PHYSICAL REVIEW APPLIED 23, 064041 (2025)
Demonstration of dispersion gas barometry
Yuanchao Yang ,
1,2
Jack A. Stone ,
1,*
and Patrick F. Egan
1,†
1
National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
2
National Institute of Metrology, Beijing 100029, China
(Received 21 February 2025; revised 25 April 2025; accepted 29 May 2025; published 17 June 2025)
Realization of the optical pascal has been limited by systematic errors caused by distortion of the optic.
In this work, distortion error is circumvented via synchronous measurement of helium refractivity at two
optical frequencies. The resultant pressure realization achieves combined standard uncertainty of 5.7 ×
10
−6
p, chiefly limited by ab initio knowledge of helium dispersion. Two-color measurements are also
presented for neon, argon, and nitrogen, which enable semiprimary realization of the pascal in a more
practical embodiment. For argon dispersion, measurement and ab initio calculation barely agree within
mutual expanded uncertainty; experiment is about 16 times more accurate than theory.
DOI: 10.1103/z9zz-lqzh
I. INTRODUCTION
Mercury manometers and piston gages are the
workhorse standards for pressure metrology [1]. In inter-
national comparisons, they have demonstrated consistency
at the level of 5 × 10
−6
p [2,3]. But having been perfected
over the past 400 and 150 years, respectively, further effort
tackling their limitations will yield minimal gains. Already
for the piston gage, the past generation of effort in dimen-
sional metrology and flow modeling has not significantly
improved the realization [2,4,5].
An alternative route [6] to the pascal is the virial
equation of state
p = ρRT(1 + B
ρ
ρ + C
ρ
ρ
2
+···),(1)
which defines pressure as density ρ at a known tempera-
ture T, with deviations from ideal gas behavior described
by density virial coefficients B
ρ
and C
ρ
. The international
system of units defines the molar gas constant R as a fixed
value without uncertainty. Modern thermometry [7] places
the limit of Eq. (1) at 5 × 10
−7
T—an order of magnitude
more accurate than the mechanical limits of a piston gage.
For the density in Eq. (1), a precision measurement may
be accessed via the extended Lorentz-Lorenz equation,
n
2
− 1
n
2
+ 2
= A
R
ρ + B
R
ρ
2
+ C
R
ρ
3
+··· (2)
*
Retired.
†
Contact author: egan@nist.gov
At first order, ρ ≈ (2/3A
R
)(n − 1) and the density limit on
Eq. (1) is either the measured refractivity n − 1 or knowl-
edge of the molar refractivity A
R
.(TheB
R
and C
R
are
refractivity virial coefficients.) Helium is the gold-standard
thermometric gas, because theory claims [8] uncertainty
below 10
−7
A
R
. Consequently, the limit realizing Eq. (1) is
measurement of n − 1, which has large uncertainty caused
by distortion of the optical device when filled with gas.
This work introduces dispersion gas barometry, which
realizes the pascal via Eqs. (1) and (2) with uncertainty
approaching that of mechanical standards. The method
interrogates a Fabry-Perot (FP) cavity at two widely sepa-
rated laser frequencies and uses the ab initio calculation
of helium dispersion to simultaneously extract both the
gas pressure and distortion coefficient of the cavity. The
method is validated by comparing the optical pressure to
a mechanically generated pressure at the highest level of
accuracy. Finally, the approach is extended to other gases
relevant to thermodynamic metrology and the first-order
dispersion coefficients of neon, argon, and nitrogen are
derived with accuracies exceeding recent ab initio calcu-
lation by more than an order of magnitude. These coeffi-
cients may serve as reference data to establish semiprimary
realization of the pascal with gases more practical for
metrology.
II. METHOD AND IMPLEMENTATION
This section begins with simplified concepts of how
optical pressure may be derived from measurement of
refractivity at two separate frequencies. Details behind the
experimental implementation are then described. Finally,
full equations underlying the analysis are given, which
formalize the initial simplified concept.
2331-7019/25/23(6)/064041(7) 064041-1 Published by the American Physical Society
