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

Abstract

Accurate modeling of geometric distortion 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 geometric distortion (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 coma, 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 pixel in translation and 1.8 arcsec 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.

Figures (12)

• Figure 1: The mosaic CCD layout of WFST. The light gray circle marks the FoV of WFST, while the red rectangles represent individual CCDs. Black coordinate axes denote the local Cartesian system of each CCD, and the blue axes indicate the global Cartesian system of the FoV. The parameter $\alpha_i$ represents the rotation angle of each CCD relative to the central CCD.
• Figure 2: Framework of global GD modeling. The green box represents the CCD calibration module, which is used to remove instrumental signals from the images. The blue box denotes the initial astrometric calibration module for extracting source catalogs from the images and provides the CD matrix together with CRVAL and CRPIX values for GD modeling. The red box indicates the precise astrometric calibration module, which outputs a combined source catalog for all CCDs after applying the GD model and corrections.
• Figure 3: Left to right shows the position offsets of the matched stars, the model global GDs with Zernike polynomicals, and the residuals between the observed offsets and the model GD, respectively. The upper panels correspond to a dense field, while the lower panels correspond to a sparse field. Arrow lengths are scaled according to the reference scale bar shown in each panel.
• Figure 4: Typical E- and B-mode correlation functions. The left panel shows the correlation functions for the exposure corresponding to panel (c) of Figure \ref{['fig:distortion']}, while the right panel shows the correlation functions averaged over all exposures in the 20250218 dataset. The solid curves denote the mean values, and the shaded regions indicate the $1\sigma$ scatter among the exposures.
• Figure 5: Global GD models and their difference maps for two pairs of consecutive exposures in the 2016HO3 field. Panels (a) and (b) show similar GD models in one pair of consecutive exposures, with panel (c) presenting their difference. Panels (d) and (e) display significantly different GD models in another pair of exposures, with panel (f) showing their difference.