Abstract
Abstract As basic research problems in practical astronomy and geodesy, the formulation of the mapping functions both of the refractive delay and of astronomical refraction are studied in an analytical manner in this paper. First, we have proved that the complementary error function can be related to expressions for the atmospheric refraction integrals of the signal delay and also of the signal bending angle as well. An improved continued fraction expansion of the complementary error function is then derived to describe the new mapping functions of the refractive delay and astronomical refraction at radio and optical frequencies, respectively. Not only do the new mapping functions have good convergence at an elevation coverage near to the horizon, but they can also be applied to various atmospheric profiles at high accuracy, better than 1 cm for refraction delay and better than 0.″3 for angular bending at an elevation angle near to 2°.5 or lower over a wide range of meteorological and geophysical conditions. Some extra corrections are also briefly summarized in this paper.
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