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

作者：Wei, Dong^*; Xiao, Muzheng; Yang, Ping

来源：Journal of the European Optical Society-Rapid Publications, 2018, 14(1): 14.

DOI：10.1186/s41476-018-0083-y

• Group refractive index
• Difference approximation
• Frequency comb
• Length measurement
• Metrology

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 Delta lambda 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 Delta lambda = 1.5 nm and 12-digit PRA accuracy. @@@ Conclusion: The approximation accuracy is less than 5 x 10(-9). Our approach can be used by non-expert users to obtain the GRA with sufficient accuracy.

• 出版日期2018-5-10
• 单位厦门大学; 北京理工大学