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

For several years we have been studying the use of Fabry-Perot interferometers for precise measurement of the refractive index of gasses, where the primary motivation has been to improve interferometer-based length measurement. Because the refractive index of a gas depends on its pressure and temperature, we can also use refractive index to monitor either of these quantities if the second is known. Recently we have embarked on a project that will utilize refractive index to infer pressure with a smaller measurement uncertainty than is currently possible, hoping to reach a relative standard uncertainty of 1.410. The projected uncertainty budget is currently dominated by uncertainty of the Boltzmann constant, but following the coming redefinition of SI units, the Boltzmann uncertainty will be replaced by uncertainty in the temperature scale, at which point refractive index measurements can be expected to play a central role in precise realization of thermodynamic temperature. Dimensional metrology with picometer uncertainties is the core of our 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. The intrinsic precision achievable with Fabry-Perot cavities far exceeds our needed accuracy, but two or more independent interferometers have never been compared to such high accuracy when undergoing macroscopic displacements. The 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. Our proposed experimental design will minimize such errors and provide additional metrology (including angle measurements with nanoradian precision) needed to correct the residual errors. Learning Objectives: Understanding sources of uncertainty in ultra-high accuracy dimensional measurements.