Issue |
J. Eur. Opt. Soc.-Rapid Publ.
Volume 14, Number 1, 2018
|
|
---|---|---|
Article Number | 14 | |
Number of page(s) | 7 | |
DOI | https://doi.org/10.1186/s41476-018-0083-y | |
Published online | 10 May 2018 |
Research
Determination of calculation parameters for difference approximation of group refractive index of air based on two-point central method
1
Department of Mechanical Engineering, Nagaoka University of Technology, 940-2188, Nagaoka City, Niigata, Japan
2
School of Mechanical Engineering, Beijing Institute of Technology, 100081, Beijing, People’s Republic of China
3
Department of Mechanical and Electrical Engineering, School of Aerospace Engineering, Xiamen University, 361006, Xiamen City, Fujian Province, People’s Republic of China
a
weidong@mech.nagaokaut.ac.jp
Received:
14
January
2018
Accepted:
2
May
2018
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.
Key words: Group refractive index / Difference approximation / Frequency comb / Length measurement / Metrology
© The Author(s) 2018
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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