# Demonstration of a Transportable Fabry–Pérot Refractometer by a Ring-Type Comparison of Dead-Weight Pressure Balances at Four European National Metrology Institutes

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## Abstract

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## 1. Introduction

## 2. Transportable Refractometer

- The system was designed to fit in a 120 cm high wheel-equipped 19-inch rack. This is obviously non-ideal in terms of stability; it would be preferable to place the system on a firm and stable surface, such as a rigid optical table. However, this overall design has the advantages that it makes it easy to move the refractometer within laboratories and, at the same time, minimizes the footprint of the system, which otherwise can be a problem at some visited laboratories. A picture of the front and back of the system is shown in Figure 1.
- The TOP assesses the temperature of the cavity by using two Pt-100 sensors whose outputs are assessed by a data acquisition (DAQ) system. This is in contrast to the stationary system that uses a thermocouple directly referred to an active gallium fixed-point cell. The reason for this downgrade in terms of accuracy is that the gallium cell adds unwanted complexity to the system that most notably increases the setup time and limits the measurement to certain time windows when the gallium is in its proper melting state. To ensure traceability, without the gallium fixed-point, an external temperature measurement device (Hart 1502A) and an accompanying calibrated Pt-100 probe was brought as hand luggage to each visit and used to calibrate the Pt-100 probes and the DAQ system of the TOP prior to each series of measurements. To evaluate the stability of the temperature assessment module, it was calibrated at RISE both before and after the measurement campaign. The discrepancy between these two calibrations was below the resolution of the instrument (1 mK), providing an estimated uncertainty limited by the resolution of the instrument of 2 ppm (see below).

## 3. Measurement Procedure

#### 3.1. Establishment of Measurement Procedures

#### 3.2. Day One—Unpacking, Setup, and Installation

#### 3.3. Day Two—Optical Alignment, Control/Verification, and Stabilization

#### 3.4. Day Three—Assessments

#### 3.5. Day Four—Spare Day and Packing

#### 3.6. Day Five—Spare Day for Packing

#### 3.7. Packing—Preparation for Shipping

## 4. Measurements and Results

#### 4.1. Initial Measurement and Characterization

#### 4.2. The Ring Comparison

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CNAM | Conservatoire National des Arts et Métiers |

DAQ | Data acquisition system |

DFPC | Dual-Fabry–Pérot cavity |

DOEs | Degrees of equivalences |

EMPIR | European Metrology Programme for Innovation and Research |

FP | Fabry–Pérot |

GAMOR | Gas modulation refractometry |

INRiM | Istituto Nazionale di Ricerca Metrologica |

KCRVs | Key comparison reference values |

LNE-CNAM | Laboratoire Commun de Métrologie (CNAM) |

NIM | National Institute of Metrology |

NIST | National Institute of Standards and Technology |

NMI | National Measurement Institute |

ppm | parts per million |

PTB | Physikalisch-Technische Bundesanstalt |

RISE | Research Institutes of Sweden |

SOP | Stationary optical pascal |

TOP | Transportable optical pascal |

UmU | Umeå University |

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**Figure 1.**Pictures of the TOP from the front (

**left**) and back (

**right**). On top of the rack sits a temperature-regulated aluminum breadboard with an isolating enclosure, within which the DFPC is located. The rack contains seven modules, denoted A–G. (A) The gas inlet system consisting of a mass flow controller and an electronic pressure controller. (B) Optics, passive fiber optical components (e.g., circulators and isolators), and opto-electronics (EOMs and AOMs). (C) Frequency counter and vacuum gauge controllers. (D) Power supplies and control unit for the heating. (E) A 230 V power distribution unit. (F) Two Er-doped fiber lasers. (G) Two digital locking modules. Reproduced with permission from Forssén et al. [22].

**Figure 2.**The first measurement series at RISE (RISE1). The red markers represent measurement data points taken by the TOP, and the solid lines and curves represent polynomial fits to them, all as a function of the pressure set by the pressure balance, ${P}_{PB}$. Panel (

**a**) shows, by the individual markers, the pressure assessed by the TOP evaluated by the standard expression for refractivity with the deformation parameter set to zero, ${P}_{TOP}$, in kPa. The solid curve represents the fit, ${P}_{TOP}^{fit}$. Panel (

**b**) displays the non-linear components of panel (

**a**) given by, for the individual data markers, ${P}_{TOP}-b{P}_{PB}$ and, for the fit, $a+c{P}_{PB}^{2}$, respectively, in Pa. Panel (

**c**) illustrates the residuals of the fit from panel (

**a**,

**b**) in relative units, i.e., $({P}_{TOP}-{P}_{TOP}^{fit})/{P}_{PB}$, in parts per million (ppm), which also represent the relative deviations in the pressure assessed by the characterized TOP, ${P}_{TOP}^{Ch}$, from the pressure set by the pressure balance, ${P}_{PB}$.

**Figure 3.**Pictures of the four different pressure balances used in the ring comparison. (

**Top left**): RISE Ruska 2465A-754, (

**top right**): PTB Fluke 2465A-754, (

**bottom left**): INRiM DHI-Fluke PG7601, (

**bottom right**): LNE DHI-Fluke PG7607.

**Figure 4.**Colored circles: deviations between the pressures assessed by the TOP refractometer, ${P}_{TOP}^{Ch}$, and the set pressures of the pressure balances, ${P}_{PB}^{i}$, from the measurements performed at the various NMIs (i.e., with i being $RISE1$, $PTB$, $INRiM$, $LNE$, and $RISE2$, respectively). Black horizontal lines: polynomial fits of the initial characterization. The dashed curves represent the uncertainty values for the pressure balance used at the corresponding NMI. The first panel, denoted as RISE1, contains the same data as in Figure 2c.

**Figure 5.**The two measurement series from RISE (RISE1 and RISE2, respectively). The shaded areas indicate the (k = 2) expanded uncertainty originating from the finite resolution of the temperature-measuring instrument.

**Table 1.**Summary of the five measurement series. For simplicity, the expanded uncertainties (k = 2) are given with a simplified notation in the format $A+B\xb7P$ , which, in reality, corresponds to ${[{A}^{2}+{(B\xb7P)}^{2}]}^{1/2}$, where A represents the pressure-independent contribution to the uncertainty while B is the coefficient in the pressure-dependent contribution.

RISE1: Borås, Sweden | Pressure Balance | Ruska 2465A-754 |

Date: 19 January 2022 | Uncertainty (k = 2) | 0.21 Pa + $19\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-6}P$ |

PTB: Berlin, Germany | Pressure Balance | Fluke 2465A-754 |

Date: 17 February 2022 | Uncertainty (k = 2) | 0.27 Pa + $19\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-6}P$ |

INRiM: Turin, Italy | Pressure Balance | DHI-Fluke PG7601 |

Date: 6 April 2022 | Uncertainty (k = 2) | 0.08 Pa + $20\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-6}P$ |

LNE: Paris, France | Pressure Balance | DHI-Fluke PG7607 |

Date: 21 June 2022 | Uncertainty (k = 2) | 0.20 Pa + $10\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-6}P$ |

RISE2: Borås, Sweden | Pressure Balance | Ruska 2465A-754 |

Date: 10 October 2022 | Uncertainty (k = 2) | 0.21 Pa + $19\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-6}P$ |

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**MDPI and ACS Style**

Forssén, C.; Silander, I.; Zakrisson, J.; Amer, E.; Szabo, D.; Bock, T.; Kussike, A.; Rubin, T.; Mari, D.; Pasqualin, S.;
et al. Demonstration of a Transportable Fabry–Pérot Refractometer by a Ring-Type Comparison of Dead-Weight Pressure Balances at Four European National Metrology Institutes. *Sensors* **2024**, *24*, 7.
https://doi.org/10.3390/s24010007

**AMA Style**

Forssén C, Silander I, Zakrisson J, Amer E, Szabo D, Bock T, Kussike A, Rubin T, Mari D, Pasqualin S,
et al. Demonstration of a Transportable Fabry–Pérot Refractometer by a Ring-Type Comparison of Dead-Weight Pressure Balances at Four European National Metrology Institutes. *Sensors*. 2024; 24(1):7.
https://doi.org/10.3390/s24010007

**Chicago/Turabian Style**

Forssén, Clayton, Isak Silander, Johan Zakrisson, Eynas Amer, David Szabo, Thomas Bock, André Kussike, Tom Rubin, Domenico Mari, Stefano Pasqualin,
and et al. 2024. "Demonstration of a Transportable Fabry–Pérot Refractometer by a Ring-Type Comparison of Dead-Weight Pressure Balances at Four European National Metrology Institutes" *Sensors* 24, no. 1: 7.
https://doi.org/10.3390/s24010007