Abstract
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.
Highlights
In recent years, femtosecond optical frequency comb (FOFC)based length measurements have gained considerable attention
Where λvacis the wavelength in a vacuum, np(λvac) is the phase refractive index of air (PRA), λcen vac is the central wavelength of the FOFC, and (dnp(λvac)/dλvac)λcen vac is the derivative of the function y = np(λvac) at λvac = λcen vac
We used the phase refractive index equations given in Ref. [16]
Summary
Femtosecond optical frequency comb (FOFC)based length measurements have gained considerable attention. Among these length measurement methods, adjacent pulse repetition interval length (APRIL)-based measurements [1]–[13] have been demonstrated to be technically feasible. The APRIL is a coherent representation of individual wavelengths. In these experiments, the APRIL was used as the ruler length instead of the wavelengths. In wavelength-based length measurements, the phase refractive index of air (PRA) is used to obtain the length in a vacuum. In APRIL-based length measurements, the group refractive index of air (GRA) must be calculated to determine the length in a vacuum
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