The accurate knowledge of the refractive index of air is very important for environmental compensation in length measurements. 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. 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. 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.

中文翻译：

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基于两点中心法的空气群折射率差近似计算参数的确定

准确了解空气的折射率对于长度测量中的环境补偿非常重要。在这项研究中，我们应用差值近似方法来简化所有可计算波长上的空气组折射率（GRA）的计算。我们的方法涉及通过在整个可计算波长上平衡两个主要误差（舍入误差和截断误差），确定步长Δλ和空气相折射率（PRA）的有效位数计算的合适组合。范围。根据我们的计算，我们发现，采用Δλ= 1.5 nm和12位PRA精度的两点中心差法可以轻松地估算出所有可计算波长范围（301.5-1698.5 nm）上的GRA计算。近似精度小于5×10-9。非专业用户可以使用我们的方法来获得足够准确的GRA。