity ringdown spectroscopy. Work is ongoing to recast the pascal in terms of quantum properties and fundamental constants and in doing so make vacuum metrology consistent with the global trend toward quantum-based metrology. NIST has ongoing projects that interrogate the index of refraction of a gas using an optical cavity for low vacuum, and count background particles in high vacuum to extreme high vacuum using trapped laser-cooled atoms.

Metrology for comparison of displacements at the picometer level

An apparatus capable of comparing displacements with picometer accuracy is currently being designed at NIST. In principle, we wish to compare one displacement in vacuum to a second, equal displacement in gas, in order to determine gas refractive index. If the gas is helium, the refractive index is expected to be amenable to high-accuracy ab initio calculations relating refractive index to gas density or to the ratio of pressure and temperature (P/T); the measured refractive index can then be used to infer (P/T) with an accuracy goal of about 1×10-6 (relative standard uncertainty). If either the pressure or temperature is known, the refractive index measurement will allow us to determine the second quantity. Our goal is to achieve an uncertainty limited primarily by the uncertainty of the Boltzmann constant (before redefinition of SI units, which will give the Boltzmann constant a defined value). The technique is an optical analog of dielectric constant gas thermometry and can be used in a similar manner. The dimensional metrology is uniquely challenging, requiring picometer-level uncertainty in the comparison of the displacements.

Quantum-based vacuum metrology at NIST

The measurement science in realizing and disseminating the unit for pressure in the International System of Units (SI), the pascal (Pa), has been the subject of much interest at the National Institute of Standards and Technology (NIST). Modern optical-based techniques for pascal metrology have been investigated, including multi-photon ionization and cavity ringdown spectroscopy. Work is ongoing to recast the pascal in terms of quantum properties and fundamental constants and in so doing, make vacuum metrology consistent with the global trend toward quantum-based metrology. NIST has ongoing projects that interrogate the index of refraction of a gas using an optical cavity for low vacuum, and count background particles in high vacuum to extreme high vacuum using trapped laser-cooled atoms.

Laser refractometer as a transfer standard of the pascal

We have developed a new low pressure sensor which is based on the measurement of (nitrogen) gas refractivity inside a Fabry-Perot (FP) cavity. We compare pressure determinations via this laser refractometer to that of well-established ultrasonic manometers throughout the range 100Pa to 100000Pa. The refractometer demonstrates 10^-6 precision for p > 50 kPa; - as good or better than the manometer - we argue that a laser refractometer represents a state-of-the-art transfer standard of the pascal. We also claim the refractometer has an accuracy of U(p_FP) = [(16mPa)² + (11.9 × 10^-6 · p)²]^1/2, as realized through the properties of nitrogen gas.

Primary pressure standard based on piston-cylinder assemblies. Calculation of effective cross sectional area based on rarefied gas dynamics

Currently, the piston-cylinder assembly known as PG39 is used as a primary pressure standard at the National Institute of Standards and Technology (NIST) in the range of 20 kPa to 1 MPa with a standard uncertainty of as evaluated in 2006. An approximate model of gas flow through the crevice between the piston and sleeve contributed significantly to this uncertainty. The aim of this work is to revise the previous effective cross sectional area of PG39 and its uncertainty by carrying out more exact calculations that consider the effects of rarefied gas flow. The effective cross sectional area is completely determined by the pressure distribution in the crevice. Once the pressure distribution is known, the elastic deformations of both piston and sleeve are calculated by finite element analysis. Then, the pressure distribution is recalculated iteratively for the new crevice dimension. As a result, a new value of the effective area is obtained with a relative difference of from the previous one. Moreover, this approach allows us to reduce significantly the standard uncertainty related to the gas flow model so that the total uncertainty is decreased by a factor of three.

Picometer metrology for precise measurement of refractive index, pressure, and temperature

Abstract: Fabry-Perot interferometers can be used for very precise measurement of the refractive index of gasses. This can enable increased accuracy of interferometer-based length measurement. In addition, because the refractive index of a gas depends on its pressure and temperature, measurements of refractive index can be used to monitor either one of these quantities if the second is known. Recently we have embarked on a project with a goal of measuring pressure with a relative standard uncertainty below 1.4 × 10−6. Dimensional metrology with picometer uncertainties is the core of this technique and is the subject of this paper. Refractive index will be measured by comparing two precisely equal displacements (150 mm), where one displacement is in vacuum and the second is in helium and will appear to be slightly longer due to the refractive index. The two displacements must be compared with < 3 pm uncertainty. Major challenges include many of the typical sources of error in dimensional measurement, such as Abbe errors, alignment errors, material dimensional stability, etc. Careful consideration must be given to second-order effects that are not normally large enough to merit mention. The proposed experimental design will minimize the major sources of error while providing additional metrology (including angle measurements with nanoradian precision) to correct residual errors.