Cosmic shear E/B-mode estimation with binned correlation function data

In this work I study the problem of E/B-mode separation with binned cosmic shear two-point correlation function data. Motivated by previous work on E/B-mode separation with shear two-point correlation functions and the practical considerations of data analysis, I consider E/B-mode estimators which are linear combinations of the binned shear correlation function data points. I demonstrate that these estimators mix E- and B-modes generally. I then show how to define estimators which minimize this E/B-mode mixing and give practical recipes for their construction and use. Using these optimal estimators, I demonstrate that the vector space composed of the binned shear correlation function data points can be decomposed into approximately ambiguous, E- and B-mode subspaces. With simple Fisher information estimates, I show that a non-trivial amount of information on typical cosmological parameters is contained in the ambiguous mode subspace computed in this formalism. Next, I give two examples which apply these practical estimators and recipes to generic problems in cosmic shear data analysis: data compression and spatially locating B-mode contamination. In particular, by using wavelet-like estimators with the shear correlation functions directly, one can pinpoint B-mode contamination to specific angular scales and extract information on its shape. Finally, I discuss how these estimators can be used as part of blinded or closed-box cosmic shear data analyses in order to assess and find B-mode contamination at high-precision while avoiding observer biases.