QuantumPascal Report A114 Pressure-induced cavity deformation in Fabry-Pérot refractometry - Characterizations and Recommendations

Fabry-Perot (FP) cavity based refractometers are subjected to pressureinduced deformation when exposed to gas that changes their lengths. Unless this is taken into consideration properly, pressure assessments can be adversely affected. It is therefore of importance to accurately assess the amount of deformation of such cavities. Two major means of doing this are simulations and experimental characterizations. In the EMPIR project ”QuantumPascal”, several FPC systems have been characterized with respect to their pressure-induced deformation, (ΔL/L)/P, by simulations. It was found that their pressure-normalized relative deformation ranges over more than a factor of 35, from 0.2 × 10⁻¹² to 7.8 × 10⁻¹² Pa⁻¹. More importantly, several of these characterizations were found to provide assessments of the deformation that are limited by either the ability to model the system in the simulation program or the uncertainty in the material parameters used, e.g. Young’s modulus and Poisson ratio, which often are in the percentage to permille range. Only two simulations demonstrated assessments of deformation with an uncertainty that allows for assessments of pressures with the 10 ppm targeted relative uncertainty. Experimental characterizations do not suffer from the same type of limitations. On the other hand, they are often restricted by various types of external disturbances. As a means to mitigate such, a novel robust methodology has been developed that allows for assessments of cavity deformation that are independent of systematic pressure-independent errors in both the reference pressure and the assessment of gas temperature, and, when carried out by use of the gas modulation refractivity (GAMOR) methodology, also is insensitive to gas leakages and outgassing. It was demonstrated that when a high-precision (sub-ppm) refractometer is characterized according to this methodology, and when high purity gases are used, the uncertainty in the deformation solely contributed to the uncertainty in the assessment of pressure of N₂ with 1 ppm, thus allowing it to be assessed in an otherwise well-characterized system well within the 10 ppm targeted uncertainty. This methodology was, in this project, applied to the assessment of deformation in several FPC systems. In total, four FPC systems were characterized by various experimental means. Recommendations for how to realize FP-based refractometer systems with a minimum of deformation are given.