**5. Conclusions and Discussion**

This paper provided scrutiny of the short-term performance capabilities of refractometry instrumentation based on the GAMOR methodology. We did so by comparing two independent refractometry systems coupled to a common dead weight piston gauge (DWPG). In contrast to conventional GAMOR-based refractometry, in which static pressures are assessed by the use of (and averaging over) a series of gas modulation cycles, the short-term assessments are performed *within* individual modulation cycles. More precisely, the short-term response is scrutinized through the use of a methodology in which the pressure, *P*(*t*), is continuously assessed by the shift in the incessantly measured unwrapped beat frequency, Δ*fUW*(*t*), during individual modulation cycles. By this, GAMOR based instrumentation can assess fluctuations of pressures on time scales below the gas modulation time period. In addition, the methodology allows for an investigation of the ability of GAMOR to assess short-term fluctuations of pressures without any influence from the pressure producing and gas delivery system.

Figures **??** and **??** display the typical cycle resolved response from one of the GAMOR instrumentations. The data show that, despite discrete mode jumps, the unwrapped beat frequency provides a continuous signal. The data also show that, in agreement with findings to be mediated by Rubin et al. [**?** ], the response settled, within the resolution of the figure, within a fraction of the gas modulation period (the data do not show any visible drifts over the 80 s long time period denoted *ts*). This vouches for the possibility to assess rapid changes in pressure during this time period.

Figure **??** shows that the simultaneous assessments performed by the two refractometry systems had a high degree of correlation; the deviations in their assessments were not only significantly smaller than those provided by the pressure gauges (which are limited by bit noise on a level orders of magnitude above that of the refractometers), they were also markedly smaller than those of the pressure assessed by either of them. A similarly excellent correlation between the pressure assessments performed by the two refractometers is shown in Figure **??**. This indicates that their precision is significantly better than the stability of the pressure they assess, which implies that the deviations of the assessed pressure are attributable to fluctuations in the pressure in the DWPG and the gas delivery system, rather than to the performance of the refractometers.

These fluctuations can potentially have several causes, e.g., the ambient pressure, the gas temperature, vibrations, or fluctuations in the pressure produced by the DWPG. However, since Figure **??** shows that they take place over seconds, most of these potential causes are improbable. Instead, we presently attribute the most likely cause of the pressure fluctuations to the pressure produced by the DWPG.

Since Figure **??**b indicates that the deviation of the difference assessment for time scales up to a few seconds was 0.04 ppm, it can be concluded that the short-term deviation of the pressure assessment by the use of a single refractometer was 0.03 ppm. Although pressure assessments of 4303 Pa have been demonstrated with an Allan deviation of 0.08 ppm assessed over 10<sup>4</sup> s (corresponding to a standard deviation) [**?** ], this shows that the refractometer systems have better precision than what so far has been demonstrated.

Since data were collected at 4 Hz (given by the finite updating time of the frequency counter) and there was no averaging process in the data acquisition, the bandwidth of the assessments shown in Figure **??** was 2 Hz (given by the Nyqvist theorem). Fundamentally though, this was limited by the cavity linewidth which, in this work, was in the order of 10's of kHz.

With the extraordinary temporal response of the refractometer, this type of instrumentation can not only be used to measure rapid pressure changes and fluctuations, to investigate processes giving rise to such, and resolve the difference between sensor responses and actual pressure changes, it can also be used for characterization of the dynamic responses of pressure gauges (such as Pirani gauges).

Another application is that if the pressure can be kept constant, e.g., within a system regulated by a DWPG or another type of pressure regulator, it can serve as an instrument to characterize the temporal responses of temperature sensors. Finally, under stable conditions, one can isolate acoustic effects in the infrasound region, and hence be used in relation to the dB-scale.

**Author Contributions:** Conceptualization, C.F. and I.S.; methodology, C.F. and M.Z.; software, C.F., I.S., and J.Z.; validation, C.F., I.S., O.A., and M.Z.; formal analysis, C.F.; investigation, C.F.; resources, O.A. and M.Z.; data curation, C.F.; writing—original draft preparation, C.F. and M.Z.; writing—review and editing, C.F., I.S., J.Z., O.A., and M.Z.; visualization, C.F. and I.S.; supervision, O.A. and M.Z.; project administration, O.A. and M.Z.; funding acquisition, O.A and M.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This project (QuantumPascal, 18SIB04) has received funding from the EMPIR programme co-financed by the Participating States and from the European Union's Horizon 2020 research and innovation programme; Vetenskapsrådet (VR) (621-2015-04374 and 621-2020-05105); the UmeåUniversity Industrial doctoral school (IDS-18); the Vinnova Metrology Programme (2017-05013, 2018-04570, and 2019-05029); the Kempe Foundations (1823.U12).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data is contained within the article.

**Conflicts of Interest:** The authors declare no conflict of interest.
