Legendre Polynomial Basis for Optical Distortion Fitting in Eclipse Astrometry

Accurate measurement of stellar positions in wide-field eclipse images requires correcting for optical distortion across the camera's focal plane. The current pipeline for the Modern Eddington Experiment (MEE2024) models distortion using a standard monomial basis, which can become numerically ill-conditioned for higher-degree fits: fitted coefficients become sensitive to small changes in the data, and adding higher-order terms can destabilize lower-order fits. We investigate replacing monomials with Legendre polynomials, an orthogonal basis on a bounded interval. Orthogonality guarantees that fitted coefficients are statistically independent and remain stable as the polynomial degree is increased, potentially improving both the precision and interpretation of the distortion model. We present an implementation of Legendre polynomial distortion fitting integrated into the MEE pipeline and a direct comparison with the monomial fits on data from the 2024 eclipse, including fitted residuals and a comparison of the inferred gravitational deflection.