Turbulence profiling with a dual beacon Hartmann turbulence sensor using simulation derived weighting functions

Atmospheric turbulence profiles were estimated for a horizontal path based upon measurements made with a dual beacon Hartmann Turbulence Sensor (HTS) using simulation derived weighting functions. These results are compared to estimates made using a weighting functions computed from theory. These results are further compared to anemometer and scintillometer based turbulence estimates for the same path. The previously published theoretical weighting functions for this situation are based upon some presumptions of geometric optics and thus ignore both diffraction and scintillation effects. All of these weighting functions quantify how turbulence at different distances along the path contributes to the expected value of the differential tilt variances measured by the HTS. In the experiment, the HTS used a 16” Meade telescope with 700 subapertures along a 511 m path roughly 2 meters above the ground. Two HeNe lasers separated by 11 cm served as beacons, each was beam expanded to well overfill the telescope aperture. The same situation was simulated with wave optics. To create simulated weighting functions, a single (usually weak) random turbulence screen was inserted at a single plane perpendicularly to the propagation path. Light from one beacon was then numerically propagated to the telescope aperture where the tilts were computed over each subaperture and saved. This propagation was then carried out for the second beacon. This random phase screen was then inserted at a different propagation plane and this procedure was repeated. When all the desired positions along the beam path had been sampled a new random phase screen was generated and this whole procedure was repeated hundreds of times. The desired weighting functions were then generated by computing the differential tilt variance between the beacons and all pairs of horizontally separated subapertures for each path position. All equivalent subaperture separations within each range bin were then averaged together to produce weighting functions which depend on path position and subaperture separation distance. The weighting functions produced in this fashion showed some differences from the theoretical ones. They were a little weaker far from the telescope, and they showed a somewhat broadened notch where the beacons overlapped compared to the theoretical ones. The effect of these differences on the resulting turbulence profile estimates will be discussed.