Abstract
BackgroundThe accurate knowledge of the refractive index of air is very important for environmental compensation in length measurements.MethodsIn 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.ResultsBased 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.ConclusionThe approximation accuracy is less than 5 × 10-9. Our approach can be used by non-expert users to obtain the GRA with sufficient accuracy.
Highlights
The accurate knowledge of the refractive index of air is very important for environmental compensation in length measurements
In addition [23], we found that the group refractive index of air (GRA) computation can be approximated by the four-point central difference approximation method and that approximation accuracies of less than 30 × 10− 9 can be achieved over the entire wavelength range (320-1680 nm) with a step size of 10 nm
Having understood the importance of environmental compensation in length measurement, we focus our attention on differential calculations by difference approximations (e.g., [24, 25])
Summary
The accurate knowledge of the refractive index of air is very important for environmental compensation in length measurements. The accurate knowledge of the refractive index of air is very important in length measurements. We determine values for air pressure, Probably the most exciting recent advancement in the field of length measurement is the development of the distance ranging technique based on the femtosecond optical frequency comb (FOFC) [5]. This technique enables us to measure length based on wavelength (e.g., [6–9]) and the adjacent pulse repetition
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