determination of calculation parameters for difference approximation of group refractive index of air based on two-point central method

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. © 2018, the author(s).