Background
The accurate knowledge of the refractive index of air is very important for environmental compensation in length measurements.
Methods
In this study, we apply difference approximation methods to facilitate the calculation of the group refractive index of air (GRA) over all calculable wavelengths. Our approach involves the determination of a suitable combination of the step size Δλ and numbers of significant digits of calculations of the phase refractive index of air (PRA) by balancing the two main errors (round-off and truncation errors) over the entire calculable wavelength range.
Results
Based on our calculations, we find that the GRA computation over the range of all calculable wavelengths (301.5-1698.5 nm) can be easily approximated by the two-point central difference method with Δλ = 1.5 nm and 12-digit PRA accuracy.
Conclusion
The approximation accuracy is less than 5 × 10-9. Our approach can be used by non-expert users to obtain the GRA with sufficient accuracy.