Weak gravitational lensing shear, a small but coherent distortion in the images of background galaxies caused by intervening mass, serves as a crucial tool for understanding the dark matter distribution and constraining cosmology model. The upcoming Rubin Observatory LSST survey promises to accurately measure the weak-lensing shear across billions of galaxies, requiring systematic control at the sub-percent level. In this presentation, I will commence with a concise overview of weak-lensing cosmology constraints in the Hyper Suprime-Cam (HSC) survey, a forerunner to the Rubin LSST. Following this, I will present a novel analytical framework specifically designed for the accurate and fast estimation of shear distortion. Then I will outline the future plans for implementing this methodology during the Rubin LSST's commissioning phase to ensure that the measurements rigorously comply with the systematic control requirements. These include conducting comprehensive tests related to shear, point-spread function, optical field distortion, and redshift estimation. Additionally, I will discuss the prospective extension of this analytical image perturbations estimation framework in broader contexts.
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