Weak lensing using only galaxy position angles
  We develop a method for performing a weak lensing analysis using only
measurements of galaxy position angles. By analysing the statistical properties
of the galaxy orientations given a known intrinsic ellipticity distribution, we
show that it is possible to obtain estimates of the shear by minimizing a
$\chi^2$ statistic. The method is demonstrated using simulations where the
components of the intrinsic ellipticity are taken to be Gaussian distributed.
Uncertainties in the position angle measurements introduce a bias into the
shear estimates which can be reduced to negligible levels by introducing a
correction term into the formalism. We generalize our approach by developing an
algorithm to obtain direct shear estimators given any azimuthally symmetric
intrinsic ellipticity distribution. We introduce a method of measuring the
position angles of the galaxies from noisy pixelized images, and propose a
method to correct for biases which arise due to pixelization and correlations
between measurement errors and galaxy ellipticities. We also develop a method
to constrain the sample of galaxies used to obtain an estimate of the intrinsic
ellipticity distribution such that fractional biases in the resulting shear
estimates are below a given threshold value. We demonstrate the angle only
method by applying it to simulations where the ellipticities are taken to
follow a log-normal distribution. We compare the performance of the position
angle only method with the standard method based on full ellipticity
measurements by reconstructing lensing convergence maps from both numerical
simulations and from the CFHTLenS data. We find that the difference between the
convergence maps reconstructed using the two methods is consistent with noise.
