Subpercent level accuracy in shear measurement is required by the Stage-IV weak lensing surveys. One important challenge is suppressing the shear bias on source images of low signal-to-noise ratios (S/N ≲ 10). Previously, it has been demonstrated that the shear estimators defined in the Fourier_Quad (FQ) method can achieve subpercent accuracy at the very faint end (S/N ≲ 5) through ensemble averaging. Later, it was found that we can approach the minimum statistical error (the Cramer–Rao Bound) by symmetrizing the full probability distribution function (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 were 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) 10⁻² at S/N ≲ 10, and the anisotropy of the point-spread function 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 S/N range for accurate shear measurement with the PDF_SYM approach.

第四阶段弱透镜测量要求剪切测量的亚百分比精度。一个重要的挑战是抑制低信噪比 (S/N ≲ 10) 源图像的剪切偏差。之前，已经证明在傅立叶四边形 (FQ) 方法中定义的剪切估计量可以通过整体平均在非常微弱的一端 (S/N ≲ 5) 实现亚百分比精度。后来，发现我们可以通过对称化 FQ 剪切估计器的全概率分布函数 (PDF)（PDF_SYM 方法）来接近最小统计误差（Cramer-Rao Bound），而不是采用整体平均值。最近，通过大量模拟星系图像，我们能够在微弱端识别 PDF_SYM 方法中的一些少量剪切偏差。乘法偏差上升到 (1–2) 10^-2在 S/N ≲ 10 处，并且点扩展函数的各向异性导致可以达到 10 ^-4几倍的加性偏差。我们发现这些偏差源于星系功率谱中的噪声源耦合。事实证明，通过向 FQ 剪切估计器添加附加项，可以在很大程度上解决这个问题。由此产生的乘法和加法偏差可以分别显着抑制到10 ^-3和10 ^-5的水平。这些修正大大扩展了可用的 S/N 范围，以便使用 PDF_SYM 方法进行精确的剪切测量。