A new cosmic shear function: Optimised E-/B-mode decomposition on a
  finite interval
  The decomposition of the cosmic shear field into E- and B-mode is an
important diagnostic in weak gravitational lensing. However, commonly used
techniques to perform this separation suffer from mode-mixing on very small or
very large scales. We introduce a new E-/B-mode decomposition of the cosmic
shear two-point correlation on a finite interval. This new statistic is
optimised for cosmological applications, by maximising the signal-to-noise
ratio (S/N) and a figure of merit (FoM) based on the Fisher matrix of the
cosmological parameters Omega_m and sigma_8.
  We improve both S/N and FoM results substantially with respect to the
recently introduced ring statistic, which also provides E-/B-mode separation on
a finite angular range. The S/N (FoM) is larger by a factor of three (two) on
angular scales between 1 and 220 arc minutes. In addition, it yields better
results than for the aperture-mass dispersion <M_ap>^2, with improvements of
20% (10%) for S/N (FoM). Our results depend on the survey parameters, most
importantly on the covariance of the two-point shear correlation function.
Although we assume parameters according to the CFHTLS-Wide survey, our method
and optimisation scheme can be applied easily to any given survey settings and
observing parameters. Arbitrary quantities, with respect to which the E-/B-mode
filter is optimised, can be defined, therefore generalising the aim and context
of the new shear statistic.
