Abstract
The Edlen empirical equations and the two-color method are the commonly used approaches to converting a length measured in air to the corresponding length in vacuum to eliminate the influence of the refractive index of air. However, it is not well known whether the two-color method is superior to empirical equations in refractive index compensation. We investigated the uncertainties of these approaches via numerical calculations of their sensitivity coefficients of environmental parameters. On the basis of a comparison of their uncertainties, we found that in a 0% humidity environment, the two-color method had potential to provide greater measurement accuracy than the empirical equations.
Highlights
IntroductionThe unit of length, is defined in vacuum. measurements of length are often carried out in air, which presents some problems
Meter, the unit of length, is defined in vacuum
Let us assume that we want to compare two geometric distances G1 and G2. These two distances are measured in air as L=1 G1 × n1 and L=2 G2 × n2, where n1 and n2 are the refractive index of air (RIA)
Summary
The unit of length, is defined in vacuum. measurements of length are often carried out in air, which presents some problems. In other words, both the spatial distribution of environmental parameters and the time-delay of measurement equipment can be ignored. These assumptions are valid only if the measurement is performed in a closed environment (e.g., a well-controlled laboratory or underground tunnel with limited variation in environmental parameters) Another approach to suppressing the influence of RIA is to apply the two-color method, which was first proposed by Bender and Owens [5] to compensate for the inhomogeneous disturbances of the RIA in an open environment. Minoshima’s group performed a twocolor method experiment in a well-controlled environment and found an agreement between RIA compensation based on the empirical equations and that of two-color method with a standard deviation of 3.8 × 10−11 throughout hours [13]. One question arises naturally: theoretically, is the two-color method superior to the empirical equations in RIA compensation? We employed a numerical approach to investigate this possibility
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