Selection of numerical differentiation method for calculation of group refractive index of air over all calculable wavelengths

In this study, we attempt the selection of a difference approximation method to facilitate calculation of the group refractive index of air (GRA) over all calculable wavelengths. Based on calculation and error analysis, we test the performance of the three-point forward, three-point backward, and four-point central difference methods. We find that the GRA computation over the range of all calculable wavelengths (320–1680 nm) can be easily approximated by the four-point central difference method with a step size of 10 nm and an approximation accuracy of less than 30 × 10⁻⁹.