Design-to-as-built distortion modeling of Korsch Telescopes for weak-lensing surveys

Weak gravitational lensing requires highly accurate galaxy shape measurements, making geometric distortion a critical systematic in wide-field space telescopes. Korsch TMAs offer excellent low-order aberration control but struggle to achieve the low distortion needed for weak-lensing surveys. This work addresses this challenge via three integrated approaches. First, a machine-learning framework identifies low-distortion solutions within wide-field Korsch design space. Second, an end-to-end observation model based on non-sequential ray tracing simulates intrinsic galaxy structure, weak-lensing shear, optical propagation, and pixel sampling in a unified 3D environment. Third, as-built mirror poses from an Integrated Metrology System generate a realistic distortion model. Comparing ML-derived designs and as-built data enables clearer separation of instrumental distortion from true gravitational shear, supporting distortion-controlled telescope development for future weak-lensing missions.