The impact of high spatial frequency atmospheric distortions on weak
  lensing measurements
  High precision cosmology with weak gravitational lensing requires a precise
measure of the Point Spread Function across the imaging data where the accuracy
to which high spatial frequency variation can be modelled is limited by the
stellar number density across the field. We analyse dense stellar fields imaged
at the Canada-France-Hawaii Telescope to quantify the degree of high spatial
frequency variation in ground-based imaging Point Spread Functions and compare
our results to models of atmospheric turbulence. The data shows an anisotropic
turbulence pattern with an orientation independent of the wind direction and
wind speed. We find the amplitude of the high spatial frequencies to decrease
with increasing exposure time as $t^{-1/2}$, and find a negligibly small
atmospheric contribution to the Point Spread Function ellipticity variation for
exposure times $t>180$ seconds. For future surveys analysing shorter exposure
data, this anisotropic turbulence will need to be taken into account as the
amplitude of the correlated atmospheric distortions becomes comparable to a
cosmological lensing signal on scales less than $\sim 10$ arcminutes. This
effect could be mitigated, however, by correlating galaxy shear measured on
exposures imaged with a time separation greater than 50 seconds, for which we
find the spatial turbulence patterns to be uncorrelated.
