Mitigating effects of telescope jitter through differentiable forward-modeling

Instabilities in telescope pointing, commonly referred to as jitter, introduce image degradation that can compromise the accuracy of critical scientific observables. This work presents a differentiable forward-modeling approach to both understand and mitigate the impact of jitter. We apply dLux -- a differentiable optical simulation framework built in the JAX numerical simulation framework -- to model the blurring effects of jitter on the final image. We categorize jitter into low-, medium-, and high-frequency regimes with respect to the camera frame rate and build simple jitter models based on its manifestation on the detector. The forward-model approach proves effective for low- and high-frequency regimes, but the inherent unpredictability of medium-frequency jitter may lead to model misspecification. As a test case we apply these models to the TOLIMAN mission, a forthcoming CubeSat telescope dedicated to detecting nearby Earth-analogue exoplanets through high-precision astrometry. Using Fisher information analysis, we quantify the effect of jitter on TOLIMAN's primary science observable -- the angular binary separation of the Alpha Centauri AB binary components. We find model misspecification does not introduce a systematic bias on the recovered binary separation except when fitting a one-dimensional jitter model to a two-dimensional motion, hence we recommend the use of a two-dimensional model. The forward-model approach offers a generalized method applicable to other telescope systems, including ongoing work with JWST's NIRISS instrument. This approach represents a significant step toward delivering higher accuracy measurements at modern observatories as demands on precision continue to rise.