Prospects for the use of Gaussian quadrature to determine the mean integral refractive index of air by its local values measured at two points of the trace

Abstract

The Earth’s atmosphere has a significant impact on the results of laser range measurements on near-earth traces. This influence is caused by the dependence of the laser signal propagation speed on the refractive index of the air, which varies along the measured trace. Correct accounting of this influence is important for the implementation of metrological traceability of linear measurements from a length measurement standard to distance measurements in large-scale construction, geodesy, geodynamics, navigation, etc. To ensure the required accuracy of such measurements, their results shall be corrected by introducing a correction for the mean refractive index of air along the signal trajectory.
 The simplest and most commonly used method for determining this correction is based on the representation of the integral of the refractive index by the quadrature trapezoidal formula in its simplest form, which requires the determination of only two local values of the refractive index at the endpoints of the trace. The accuracy of this method is often insufficient. In this regard, this paper presents the results of the research that will further substantiate a more accurate model for determining the correction under discussion based on two local refractive index values. The proposed model is based on the use of Gaussian quadrature, for which local values are determined not at the end points of the trace, but within the integration interval.