Abstract The correction of Astronomical Atmospheric Refraction(AAR) is one of the important topics in astronomy and geodesy.On the basis of the literature 1 and 2,series expansion theory of AAR was restudied, a new series expansion was provided. The new expansion can expanded to the arbitrary order and times items, and reached the submilliarcsecond theoretical accuracy. In addition, the phase atmospheric refractive index near the ground had been extracted from the expansion, as a single unknown parameter,so, new expansion can be adapted to different observation wavelengths processing of optical technology. Finally, the new series expansion making tangent of visual zenith distance as a argument is given. This work will completely replace the formula in AAR table of Pulkovo Observatory. This method can also be applied to the theory of ray tracing.
