Astrometric Reduction of the Wide-Field Images

  • Volodymyr Akhmetov
  • Sergii KhlamovEmail author
  • Vladislav Khramtsov
  • Artem Dmytrenko
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1080)


In this paper we presented the new algorithm for astrometric reduction of the images received from modern large telescopes with very wide field of view. This algorithm is based on the iterative using of the method of ordinary least squares (OLS) and statistical Student t-criterion. The paper contains information about selecting the appropriate reduction model and system of conditional equations for determination of the reduction model parameters with the aim to solve it using the OLS method. The proposed algorithm also provides the automatic selection of the most probabilistic reduction model. At the first iteration the fifth degree polynomial is used, which provides 21 constant plates. The reduction error from the each iteration is used in the next iteration to eliminate reference objects whose residuals more than three sigma. In the developed algorithm the statistical Student t-criterion of reliability is applied after several iterations of getting rid of the noisy objects. This approach allows us to eliminate almost all systematic errors that are caused by imperfections of the optical system of modern large telescopes. The developed software based on the proposed algorithm was applied to perform the astrometric reduction of all measured positions of objects on the digitized photographic plates of SuperCOSMOS data. The research results showed that the new proposed algorithm allows performing the reduction into the system of reference catalogue with the highest accuracy level.


Database Big data Catalogue Astrometry Reduction Wide field Data analysis 



This research has made using the data obtained from the SuperCOSMOS Science Archive, prepared and hosted by the Wide Field Astronomy Unit, Institute for Astronomy, University of Edinburgh, which is funded by the UK Science and Technology Facilities Council.

This work has made using the data from the European Space Agency (ESA) mission Gaia [30], processed by the Gaia Data Processing and Analysis Consortium (DPAC) [31]. Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement [32].


  1. 1.
    Khlamov, S., Savanevych, V., Briukhovetskyi, O., Pohorelov, A., Vlasenko, V., Dikov, E.: CoLiTec software for the astronomical data sets processing. In: Proceedings of the IEEE 2nd International Conference on Data Stream Mining and Processing, DSMP 2018, pp. 227–230 (2018)Google Scholar
  2. 2.
    Khlamov, S., Savanevych, V., Briukhovetskyi, O., Pohorelov, A.: CoLiTec software – detection of the near-zero apparent motion. In: Proceedings of the International Astronomical Union, vol. 12(S325), pp. 349–352. Cambridge University Press (2017)Google Scholar
  3. 3.
    Raab, H.: Astrometrica: Astrometric Data Reduction of CCD Images. Astrophysics Source Code Library, record: 1203.012 (2012)Google Scholar
  4. 4.
    Masson, M.E.J.: A tutorial on a practical Bayesian alternative to null-hypothesis significance testing. Behav. Res. Methods 43, 679–690 (2011)CrossRefGoogle Scholar
  5. 5.
    Morey, R.D., Wagenmakers, E.-J.: Simple relation between Bayesian order-restricted and point-null hypothesis tests. Stat. Probab. Lett. 92, 121–124 (2014)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Gunawan, S., Panos, Y.P.: Reliability optimization with mixed continuous-discrete random variables and parameters. J. Mech. Des. 129(2), 158–165 (2006)CrossRefGoogle Scholar
  7. 7.
    Savanevych, V., Briukhovetskyi, O., Sokovikova, N., Bezkrovny, M., Vavilova, I., Ivashchenko, Yu., Elenin, L., Khlamov, S., Movsesian, Ia., Dashkova, A., Pogorelov, A.: A new method based on the subpixel Gaussian model for accurate estimation of asteroid coordinates. MNRAS 451(3), 3287–3298 (2015)Google Scholar
  8. 8.
    Savanevych, V., Khlamov, S., Vavilova, I., Briukhovetskyi, A., Pohorelov, A., Mkrtichian, D., Kudak, V., Pakuliak, L., Dikov, E., Melnik, R., Vlasenko, V., Reichart, D.: A method of immediate detection of objects with a near-zero apparent motion in series of CCD-frames. A & A 609(A54), 11 (2018)Google Scholar
  9. 9.
    Khlamov, S., Savanevych, V., Briukhovetskyi, O., Oryshych, S.: Development of computational method for detection of the object’s near-zero apparent motion on the series of CCD–frames. Eastern-Eur. J. Enterp. Technol. 2(9(80)), 41–48 (2016)CrossRefGoogle Scholar
  10. 10.
    Miura, N., Kazuyuki, I., Naoshi, B.: Likelihood-based method for detecting faint moving objects. Astron. J. 130, 1278–1285 (2005)CrossRefGoogle Scholar
  11. 11.
    König, A.: Astrometry with Astrographs. University Chicago Press, Chicago (1964). Edited by Hiltner, W.A. Chapter 20Google Scholar
  12. 12.
    Skidmore, W., et al.: Thirty Meter Telescope Detailed Science Case: 2015. Res. Astron. Astrophys. 15(12), 1945–2140 (2015)CrossRefGoogle Scholar
  13. 13.
    Tuell, M., Martin, H., Burge, J., Gressler, W., Zhao, C.: Optical testing of the LSST combined primary/tertiary mirror. In: Modern Technologies in Space- and Ground-based Tele-scopes and Instrumentation, p. 77392V (2010)Google Scholar
  14. 14.
    Kiselev, A.: Theoretical fundamentals of photographic astrometry, 264 p. Moscow, Izdatel’stvo Nauka (1989). (in Russian)Google Scholar
  15. 15.
    Hambly, N., et al.: The Super COSMOS Sky Survey – I. Introd. Descr. MNRAS 326(4), 1279–1294 (2001)Google Scholar
  16. 16.
    Akhmetov, V., Fedorov, P., Velichko, A.: The PMA catalogue as a realization of the extragalactic reference system in optical and near infrared wavelengths. In: Proceedings of the IAU, vol. 12(S330), pp. 81–82. Cambridge University Press (2018)Google Scholar
  17. 17.
    Akhmetov, V., Fedorov, P., Velichko, A., Shulga, V.: The PMA catalogue: 420 million positions and absolute proper motions. MNRAS 469(1), 763–773 (2017)CrossRefGoogle Scholar
  18. 18.
    Collaboration, G.: Summary of the astrometric, photometric, and survey properties. A & A 595(A2), 23 (2016)CrossRefGoogle Scholar
  19. 19.
    Cutri, R., Skrutskie, M., Van, D., Beichman, C., Carpenter, J., Chester, T., Cambresy, L., Evans, T., Fowler, J., Gizis, J., Howard, E., Huchra, J., Jarrett, T., Kopan, E., Kirkpatrick, J., Light, R., Marsh, K., McCallon, H., Schneider, S., Stiening, R., Sykes, M., Weinberg, M., Wheaton, W., Wheelock, S., Zacarias, N.: The 2MASS All-Sky Catalog of Point Sources. CDS/ADC Collection of Electronic Catalogues, p. 2246 (2003)Google Scholar
  20. 20.
    Wells, D., Greisen, E., Harten, R.: FITS: A Flexible Image Transport System. Astron. Astrophy. Suppl. Ser. 44, 363–370 (1981)Google Scholar
  21. 21.
    Greisen, E., Calabretta, M.: Representations of world coordinates in FITS. A & A 395(3), 1061–1075 (2002)CrossRefGoogle Scholar
  22. 22.
    Hambly, N., Irwin, M., MacGillivray, H.: The SuperCOSMOS Sky Survey – II. Image Detect. Parametrization Classif. Photom. MNRAS 326(4), 1295–1314 (2001)Google Scholar
  23. 23.
    The GNU Multiple Precision Arithmetic Library GMP «Arithmetic without limitations». Accessed 11 July 2019
  24. 24.
    Kudzej, I., Savanevych, V., Briukhovetskyi, O., Khlamov, S., Pohorelov, A., Vlasenko, V., Dubovský, P., Parimucha, Š.: CoLiTecVS – a new tool for the automated reduction of photometric observations. Astron. Nachr. 340(1–3), 68–70 (2019)CrossRefGoogle Scholar
  25. 25.
    CoLiTec – Collection Light Technology. Accessed 11 July 2019
  26. 26.
    Savanevych, V., Briukhovetskyi, A., Ivashchenko, Yu., Vavilova, I., Bezkrovniy, M., Dikov, E., Vlasenko, V., Sokovikova, N., Movsesian, Ia., Dikhtyar, N., Elenin, L., Pohorelov, A., Khlamov, S.: Comparative analysis of the positional accuracy of CCD measurements of small bodies in the solar system software CoLiTec and Astrometrica. Kinematics Phys. Celestial Bodies 31(6), 302–313 (2015)Google Scholar
  27. 27.
    Astrometrica. Accessed 11 July 2019
  28. 28.
    Fedorov, P., Akhmetov, V., Shulga, V.: The reference frame for the XPM2. MNRAS 440(1), 624–630 (2014)CrossRefGoogle Scholar
  29. 29.
    Akhmetov, V., Khlamov, S., Dmytrenko, A.: Fast coordinate cross-match tool for large astronomical catalogue. Adv. Intell. Syst. Comput. 871, 3–16 (2019)Google Scholar
  30. 30.
    European Space Agency (ESA) Gaia Science Community., Accessed 21 Aug 2019
  31. 31.
    DPAC Consortium. Accessed 21 Aug 2019
  32. 32.
    Akhmetov, V., Khlamov, S., Khramstov, V., Dmytrenko, A.: New algorithm for astrometric reduction of the widefield images. In: Proceedings of International Scientific Conferece “Computer Sciences and Information Technologies” (CSIT-2019), pp. 106–109. IEEE v. 2 (2019)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.V. N. Karazin Kharkiv National UniversityKharkivUkraine

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