Image Field Deformation of LAMOST due to Differential Atmospheric Refraction

A vectorial expression of the image field deformation of LAMOST due to the differential atmospheric refraction is presented. The calculated results are compared with those from previous analyses based on the traditional spherical trigonometric formulas. It is demonstrated that different tangential displacements of star images during the observation tracking given by various authors are simply due to different reference points adopted. It is pointed out that the observational celestial pole is the center of the apparent diurnal motion, that, by referring to the observational celestial pole, the effect of the differential refraction on the image field of LAMOST during the 1.5-hour tracking period is approximately equivalent to a constant rotation of −13.65'' for all declination belts. It is therefore unnecessary to design a particular tracking velocity for each observation, and this will be obviously advantageous to the observation implementation. If the maximum tracking error of the fibers is 0.2'', then the fibers are required to be able to re-position during observational tracking for sky regions south of declination +20° and north of declination +60°