A deeper solution to the actual geometry of CCD mosaic chips
Authors: Zheng Z. J. , Peng Q. Y. , Vienne A. , Lin F. R. , Guo B. F. 
Published: February 2022

Context. For charge-coupled device (CCD) mosaic chips in the focal plane of a large telescope, the unification for all the measurements of each chip is vital to some scientific projects, such as deep astrometric standards or construction for deeper images that can also seamlessly cover a larger area of the sky. A key part of the reduction involves the accurate geometric distortion (GD) correction and the precise determination of the relative positions of the CCD chips. The short-term and long-term stabilities of them are also important when it comes to studying whether there are systematic variations in the optical system of the telescope.
Aims. We present a solution to determine the actual or physical relative positions between CCD chips. Due to the limited depth of the Gaia catalogue, there may be few stars identified from the Gaia catalogue for astrometric calibration on the deep observation of a large, ground-based or space-based telescope, such as the planned two-metre Chinese Space Station Telescope (CSST). For this reason, we referred to the idea from the Hubble Space Telescope (HST) astrometry to only use stars’ pixel positions to derive the relative positions between chips. We refer to the practice as differential astrometry in this paper. In order to ensure the results are reliable, we took advantage of Gaia EDR3 to derive the relative positions between chips, to provide a close comparison. We refer to the practice as photographic astrometry.
Methods. By taking advantage of the GD solution and the common distortion-free frame derived from the observations, we related the physical positions of the adjacent pixel edges of two CCD chips and estimated the actual relative positions between chips. We implemented the technique for the CCD mosaic chips of the Bok 2.3-m telescope at Kitt Peak based on two epochs of observations (January 17, 2016 and March 5, 2017).
Results. There is a good agreement between the two types of astrometry for the relative positions between chips. For the two epochs of observations, the averages of the gaps derived from photographic astrometry and differential astrometry differ to about 0.046 pixels (~0.021 arcsec) and 0.001 pixels (<0.001 arcsec), respectively, while the average precisions of the gaps are about 0.018 pixel (~0.008 arcsec) and 0.028 pixels (~0.013 arcsec), respectively. The results provide us with more confidence in applying this solution for the CCD mosaic chips of the CSST by means of differential astrometry. Compared with the solution described by Anderson & King, which has been used to determine the interchip offset of Wide Field Planetary Camera 2 (WFPC2) chips and Wide Field Camera 3 (WFC3) chips at the HST, the solution proposed in this paper shows at least a factor of two improvement in precision, on average.
Conclusions. We think there are two definite advantages of our method. On one hand, we perform the measurements for two adjacent edges instead of two individual chips, allowing the results to be as local as possible, and meanwhile we alleviate the propagated error of residual distortions of each observation deviating from the average solution throughout the field of view (FOV). On the other hand, the final outcome is not mixed up with GD effects, which would bias the realistic geometry of the CCD mosaic chips. Therefore, the proposed method is expected to be an effective technique to monitor the stability of the CCD mosaic chips in the CSST and other ground-based CCD mosaic as well.