Power spectra estimation for weak lensing

We develop a method for estimating the shear power spectra from weak-lensing observations and test it on simulated data. Our method describes the shear field in terms of angular power spectra and the cross-correlation of the two shear modes, which differ under parity transformations. Two of the three power spectra can be used to monitor unknown sources of noise in the data. The power spectra are decomposed in a model-independent manner in terms of "band powers," which are then extracted from the data using a quadratic estimator to find the maximum of the likelihood and its local curvature (for error estimates). We test the method against simulated data from Gaussian realizations and cosmological N-body simulations. In the Gaussian case, the mean band powers and their covariance are well recovered even for irregular (or sparsely) sampled fields. The mild non-Gaussianity of the N-body realizations causes a slight underestimation of the errors that becomes negligible for scales much larger than several arcminutes and does not bias the recovered band powers. These techniques can also be directly applied to cosmic microwave background polarization E and B mode analyses on small fields.