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

Martin Zelán, Isak Silander+2 more|arXiv (Cornell University)|Apr 3, 2017

Spectroscopy and Laser Applications3 citations

TL;DR

This paper presents a fast-switching dual Fabry-Perot cavity (FS-DFCB-OR) optical refractometer that enables high-precision, drift-free measurement of gas refractivity and density with sub-ppm accuracy. It achieves a precision of 10⁻⁹ under standard temperature and pressure, minimal temperature dependence (~10⁻⁸/°C), and demonstrates that internal accuracy can exceed absolute accuracy by several orders of magnitude due to stable internal referencing.

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$^{-9}$ 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$^{-8}$ to 10$^{-7}$/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.

Motivation & Objective

• To develop a drift-free, high-precision optical refractometry system for accurate assessment of gas refractivity and density.
• To address performance limitations of conventional dual Fabry-Perot cavity (DFCB-OR) systems caused by thermal and mechanical drifts.
• To evaluate the precision, accuracy, and temperature dependence of the fast-switching DFCB-OR (FS-DFCB-OR) configuration.
• To provide design guidelines for optimizing FS-DFCB-OR systems for maximum performance in gas refractivity and density measurements.

Proposed method

• The system employs two Fabry-Perot cavities operating in a fast-switching mode to enable differential measurement between a reference gas and a sample gas.
• It uses a dual-cavity configuration to cancel common-mode drifts, particularly thermal and mechanical instabilities.
• The method relies on phase or frequency tracking of the cavity modes to extract refractivity and density from optical path length changes.
• It applies accurate expressions for virial coefficients and cavity deformation to correct for non-ideal gas behavior and mechanical distortions.
• The system is calibrated using an internal reference, enabling high internal accuracy independent of absolute calibration uncertainty.
• Thermal expansion of the cavity spacer material is modeled to quantify and minimize temperature-induced errors.

Experimental results

Research questions

• RQ1 What is the achievable precision of FS-DFCB-OR for measuring gas refractivity and density under standard conditions?
• RQ2 How does the absolute accuracy of FS-DFCB-OR depend on the accuracy of cavity deformation and virial coefficient measurements?
• RQ3 What is the temperature dependence of the FS-DFCB-OR system, and what physical factors dominate it?
• RQ4 How does the internal accuracy of FS-DFCB-OR compare to its absolute accuracy, and what enables this difference?
• RQ5 What design principles optimize the performance of FS-DFCB-OR for high-precision gas metrology?

Key findings

• FS-DFCB-OR achieves a precision of 10⁻⁹ in refractivity and gas density measurements under standard temperature and pressure (STP) conditions.
• The absolute accuracy is primarily limited by uncertainties in the measurement of cavity deformation and higher-order virial coefficients.
• Internal accuracy—defined as the system’s ability to resolve differences relative to an internal standard—can be several orders of magnitude better than absolute accuracy.
• The temperature dependence of the system is exceptionally low, typically in the range of 10⁻⁸ to 10⁻⁷ /°C, with thermal expansion of the cavity spacer material being the dominant source.
• The system’s performance is robust against drift, making it suitable for long-term, high-precision gas refractometry.
• The results provide a foundation for realizing next-generation optical refractometers that fully exploit the potential of Fabry-Perot cavity-based refractometry.