A Robust Geometric Distortion Solution for Main Survey Camera of CSST

Abstract

The advancement in sensitivity and field of view of next-generation wide-field survey telescopes requires astrometric measurements with high precision, even in the presence of significant geometric distortions. To address this challenge, we develop a Weighted Polynomial Distortion Correction in 2-Phase (WPDC-2P) method. This approach enhances stellar cross-matching, incorporates distance-based weighting into the traditional polynomial fitting, and employs a look-up table to absorb the remaining distortion residuals. Validated on simulated data from the Main Survey Camera of the \emph{Chinese Space Station Survey Telescope} (CSST), incorporating geometric distortions up to approximately $200$ pixels, the method achieves astrometric standard deviation ranging from 0.013 to 0.107 pixels (0.03 pixels for the $g$-1 detector) across all 18 detectors. Under extreme crowding conditions (e.g., globular cluster NGC 2298), the astrometric precision for the $g$-1 detector reaches 0.05-pixel level within the central region ($r_d < 4000$), despite a centroiding precision of $\sim$0.04 pixels. When applied to the Beijing-Arizona Sky Survey data, for which the standard pipeline delivers an astrometric uncertainty of $\sim$20 mas, our method reduces the positional scatter to $ σ_{Δα}=5.494$ mas (0.01 pixels) and $ σ_{Δδ}=9.981$ mas (0.02 pixels) using only a weighted 3rd-order polynomial correction. The method has been integrated into the CSST data processing pipeline and is prepared for further refinement using on-orbit calibration data.

Figures (10)

• Figure 1: The distortion map of the MSC's 18 photometric detectors, derived from a subset of CSST 25-square-degree simulation program. Detector name and number are shown in blue on the central region of each detector box. The size of distortion vector marked in red is magnified by a factor of 10.
• Figure 2: Centroiding residuals as a function of source magnitude for 25 simulated CSST $g$-1 images with an exposure time of 150 seconds. The left and right panels show $\Delta X_{\rm PSF} = X_{\rm PSF} - X_{\rm ref}$ and $\Delta Y_{\rm PSF} = Y_{\rm PSF} - Y_{\rm ref}$, respectively, where $X_{\rm PSF}$ and $Y_{\rm PSF}$ are the centroid positions measured from PSF fitting, and $X_{\rm ref}$ and $Y_{\rm ref}$ are the corresponding simulated truth positions from mock reference catalog. Gray points represent individual stars, while red solid lines with error bars indicate the mean offsets and the corresponding $1\sigma$ centroiding precision in 0.5 mag bins.
• Figure 3: Workflow of the DiGStar algorithm for cross-matching. The process involves: (1) Data clipping and source extraction, (2) Grid-based local star density ratio analysis of the image, (3) KD-tree construction for efficient neighbor searches and relative position feature extraction, (4) Two-stage matching with outlier rejection (MAD filtering). Finally merging matched pairs with source metadata.
• Figure 4: Cumulative distribution functions of the positional residuals obtained from the four weighting functions in different color. The accuracy $d80$ denotes the width of $\Delta X$ between the 20% and 80% CDF level. The $w_1(r_d)$ scheme shows significantly better performance than the other weighting functions.
• Figure 5: Positional residuals $(\Delta X_{\rm PV}, \Delta Y_{\rm PV})$ obtained after the 3rd-order $PV$ parameter fitting. The blue and red points represent the mean residuals of non-weighted and weighted solutions, respectively, computed in slices of 512 pixels. The corresponding blued and red error bars are defined as the 68.27th percentile of the residual distribution (after a $3\sigma$ clipping). However, overweighting the central region results in systematic deviations of the GD correction at the edges, with larger central-to-edge weight differences producing greater accuracy errors. All the sources shown have $\mathrm{S/N} > 10$ in the detector $g$-1 detector.