SI Length and Traceability

Summary

To enable our highest accuracy calibrations and NIST advanced research efforts, we maintain and develop methods to provide traceability to the meter via laser frequency/wavelength. The most significant source of uncertainty in most very high accuracy length measurements is the value of the index of refraction of air. The development of accurate refractometers will increase the accuracy of nearly all laser-based length measurements and is crucial to meet increasing demands from industry for high accuracy traceability. Our efforts also enabling new high-accuracy optical wavelength-based methods to realize pressure and temperature.

Description

Laser interferometry, which measures distances in terms of light wavelength, provides the backbone of top-level length metrology in industry and science. This project develops techniques to facilitate the tie between interferometer-based length measurements and the SI definition of length (in terms of the second). Integral to providing this link are:

1. Optical frequency combs, which can use GPS timing signals to provide optical frequency/vacuum wavelength standards at almost any desired wavelength and anywhere in the world. These wavelengths are directly traceable to the definition of the meter and can be of arbitrarily high accuracy. The broad range of wavelengths available from a comb allows calibration of new sources at useful wavelengths for dimensional metrology, thus enabling innovation.
2. Refractometers, linking vacuum wavelength to air wavelength. Determination of vacuum wavelength is straightforward via the comb, but practical interferometry must be done in air, and the air refractive index is often a limiting factor for ultra-high accuracy measurements. To overcome this problem, we are developing refractometers to measure the refractive index of air with a target uncertainty below 1 part in 10⁸.

Background

• Our customers demand ever-lower calibration uncertainties, which for longer lengths are often limited by uncertainty in air refractive index. The semiconductor industry envisages a need for fractional accuracies of dimensional measurement in the 10^-8 regime (ITRS roadmap).
• Currently, this low level of uncertainty can only be attained working in vacuum, but this option is not attractive (low throughput, inconvenience, and expense) whether in a production environment (such as a stepper) or in the laboratory (such as the next-generation NIST Linescale).
• If we are to maintain leadership and provide tomorrow's tools for length metrology at the highest levels of accuracy, we must solve the problem of air refractive index measurement, reducing uncertainties well below 1 part in 10⁸.

This project has made important steps toward reaching that goal. Excellent results have been achieved for dry gases (absolute refractometry to ±2 parts in 10¹⁰), and current efforts focus on overcoming problems associated with air humidity.

Major Accomplishments

Wavelength metrology

• 2010: Developed a procedure to accurately calibrate a red helium neon laser against an optical frequency comb. Article available: https://doi.org/10.6028/jres.115.028
• 2024: Introduced a method to calibrate a wavemeter directly traceable to the SI second via the optical frequency comb. Demonstrated wavelength metrology capability at 633 nm, 1310 nm, 1520 nm to 1570 nm, and 1625 nm. Article available: https://doi.org/10.1088/1681-7575/ad8927. Publicity release: NIST Offers New Calibration Service for Wavemeters

Refractometry

• 2011: Developed a refractometer based on an ultrastable Fabry-Perot cavity. Refractive index was read out via change in the resonance frequency of the cavity. Some problems with adsorption of water into mirror coatings were identified. Article available: https://doi.org/10.1364/AO.50.003076
• 2013: Introduced the concept of using "weak value amplification" to boost the angular deflection in a prism-based refractometer. Simple optics created a thermostat with 0.2 mK sensitivity. Article available: https://doi.org/10.1364/OL.37.004991
• 2015: Experimentally demonstrated a dual Fabry-Perot cavity design. The device does not require an external stabilized laser source, and it has reduced distortion error and dimensional drift. Article available: https://doi.org/10.1364/OL.40.003945. Publicity release: Thin, Strong Bond for Vacuum Seal. Publicity release: World's First Photonic Pressure Sensor Outshines Traditional Mercury Standard.
• 2017: Introduced MIRE—the monolithic interferometer for refractometry. The system was based on a gas cell inserted into the arms of a heterodyne interferometer. The system demonstrated ±50 pm stability over 10 h, making it one of the world's most stable Michelson interferometers. Article available: https://doi.org/10.1364/OL.42.002944. Publicity release:  Better Accuracy Out of Thin (or Thick) Air.
• 2022:  Outline a procedure on how a commercial refractive index “tracker” may be used to compensate for the absolute refractive index of air. The procedure is essentially a three-gas calibration.  Two gases—say helium and argon—are used to calibrate the optical pathlength and distortion coefficient of the tracker. The third gas—water vapor—corrects for the influence of water adsorption into mirror coatings. Article available: https://doi.org/10.1016/j.precisioneng.2022.04.011.  Script implementation for two candidate systems also available: https://doi.org/10.18434/mds2-2568
• 2024: Optimized the thermal response time of a Fabry-Perot refractometer. Settling times as fast as 800 s have been demonstrated for gas charges are large as 0.1 MPa. Article available: https://doi.org/10.1063/5.0234184

Material measures and reference artifacts

• 2018: Assisted colleagues to establish the refractive index of the refrigerants R-1234yf and R-1234ze(E). The application was particle physics experiments at CERN which employ Cherenkov detectors. At present, Cherenkov detectors at CERN use gases which either have a high Ozone Depletion Potential (and would be phased-out under the Montreal Protocol) or a high Global Warming Potential. Measurements revealed that the compounds studied would be ideal replacements for the high ODP refrigerants currently used. Article available: https://doi.org/10.1016/j.nimb.2018.04.006
• 2019: Outlined a framework on how the optical properties of gases might be used to establish an optical pressure scale, with a traceability path to the SI kelvin. Article available: https://doi.org/10.1116/1.5092185
• 2024: Established highly accurate measurement of water vapor refractivity at 633 nm and 1542 nm, and compared with past measurements, existing reference formulations, and recent ab initio calculation. Arguably, uncertainty in the refractivity of water vapor (at wavelengths apart from 633 nm) is the main limitation on the accurate equation-based compensation of air refractive index, used throughout the world in all high accuracy dimensional metrology labs. Article at 633 nm: https://doi.org/10.1007/s10765-024-03380-w. Article at 1542 nm: https://doi.org/10.1007/s10765-024-03412-5
• 2024: Measured the thermal expansion coefficient of fused quartz glass to within 6 x 10^-10 /K. The establishment of such a material standard is crucial for the accurate calibration of a more practical dilatometer. Article available: https://doi.org/10.1007/s10765-024-03422-3. Dataset also available: https://doi.org/10.18434/mds2-2697
• 2024: Outlined a procedure to convert a dimensional dataset of a piston and cylinder to the effective area of a mechanical pressure generator. The procedure established the nation’s most accurate mechanical pressure scale, traceable to the SI meter (via diameter measurement). Article available: https://doi.org/10.1088/1681-7575/ad77db. Dataset and conversion scripts also available: https://doi.org/10.18434/mds2-2698

Figure 4.  Rapid thermal response refractometer.  The cavity mode (laser beam passing through the mirrors) and the thermometer are both enclosed in the same block of aluminum.  When the pressure vessel is filled with gas, the gradients between the cavity mode and thermometer settle to within 0.1 mK after 800 s.

Credit: NIST

Figure 5.  The “birdcage” of a piston-cylinder assembly is constructed from accurate measurements of two-point diameter and highly precise traces of roundness and straightness.  Combining all dimensional measurement together allows an estimate of the “effective area” of the artifact, which is roughly the cross-sectional area at the halfway point between piston and sleeve.  The effective area of a piston-cylinder assembly underpins the nation’s pressure scale.

Credit: NIST

Technology transfer

Much of the refractometry work is available for licensing. Patent from 2019 available: Deformometer for Determining Deformation of an Optical Cavity Optic

Requests for specialty measurements of thermal expansion or dimensional stability could be accommodated via cooperative research and development agreement.  See mechanisms at the technology partnership office.