Comparative analysis of the accuracy requirements of the equipment for determining the mean integral refractive index of air using different realizations of the gradient method

Abstract

The speed of propagation of electromagnetic waves in the Earth’s atmosphere differs from the speed of their propagation in a vacuum, which is one of the main factors that have a significant impact on the accuracy of long distance measurement. This influence is taken into account in long distance measurement with the correction for the mean integral group refractive index of air, which depends on such meteorological parameters as temperature, atmospheric pressure and relative air humidity. The purpose of this work is to compare the accuracy requirements for equipment designed to measure temperature, pressure, and relative humidity required to determine the above correction by the gradient method using the Euler-Maclaurin quadrature formula (hereafter, the Euler-Maclaurin method) and the formula based on Hermite interpolation polynomials (hereafter, the Hermite method). The requirements for the uncertainty of measurements carried out with the sensors of meteorological parameters, allowing to find the mean integral group refractive index of air, providing length measurements of the baselines of up to 5 km with an expanded uncertainty of not more than 1 mm, are established. Keywords: atmosphere; mean integral group refractive index of air; laser long distance measurement