Global tilt removal on a Hartmann turbulence sensor

A Hartmann Turbulence Sensor (HTS) was used to quantify the atmospheric turbulence along a 1 km near ground-level path. This study examines the effect of removing the average tilt over all subapertures from each subaperture in the data analysis. The HTS captures a laser beam projected along a path of interest with a telescope; a lenslet array in the detector system breaks the beam up into 700 subapertures spread across the telescope pupil, and then forms images of the laser source from each of these subapertures onto a fast camera. Turbulence along the path induces tilts in the laser wavefront which are captured as centroid motion of the many laser spots in the camera image. This motion is used to quantify the turbulence. The raw spot positions contain undesired image motion due to telescope motion and vibration. This motion can be removed from the data by subtracting the average centroid motion of all subapertures from each subaperture. This subtraction changes the data in other ways, and this detail must be included in the analysis. The result can be exactly represented as weighted sum over the differential tilt variances between subapertures pairs. The tilt-removed variance averaged over all the subapertures is shown to be one-half of the average variance over all subaperture pairs. This work also resolves some discrepancies in previous results involving the expected variances of these differential tilts.