Issue |
J. Eur. Opt. Soc.-Rapid Publ.
Volume 11, 2016
|
|
---|---|---|
Article Number | 16013 | |
Number of page(s) | 4 | |
DOI | https://doi.org/10.2971/jeos.2016.16013 | |
Published online | 23 February 2016 |
Regular paper
Group refractive index calculation by difference approximation for length measurement
1
Department of Mechanical Engineering, Nagaoka University of Technology, Nagaoka City, Niigata 940-2188, Japan
2
School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, People’s Republic of China
3
Department of Mechanical and Electrical Engineering, School of Aerospace Engineering, Xiamen University, Xiamen City, Fujian Province, 361006, People’s Republic of China
* weidong@mech.nagaokaut.ac.jp
Received:
20
October
2015
Revised:
30
January
2016
In this study, the possibility of employing a difference approximation to facilitate calculation of the group refractive index of air (GRA) was investigated. The forward, backward, and central difference methods were used to numerically approximate the first-order derivatives of the phase refractive index based on the Edlè-empirical equations. To confirm the validity of the calculations, the calculated results were compared with the theoretical analysis results and the values in a related paper. It was found that the GRA computation could be easily approximated by the two-point central difference method with a step size of 10 nm.
Key words: Group refractive index / difference approximation / frequency comb / length measurement / metrology
© The Author(s) 2016. All rights reserved.
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