Fast Switching Dual Fabry-Perot-Cavity-based Optical Refractometry for Assessment of Gas Refractivity and Density - Estimates of Its Precision, Accuracy, and Temperature Dependence

Abstract: Dual Fabry-Perot-Cavity-based Optical Refractometry (DFCB-OR) have been shown to have excellent potential for characterization of gases, in particular their refractivity and density. However, its performance has in practice been found to be limited by drifts. To remedy this, drift-free DFPC-OR (DF-DFCB-OR) has recently been proposed. Suggested methodologies for realization of a specific type of DF-DFCB-OR, termed Fast Switching DFCB-OR (FS-DFCB-OR), have been presented in an accompanying work. This paper scrutinizes the performance and the limitations of both DF- and FS-DFCB-OR for assessments of refractivity and gas density, in particular their precision, accuracy, and temperature dependence. It is shown that both refractivity and gas density can be assessed by FS-DFCB-OR with a precision in the 10$<sup>{-9}$ range under STP conditions. It is demonstrated that the absolute accuracy is mainly limited by the accuracy by which the instantaneous deformation of the cavity or the higher order virial coefficients can be assessed. It is also shown that the internal accuracy, i.e. the accuracy by which the system can be characterized with respect to an internal standard, can be several orders of magnitude better than the absolute. It is concluded that the temperature dependence of FS-DFCB-OR is exceptionally small, typically in the 10$<sup>{-8}$ to 10$<sup>{-7}$/C range, and primarily caused by thermal expansion of the FPC-spacer material. Finally, this paper discusses means on how to design a FS-DFCB-or system for optimal performance and epitomizes the conclusions of this and our accompanying works regarding both DF- and FS-DFCB-OR in terms of performance and provides an outlook for both techniques. Our works can serve as a basis for future realizations of instrumentation for assessments of gas refractivity and density that can fully benefit from the extraordinary potential of FPC-OR.