WFST Astrometric Calibration. I. Modeling Global Geometric Distortion with Zernike Polynomials

Accurate modeling of geometric distortion (GD) is essential for precise astrometric calibration in wide-field imaging surveys. We present a self-calibration method based on Zernike polynomials, applied to imaging data from the Wide Field Survey Telescope (WFST). Our approach constructs a global GD model from the position offsets of stars in the WFST r band relative to Gaia DR3, achieving a median systematic uncertainty of below 10 mas for individual exposures. The correspondence between Zernike polynomials and optical aberrations reveals that the global GD of WFST is dominated by comae, inherent to the optical design, while rapid variations are likely attributed to the atmospheric dispersion corrector. Applying this method to 82 exposures from a single night (20250218), we find that the relative positions of the WFST CCDs remain stable, with standard deviations of less than 0.1 pixels in translation and 1.″8 in rotation. The corrected WFST astrometric system is thereby tied to the Gaia DR3 coordinate frame, with further refinements to be presented in future work.