Capability of commercial trackers as compensators for the absolute refractive index of air

Abstract

A procedure is presented which calibrates a wavelength/refractive-index tracker, so that it can compensate for the absolute refractive index of air within 3 × 10−8 ⋅ n. The procedure employs ultrahigh-purity helium and argon as reference gases of known n(p, T) to deduce the two unknown parameters in the working equation of the tracker: gas pathlength and pressure-induced distortion error. The performance of the gas calibration procedure is evaluated by comparing the corrected tracker against a master refractometer based on a Fabry–Perot cavity in nitrogen, a third reference gas of known n(p, T). In nitrogen, the calibrated trackers demonstrate accuracy at the level of 4 × 10−9 ⋅ n. Testing in a fourth reference gas—water vapor—reveals that the working equation of the trackers must include a third unknown parameter: an end-effect caused by a moisture-dependence of the reflection phase-shift. Correcting for this moisture-related error represents the largest contribution to measurement uncertainty, and explains why performance of the calibrated trackers is an order-of-magnitude worse in moist air than in pure gas. In air, the Fabry–Perot cavity-based refractometer performs within 5 × 10−9 ⋅ n, but is not a commercially-available device.