LensMC is a weak lensing shear measurement method developed for Euclid and Stage-IV surveys. It is based on forward modelling in order to deal with convolution by a point spread function (PSF) with comparable size to many galaxies; sampling the posterior distribution of galaxy parameters via Markov Chain Monte Carlo; and marginalisation over nuisance parameters for each of the 1.5 billion galaxies observed by Euclid. We quantified the scientific performance through high-fidelity images based on the Euclid Flagship simulations and emulation of the Euclid VIS images; realistic clustering with a mean surface number density of 250 arcmin$^{-2}$ ($I_{\rm E}<29.5$) for galaxies, and 6 arcmin$^{-2}$ ($I_{\rm E}<26$) for stars; and a diffraction-limited chromatic PSF with a full width at half maximum of $0.^{\!\prime\prime}2$ and spatial variation across the field of view. LensMC measured objects with a density of 90 arcmin$^{-2}$ ($I_{\rm E}<26.5$) in 4500 deg$^2$. The total shear bias was broken down into measurement (our main focus here) and selection effects (which will be addressed elsewhere). We found measurement multiplicative and additive biases of $m_1=(-3.6\pm0.2)\times10^{-3}$, $m_2=(-4.3\pm0.2)\times10^{-3}$, $c_1=(-1.78\pm0.03)\times10^{-4}$, $c_2=(0.09\pm0.03)\times10^{-4}$; a large detection bias with a multiplicative component of $1.2\times10^{-2}$ and an additive component of $-3\times10^{-4}$; and a measurement PSF leakage of $\alpha_1=(-9\pm3)\times10^{-4}$ and $\alpha_2=(2\pm3)\times10^{-4}$. When model bias is suppressed, the obtained measurement biases are close to Euclid requirement and largely dominated by undetected faint galaxies ($-5\times10^{-3}$). Although significant, model bias will be straightforward to calibrate given the weak sensitivity. LensMC is publicly available at https://gitlab.com/gcongedo/LensMC

翻译：LensMC 是为欧几里得及第四阶段巡天项目开发的弱引力透镜剪切测量方法。该方法基于前向建模以处理点扩散函数（PSF）对众多星系尺度相当的卷积效应；通过马尔可夫链蒙特卡洛采样星系参数的后验分布；并对欧几里得观测到的15亿个星系逐一进行冗余参数的边际化处理。我们通过基于欧几里得旗舰模拟的高保真图像与欧几里得VIS图像仿真，量化了其科学性能：星系采用平均面数密度为250 arcmin$^{-2}$（$I_{\rm E}<29.5$）、恒星为6 arcmin$^{-2}$（$I_{\rm E}<26$）的真实空间聚类分布；并采用半高全宽为$0.^{\!\prime\prime}2$、随视场空间变化的衍射极限色散PSF。在4500 deg$^2$天区内，LensMC以90 arcmin$^{-2}$（$I_{\rm E}<26.5$）的面密度测量了目标天体。总剪切偏差被分解为测量效应（本文重点）与选择效应（将在其他文献探讨）。我们测得测量乘性偏差与加性偏差分别为 $m_1=(-3.6\pm0.2)\times10^{-3}$、$m_2=(-4.3\pm0.2)\times10^{-3}$、$c_1=(-1.78\pm0.03)\times10^{-4}$、$c_2=(0.09\pm0.03)\times10^{-4}$；检测偏差较大，其乘性分量为$1.2\times10^{-2}$，加性分量为$-3\times10^{-4}$；测量PSF泄漏为$\alpha_1=(-9\pm3)\times10^{-4}$与$\alpha_2=(2\pm3)\times10^{-4}$。当模型偏差被抑制时，所得测量偏差接近欧几里得任务要求，且主要受未检测到的暗弱星系影响（$-5\times10^{-3}$）。尽管模型偏差显著，但其弱敏感性使得校准工作较为直接。LensMC已在 https://gitlab.com/gcongedo/LensMC 公开。