Astrometric solving or Plate solving or Astrometric calibration of an astronomical image is a technique used in astronomy and applied on celestial images. Solving an image is finding match between the imaged stars and a star catalogue. The solution is a math model describing the corresponding astronomical position of each image pixel.[1] The position of reference catalogue stars has to be known to a high accuracy so an astrometric reference catalogue is used such as the Gaia catalogue.
The image solution contains a reference point, often the image centre, image scale, image orientation and in some cases an image distortion model.
With the astrometric solution it is possible to:
Calculate the celestial coordinates of any object on the image.
Synchronize the telescope mount or satellite pointing position to the center of the image taken.
In the past, plate solving was done manually by accurately measuring photographic glass plates taken with an astrograph (astrographic camera)[2][3]
Currently, astrometric solving is exclusively done by software programs. The program extracts the star x,y positions from the celestial image, groups them in three-star triangles or four-star quads. Then it calculates for each group a geometric hash code based on the distance and/or angles between the stars in the group. It then compares the resulting hash codes with the hash codes created from catalogue stars to find a match. If it finds sufficient statistically reliable matches, it can calculate transformation factors.[4] The solver should be fast and reliable with no false matches.
There are several conventions to model the transformation from image pixel location to the corresponding celestial coordinates. The simplest linear model is called the World Coordinate System. A more advanced convention is SIP (Simple Imaging Polynomial) describing the transformation in polynomials to cope with non-linear geometric distortion in the celestial image, mainly caused by the optics.
^Sam Roweis; Dustin Lang; Keir Mierle; David Hogg; Michael Blanton (2006-09-28). "Making the Sky Searchable: Fast Geometric Hashing for Automated Astrometry" (PDF). [cosmo].
^W. M. Smart (1977). "XII Astronomical Photography". Spherical-astronomy (6th ed.). ISBN 0-521-21516-1.
^Oliver Montenbruck; Thomas Pfleger (1998). "Chapter 12 Astrometry". Astronomy on the Personal Computer (3rd ed.). Springer-Verlag. ISBN 3-540-63521-1.
^Dustin Lang; David W. Hogg; Keir Mierle; Michael Blanton; Sam Roweis (2010). "Astrometry.net: Blind astrometric calibration of arbitrary astronomical images". The Astronomical Journal. 139 (5): 1782–1800. arXiv:0910.2233. Bibcode:2010AJ....139.1782L. doi:10.1088/0004-6256/139/5/1782. S2CID 51763695.
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Astrometricsolving or Plate solving or Astrometric calibration of an astronomical image is a technique used in astronomy and applied on celestial images...
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Retrieved 1 July 2021. Morley, T. A. (1989). "A catalogue of ground-based astrometric observations of the Martian satellites, 1877-1982". Astronomy and Astrophysics...
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K. C. (2022). "An Isolated Stellar-Mass Black Hole Detected Through Astrometric Microlensing". Astrophysical Journal. 933 (1): 83. arXiv:2201.13296....
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Martín, Eduardo L.; Queloz, D.; Mayor, M.; Udry, S. (August 2013). "Astrometric orbit of a low-mass companion to an ultracool dwarf". Astronomy & Astrophysics...
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Retrieved 12 September 2006. Morley, T. A.; A Catalogue of Ground-Based Astrometric Observations of the Martian Satellites, 1877-1982, Astronomy and Astrophysics...
Phillips, Robert B.; Hodges, Mark W.; Preston, Robert A. (June 1993). "VLBI astrometric identification of the radio emitting region in Algol and determination...
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