Measuring cosmic shear with the ring statistics
  Commonly used methods to decompose E- and B-modes in cosmic shear, namely the
aperture mass dispersion and the E/B-mode shear correlation function, suffer
from incomplete knowledge of the two-point correlation function (2PCF) on very
small and/or very large scales. The ring statistics, the most recently
developed cosmic shear measure, improves on this issue and is able to decompose
E- and B-modes using a 2PCF measured on a finite interval. First, we improve on
the ring statistics' filter function with respect to the signal-to-noise ratio.
Second, we examine the ability of the ring statistics to constrain cosmology
and compare the results to cosmological constraints obtained with the aperture
mass dispersion. Third, we use the ring statistics to measure a cosmic shear
signal from CFHTLS (Canada-France-Hawaii Telescope Legacy Survey) data. We
consider a scale-dependent filter function for the ring statistics which
improves its signal-to-noise ratio. In addition, we show that there exist
filter functions which decompose E- and B-modes using a finite range of 2PCFs
(EB-statistics) and have higher S/N ratio than the ring statistics. However, we
find that data points of the latter are significantly less correlated than data
points of the aperture mass dispersion and the EB-statistics. As a consequence
the ring statistics is an ideal tool to identify remaining systematics
accurately as a function of angular scale. We use the 2PCF of the latest CFHTLS
analysis and therefrom calculate the ring statistics and its error bars.
