Temperature, by itself, doesn’t directly impact the gas cell line center wavelengths. It does, however, impact the gas cell pressure, and the different gas cell lines have different pressure coefficients.

From the ideal gas law, P = nRT/V . Fused silica has a very small thermal expansion coefficient, so the volume expansion of the cell can be ignored. Therefore, pressure rises in proportion to absolute temperature. Lets say the temp rises 29.5 degrees K from a start temp of 295 K for a relative increase of 10%, and that we are using a 25 Torr cell. So our 25 Torr cell turns into a 27.5 Torr cell – what is the impact on the error in the wavelength span that we measure?

It turns out that the pressure shift coefficients have a local maximum near the center of our tuning range. Thus there is very little slope change to the gas cell fit. An offset to the wavelength calibration won’t cause a length accuracy issue; only a slope change would.

Luna has calculated the gas cell center wavelengths vs pressure, using the NIST pressure coefficients. When these values are compared via a linear regression, a slope of 0.999998 was calculated. Therefore, the length scaling error is 2 parts per million. So a 29.5 K change in gas cell temp appears to cause a negligible change in length accuracy.