Analytical noise bias correction for weak lensing shear analysis with ERA

Highly precise weak lensing shear measurement is required for statistical weak gravitational lensing analysis such as cosmic shear measurement to achieve stringent constraints on the cosmological parameters. For this purpose, an accurate shape measurement of background galaxies is crucial in which all systematic errors in the measurement should be carefully corrected. One of the main systematic errors comes from the photon Poisson noise, which comes from the sky brightness (noise bias). We investigate how the photon noise biases the shear measurement within the framework of the ERA method, then develop an analytical noise bias correction method evaluated to the second order. We find that the photon noise does not bias cases of Gaussian profile galaxies with no point spread function (PSF). We also develop noise correction with PSF correction, and tested using simulations based on real galaxy images. The simulations show that the noise bias can be reduced to 0.1 per cent for the case of galaxies with signal-to-noise ratio between 5 and 100.