Shear power spectrum reconstruction using the pseudo-spectrum method

We develop a pseudo-power-spectrum technique for measuring the lensing power spectrum from weak lensing surveys in both the full-sky and the flat-sky limits. The power spectrum approaches have a number of advantages over the traditional correlation function approach. We test the pseudo-spectrum method by using numerical simulations with a square-shape boundary that includes masked regions with complex configuration due to bright stars and saturated spikes. Even when 25 per cent of the total area of the survey is masked, the method recovers the -mode power spectrum at a sub-per cent precision over a wide range of multipoles 100 ≲ℓ≲ 10⁴. The systematic error is smaller than the statistical errors expected for a 2000-deg² survey. The residual -mode spectrum is well suppressed in the amplitudes at less than a per cent level relative to the mode. We also find that the correlated errors of binned power spectra caused by the survey geometry effects are not significant. Our method is applicable to the current and upcoming wide-field lensing surveys.