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This report models the refractive index above a telescope site by anatmosphere with exponential decay of the refractive index (susceptibility) as afunction of altitude. The air is represented as a spherical hull around thesurface. We compute (i) the differential zenith angle -- the difference betweenthe actual zenith angle at arrival of rays at the telescope and a hypotheticalzenith angle without the atmosphere -- and (ii) the optical path lengthdistribution of rays at arrival in the entrance pupil as a function of thedistance to the pupil center. The key technique in this work is to expand someintegrals -- that depend on the refractive index profile along the curved pathof each ray from some virtual plane in the direction of the star up to theentrance pupil -- in power series of small parameters.

A Barometric Exponential Model of the Atmosphere's Refractive Index: Zenith Angles and Second Order Aberration in the Entrance Pupil