ner_tags: O O O O O O O O O O B-Model O O O O B-Model O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O B-Model O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O B-Model O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O B-Model I-Model O O O O O O O O O O O O B-Citation I-Citation O O B-Model I-Model O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O B-Dataset I-Dataset O O O O O O O O O O B-Dataset O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope I-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O B-Model I-Model I-Model O O O O O B-Model O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O B-Citation I-Citation I-Citation O O O
tokens: aberrations and we anticipate good astrometry results with the mean PSFs of each cluster. However, PSFs from stars with a magnitude of 11 have small and almost randomly distributed clusters. Although the mean PSFs of two different clusters are almost the same in Fig. 12(f) , this might be induced by the average of many different PSFs. To fully reflect the classification performance, we perform PSF-fitting astrometry in these data, using the Fourier-based registration method (Stone et al. 2001 ) with the mean PSFs obtained from our method. This method assumes that the PSFs in the same cluster are morphologically similar and only have a different subpixel shift. We can obtain this subpixel shift by maximizing the correlation coefficients between the stamp images of stars and the mean PSFs in an oversampled Fourier domain. The subpixel shift and the position of the brightest pixels in the images of the celestial objects can then be used to calculate the star's position in the image. For comparison, we also use the Gaussian function as a PSF template and we calculate the positions of stars with the least-squares fitting method (Stone 1989 ). The Gaussian function has a FWHM of 2 pixels. The positions we calculated with the above two methods are compared with the Tycho-2 catalogue (Høg et al. 2000 ) as follows. We obtain the star positions (α i , ξ i ) from the Tycho-2 catalogue as the theoretical positions of these stars and we construct the association between that position and the position of these stars in the image using as proposed in Sun, Zhao Zhang ( 2013 ). Here, (α 0 , δ 0 ) is the corresponding equatorial position of the frame centre. With this association, the observed position (α c , ξ c ) of these stars can be obtained from the pixel position ( x c , y c ), and the residual position errors of each star (α c − α i , δ c − δ i ) are obtained. The astrometry error of these two methods from the Tycho-2 catalogue is shown in Fig. 13 . The systematic errors of Tycho-2 are nearly 0.01 arcsec so this does not have an effect on the calculation. Compared with the Gaussian fitting method, we can see that stars with a magnitude of 10 have better astrometric accuracy with the mean PSF and stars with a magnitude of 11 have almost the same astrometric accuracy. Figure 13. Astrometric residuals of stars with magnitudes of 10 and 11 of telescope B. The number of stars with the magnitude of 10 is 517 and the number with the magnitude of 11 is 737. Top: the residuals of right ascension. Bottom: the residuals of declination. Crosses indicate Gaussian PSF-fitting centroid and circles indicate mean PSF fitting. It is worth noting that PSF classification is a clustering problem and for stars with the magnitude of 11, we do not know why the PSFs are not clustered distinctly. There are two possibilities: (i) these PSFs are nearly the same essentially, so applying the average of these PSFs for subsequent processing is a sound method (Sun Jia 2017 ); (ii) the