Measured relationship between thermodynamic pressure and refractivity for six candidate gases in laser barometry.

Laser refractometers are approaching accuracy levels where gas pressures in the range 1 Pa < p < 1 MPa inferred by measurements of gas refractivity at a known temperature will be competitive with the best existing pressure standards and sensors. Here, the authors develop the relationship between pressure and refractivity p = c 1 ⋅ ( n - 1 ) + c 2 ⋅ ( n - 1 ) 2 + c 3 ⋅ ( n - 1 ) 3 + ⋯ , via measurement at T = 293.1529(13) K and λ = 632.9908(2) nm for p ≤ 500 kPa. The authors give values of the coefficients c 1, c 2, c 3 for six gases: Ne, Ar, Xe, N2, CO2, and N2O. For each gas, the resulting molar polarizability A R ≡ 2 R T 3 c 1 has a standard uncertainty within 16 × 10-6·A R . In these experiments, pressure was realized via measurements of helium refractivity at a known temperature: for He, the relationship between pressure and refractivity is known through calculation much more accurately than it can presently be measured. This feature allowed them to calibrate a pressure transducer in situ with helium and subsequently use the transducer to accurately gage the relationship between pressure and refractivity on an isotherm for other gases of interest.

Cell-based refractometer for pascal realization.

We describe a method for determining the density of helium via measurements of optical refractivity. In combination with the equation of state, this allows realization of the pascal. Our apparatus is based on the integration of a gas triple-cell into a quasi-monolithic heterodyne interferometer: the stability of the interferometer is ±50 pm over 10 h. We claim the contribution of cell window thinning to pathlength uncertainty can be canceled within an uncertainty of 0.37 fm/Pa per window pass, of which for our 25 cm cell length corresponds to a fractional error of 9.3×10-6 in the measure of helium refractivity. We report the ratio (n-1)N2 /(n-1)He=8.570354(13) at p=367.420(4) kPa, T=293.1529(13) K and λ=632.9908(6) nm, which can be used to calibrate less-accurate refractometers. By measuring helium refractivity at known temperature and pressure, we determined the Boltzmann constant with standard uncertainty kB=1.380652(17)×10-23 JK-1.

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.

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.

Weak-value thermostat with 0.2 mK precision.

A new laser-based thermostat sensitive to 0.2 mK at room temperature is reported. The method utilizes a fluid-filled prism and interferometric weak-value amplification to sense nanoradian deviations of a laser beam: due to the high thermo-optic coefficient of the fluid (colorless fluorocarbon), the deviation angle through the prism is sensitive to temperature. We estimate the daily stability of our device to be 0.2 mK, which is limited by drifts in the apparatus, and the narrow 20 mK capture range is the price paid for the weak measurement.

Absolute refractometry of dry gas to ±3 parts in 109.

We present a method of measuring the refractive index of dry gases absolutely at 632.8 nm wavelength using a Fabry-Perot cavity with an expanded uncertainty of <3×10⁻9 (coverage factor k=2). The main contribution to this uncertainty is how well vacuum-to-atmosphere compression effects (physical length variation) in the cavities can be corrected. This paper describes the technique and reports reference values for the refractive indices of nitrogen and argon gases at 100 kPa and 20 °C with an expanded uncertainty of <9×10⁻9 (coverage factor k=2), with the additional and larger part of this uncertainty coming from the pressure and temperature measurement.

An Optical Frequency Comb Tied to GPS for Laser Frequency/Wavelength Calibration.

Optical frequency combs can be employed over a broad spectral range to calibrate laser frequency or vacuum wavelength. This article describes procedures and techniques utilized in the Precision Engineering Division of NIST (National Institute of Standards and Technology) for comb-based calibration of laser wavelength, including a discussion of ancillary measurements such as determining the mode order. The underlying purpose of these calibrations is to provide traceable standards in support of length measurement. The relative uncertainty needed to fulfill this goal is typically 10(-8) and never below 10(-12), very modest requirements compared to the capabilities of comb-based frequency metrology. In this accuracy range the Global Positioning System (GPS) serves as an excellent frequency reference that can provide the traceable underpinning of the measurement. This article describes techniques that can be used to completely characterize measurement errors in a GPS-based comb system and thus achieve full confidence in measurement results.

Uncertainties in Small-Angle Measurement Systems Used to Calibrate Angle Artifacts.

We have studied a number of effects that can give rise to errors in small-angle measurement systems when they are used to calibrate artifacts such as optical polygons. Of these sources of uncertainty, the most difficult to quantify are errors associated with the measurement of imperfect, non-flat faces of the artifact, causing the instrument to misinterpret the average orientation of the surface. In an attempt to shed some light on these errors, we have compared autocollimator measurements to angle measurements made with a Fizeau phase-shifting interferometer. These two instruments have very different operating principles and implement different definitions of the orientation of a surface, but (surprisingly) we have not yet seen any clear differences between results obtained with the autocollimator and with the interferometer. The interferometer is in some respects an attractive alternative to an autocollimator for small-angle measurement; it implements an unambiguous and robust definition of surface orientation in terms of the tilt of a best-fit plane, and it is easier to quantify likely errors of the interferometer measurements than to evaluate autocollimator uncertainty.