A Deeper Solution to the Actual Geometry of CCD Mosaic Chips

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. We implemented the technique for the CCD mosaic chips of the Bok 2.3-m telescope based on two epochs of observations (Jan 17,2016 and Mar 5,2017). 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.