Effect of Coudé pupil rotation on sodium laser beacon perspective elongation

Laser beacons are commonly used to measure the atmospheric turbulence through a given volume of the atmosphere. One of the imperfections of using laser beacons is the elongation of the laser spot when viewed from an off-axis perspective. Further complications arise when the telescope uses a Coude path without a de-rotation system, thereby allowing the wavefront sensor to optically rotate relative to the telescope's entrance pupil. This paper examines the effect of Coudé rotation on Shack-Hartmann wavefront sensor measurements for a 3.5 m telescope operating with a side launched sodium-wavelength laser. This paper also considers the effect of laser tilt and sodium layer depth on wavefront measurements. Finally, a semi-analytic model is developed to allow greater analysis of the effects of pupil rotation and beacon elongation on these measurements.