E- and B-mode mixing from incomplete knowledge of the shear correlation

Context. Aims. We quantify the mixing of the measured cosmic-shear E- and B-modes caused by the lack of shear-correlation measurements on small and large scales, arising from a lack of close projected galaxy pairs and the finite field size, respectively. Methods. We calculate the aperture-mass statistics $\langle M_{\rm ap, \perp}^2 \rangle$ and the E-/B-mode shear-correlation functions $\xi_{\rm E, B \pm}$ where small- and large-scale cutoffs are taken into account. We assess the deviation of the obtained E-mode to the true E-mode and the introduction of a spurious B-mode. Results. The measured aperture-mass dispersion is underestimated by more than 10% on scales smaller than 12 times the lower cutoff. For a precise measurement of the E- and B-modes at the percent level using a combination of $\xi_{\rm E, B +}$ and $\xi_{\rm E, B -}$, a field as large as 7 (2.4) degrees is necessary for ground-based (space-based) observations.