Mitigating the Noise-Source Coupling Effect in Shear Measurement

Sub-percent level accuracy in shear measurement is required by the Stage-IV weak lensing surveys. One important challenge is about suppressing the shear bias on source images of low signal-to-noise ratios (SNR$\lesssim10$). Previously, it has been demonstrated that the shear estimators defined in the Fourier_Quad (FQ) method can achieve sub-percent accuracy at the very faint end (SNR$\lesssim5$) through ensemble averaging. Later, it is found that we can approach the minimum statistical error (the Cramer-Rao Bound) by symmetrizing the full PDF of the FQ shear estimators (the PDF_SYM approach), instead of taking ensemble averages. Recently, with a large amount of mock galaxy images, we are able to identify some small amount of shear biases in the PDF_SYM approach at the faint end. The multiplicative bias goes up to $1-2\times10^{-2}$ at SNR $\lesssim 10$, and the anisotropy of the point spread function (PSF) causes an additive bias that can reach a few times $10^{-4}$. We find that these biases originate from the noise-source coupling in the galaxy power spectrum. It turns out that this problem can be largely fixed by adding additional terms to the FQ shear estimators. The resulting multiplicative and additive biases can be significantly suppressed to the level of $10^{-3}$ and $10^{-5}$ respectively. These corrections substantially extend the available SNR range for accurate shear measurement with the PDF_SYM approach.