*4.5. Evaluation of the Degree of Short-Term Concordance between the Two Refractometers*

To properly evaluate the degree of short-term concordance between assessments made by the two refractometers, they were jointly connected to the DWPG while extraordinarily long gas modulation cycles (300 s) were used (each comprising filling and evacuation periods of 250 and 50 s, respectively). A series of 20 such gas modulation cycles (which thus took 100 min) were performed. To reduce the load on the turbo pump, which was significantly affected by the repeated out pumping of gas at high pressure, this evaluation was performed at a set pressure of 16 kPa.

Figure **??** shows two typical consecutive modulation cycles. Figure **??**a–c encompass the same information, although Figure **??**b,c are zooms of the data with 102 and 104 times magnification of (a), respectively.

The set pressure of the DWPG, estimated by use of Equation (**??**), is marked with the black (almost fully horizontal) curve. The pressure readings from the pressure gauges in the SOP and TOP systems, *GS*.1 and *GT*.1, respectively, are represented by the green and purple curves, respectively. The SOP and TOP refractometry signals are represented by the blue and red curves, respectively. In this comparison, the gauges and the refractometers have, for clarity, been adjusted by an offset (for SOP and TOP by 0.11 and 0.12 Pa, respectively) to overlap the set pressure of the DWPG. It is worth noting that said adjustments are well within their uncertainty budgets and the uncertainty of the DWPG (from the uncertainty presented in Section **??**, at 16 kPa the SOP, TOP, and DWPG uncertainties are 0.16, 0.45, and 0.66 Pa, respectively). It also does not affect their short-term performance.

It is noteworthy that, in Figure **??**a,b, the refractometer signals are not visible. This is due to the fact that they fluctuated less than the thickness of the DWPG curve and are hence hidden behind it. In Figure **??**b, the pressure gauge readings (the green and purple curves) show bit noise; i.e., they fluctuate between two bits, an amount of 4 Pa (corresponding to 250 ppm of 16 kPa).

In Figure **??**c, the gauges are off-scale, but the fluctuations of the refractometer signals are clearly visible. It is also worth noting that although there are significant fluctuations in both refractometer signals, there is a large degree of concordance between them. There is a slight tendency (predominantly seen during the first 50 s of the cycles) that the response of the TOP drifts with respect to that of the SOP. This is attributed to the fact that the gas lines to the TOP, because of practical reasons, had to be significantly longer than those to the SOP. This implies that the evacuation of the TOP during the evacuation cycle was

not as efficient as that of the SOP. Hence, when the gas filling cycle commenced, there was a slightly higher residual pressure in the reference cavity of the TOP than that of the SOP. During the gas filling cycle, in which the data in Figure **??**c were taken, and during which the reference cavities were constantly evacuated, the reference cavity of the TOP was further pumped down, resulting in an artificial drift of the TOP signal during the first 50 s of the gas filling cycle. It is important to note that this neither affects the level of correlation, nor does it imply that the GAMOR refractometers drift under normal working conditions; this drift takes place only because of the fact that the TOP system in this work, because of practical reasons, had to be connected to the gas system with unusually long gas lines.

To emphasize the degree of concordance of the two refractometer signals, 70 s of the pressures assessed by the refractometers depicted in the first cycle of Figure **??** are plotted at an enlarged scale in Figure **??**a.

**Figure 7.** The 250 s parts of two consecutive (300 s long) gas modulation cycles when the measurement cavities contain gas for a DWPG set pressure of 16 kPa. The three panels display the same data centered around the set pressure but with dissimilar y-scales: in panel (**a**) with a scale of ±3%; panel (**b**) with a scale of ±300 ppm; and panel (**c**) with a scale of ±3 ppm. Black curves: the DWPG; green curves: the SOP gauge; purple curves: the TOP gauge; blue curves: the SOP; and red curves: the TOP.

The degree of concordance between the two refractometer signals in Figure **??**a is striking and impressive; they jointly and concurrently illustrate a common fluctuating pressure. The fact that they detected in unison the same fluctuation indicates that the signals originated from the DWPG and gas delivery system rather than from the refractometers.

To assess the degree of correlation between the two refractometer signals, they are plotted against one another in Figure **??**b. The data show that while the pressure produced by the DWPG and the gas delivery system fluctuated more than 5 ppm, the two refractometer signals differed significantly less than 0.5 ppm. A correlation analysis of the data provides a remarkable correlation coefficient of the two refractometry signals of 0.995.

To complement the correlation analysis above, the measurement data were also exposed to an Allan variance evaluation. Figure **??** displays, in terms of Allan deviations, the pressure assessments made by the SOP (blue curves), the TOP (the red curves), and their difference (yellow curves). Figure **??**a displays all 20 assessments separately, and Figure **??**b shows their average.

This figure shows a large degree of concordance also between the Allan plots of the 20 individual assessments for both the SOP and the TOP (as well their difference). This indicates that both refractometry systems were stable over the total period of the measurements. The standard deviation of the individual readings of each refractometer (the left-most points in Figure **??**b) was 0.1 ppm, and their difference only had a standard deviation of 0.04 ppm.

**Figure 8.** (**a**) An enlargement of 70 s of the refractometry data shown in the first cycle of Figure **??**. (**b**) A correlation plot of the same data. The *x* and the *y*-axes represent the pressures assessed by the SOP and the TOP, respectively. In the latter, time is represented by the color, where the first data points are marked with orange and the last ones are in black.

**Figure 9.** (**a**) The Allan deviation (as a function of averaging time) for the SOT refractometer (blue curves), the TOP refractometer(red curves), and their difference (yellow curves) assessed over 20 cycles. (**b**) The average of each set of data in panel (**a**).
