A new cosmic shear function: optimized 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 optimized for cosmological applications, by maximizing the signal-to-noise ratio (S/N) and a figure of merit (FoM) based on the Fisher matrix of the cosmological parameters Ωm and σ8. 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 3 (2) on angular scales between 1 and 220 arcmin. In addition, it yields better results than for the aperture-mass dispersion 〈M2ap〉, with improvements of 20 per cent (10 per cent) 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 optimization 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 optimized, can be defined, therefore generalizing the aim and context of the new shear statistic.