Patrick F. Egan

Absolute refractometry of dry gas to ±3 parts in 10 9

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.

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.

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.

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.

Calibrating Laser Vacuum Wavelength With a GPS-Based Optical Frequency Comb

Abstract: The Global Positioning System (GPS) can deliver an exceptionally accurate frequency standard to any point in the world. When the GPS signal is used to control an optical frequency comb, the comb + GPS system provides laser light with well-known frequencies (or equivalently, vacuum wavelengths) over much of the optical spectrum between 0.53 μm and 2 μm. The comb vacuum wavelengths can serve as primary length standards for calibration of the wavelength of metrology lasers, and the uncertainties of the comb wavelengths are sufficiently low to be suitable for almost any imaginable task associated with length metrology. The GPS signal is “traceable” in the sense that its uncertainty is continually assessed via measurements at NIST/Boulder, and results of the measurements (in effect, “calibration reports”) are published on the web. Thus it can potentially deliver a traceable standard of unprecedented accuracy to any laboratory, but how can the user be certain that the resulting laser calibrations have comparable accuracy? These calibrations depend not only on the GPS signal but also on much additional equipment (including a disciplined oscillator, optical frequency comb, and optics/electronics for beat frequency measurement), and any such system might contain additional sources of error if it is poorly designed or operated by inexperienced personnel. However, it is shown that internal consistency checks can be effectively used to verify the proper operation of the measurement system. In many respects these internal consistency checks provide better confidence in the results than what is likely to be achieved by more traditional methods of establishing traceability, such as sending an instrument or artifact to a national metrology institute for calibration. A relative expanded uncertainty of less than 2 × 10−12 can be verified for laser calibrations, and this is sufficient even for the most demanding applications of dimensional metrology.

Candidates to replace R-12 as a radiator gas in Cherenkov detectors

Dichlorodifluoromethane (R-12) has been widely used as a radiator gas in pressure threshold Cherenkov detectors for high-energy particle physics. However, that compound is becoming unavailable due to the Montreal Protocol. To find a replacement with suitably high refractive index, we use a combination of theory and experiment to examine the polarizability and refractivity of several non-ozone-depleting compounds. Our measurements show that the fourth-generation refrigerants R-1234yf (2,3,3,3-tetrafluoropropene) and R-1234ze(E) (trans-1,3,3,3-tetrafluoropropene) have sufficient refractivity to replace R-12 in this application. If the slight flammability of these compounds is a problem, two nonflammable alternatives are R-218 (octafluoropropane), which has a high Global Warming Potential, and R-13I1 (trifluoroiodomethane), which has low Ozone Depletion Potential and Global Warming Potential but may not be sufficiently inert.

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.

Temperature Stabilization System with Millikelvin Gradients for Air Refractometry Measurements Below the 10^-8 Level

Abstract: Refractometry of air is a central problem for interferometer-based dimensional measurements. Refractometry at the 10−9 level is only valid if air temperature gradients are controlled at the millikelvin (mK) level. Very precise tests of second-generation National Institute of Standards and Technology (NIST) refractometers involve comparing two instruments (two optical cavities made from ultralow expansion glass) that are located in nominally the same environment; temperature gradients must be kept below a few millikelvin to achieve satisfactory precision of these tests. This paper describes a thermal stabilization scheme that maintains < 1 mK thermal gradients over 100 h in a 0.5 m × 0.15 m × 0.15 m volume. The approach uses passive (aluminum envelopes and foam insulation) and active (thermistors, foil heaters, and proportional–integral–derivative control) temperature stabilization. Thermal gradients are sensed with thermocouples and a nanovoltmeter and switch; the reference junctions of the thermocouples being in thermal contact with a thermistor temperature standard. Indirect evidence shows that performance is better than the < 1 mK uncertainty of measuring temperature gradients, the uncertainty of which is due to limitations of the nanovoltmeter and switch.

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.