Corrigendum: Correction for stress-induced optical path length changes in a refractometer cell at variable external pressure (2019 Metrologia 56 015001)

In the derivation of equation (10) a term is missing, which takes into account the replacement of glass material by the gas medium when the refractometer cell is compressed by the external pressure. As a consequence, instead of the change of the optical path length, i.e. the distance between two fixed points independent of the material boundaries, unintentionally only the change of the optical thickness is represented by equation (10). This can be resolved by setting up equation (4) as follows:

In the derivation of equation (10) a term is missing, which takes into account the replacement of glass material by the gas medium when the refractometer cell is compressed by the external pressure. As a consequence, instead of the change of the optical path length, i.e. the distance between two fixed points independent of the material boundaries, unintentionally only the change of the optical thickness is represented by equation (10). This can be resolved by setting up equation (4) as follows: Then, proceeding with the subsequently described conversion steps and additionally applying the relation δl c,in = δl c,out + δl c,bend yields the expression for the refractivity n air − 1 (previously equation (12)) which is approximated by

Corrigendum
Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. demonstrated that particularly for the interior beam path of our refractometer cell the calculation of the window's refractive index change described above may lack accuracy due to the non-isotropic distribution of strain inside the window. Instead of our previously used average representation of that effect, the FEM-based numerical integration appears to evaluate it more accurately. Applying their approach to our particular window geometry at 1000 hPa external pressure yields δl w,in = 2 · (−0.7 nm ± 0.2 nm), δl w,out = 2 · (−4.6 nm ± 0.2 nm), δn f.s.,in = (7.6 ± 0.2) · 10 −7 and δn f.s.,out = (8.7 ± 0.2) · 10 −7 with the uncertainties taking into account the mesh-dependent variability of the FEM results. The air refractivity can then be calculated via the adapted equation The resulting implications are pointed out below.

Corrigendum: Appendix. Refractive index changes
Following [2] and [3] we applied the Lorentz-Lorenz relation to calculate the change of the refractive index of fused silica induced by external pressure. Unfortunately, this approach is in conflict with experimental data of Vedam et al [4], Ritland [5], Spinner et al [6] and Waxler et al [7]. These publications provide experimental evidence that the relation between the refractive index and the density of solid materials, in par ticular of fused silica, is not compatible with the Lorentz-Lorenz relation (i.e. with the assumption of a constant value of the polarizability). Therefore, instead of the previous equation (A.2) the relation between the relative change of the refractive index and the relative density change should be expressed by (similar to [8]) with a = 0.226 ± 0.010 being a fit parameter which is determined by linear regression of the exper imental results from [4] for fused silica. Consequently, the experimentally-based factor L must read

Conclusion
Considering the corrections described above, the partially FEM-based approach from [9] yields the updated figure 6 which shows the dependence between the resulting corrections and the external gas pressure affecting the cell windows of our particular cell geometry. However, as mentioned above, the all-FEM-based approach from Egan et al [1] provides more reliable results and yields the pressure-dependent correction shown in figure 7.
Compared to the previously published correction in [9] its magnitude is decreased so that, for instance, at 1000 hPa  the contribution to the air refractivity is of the order of 2.4 nm/420 mm ≈ 6 × 10 −9 which corresponds to a relative effect of approximately 2 × 10 −5 at standard conditions.