Mathematics
Scientific paper
Oct 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993a%26a...278..301b&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 278, no. 1, p. 301-106
Mathematics
9
Astrometry, Optimization, Orthogonal Functions, Schmidt Cameras, Coordinates, Standard Deviation, Transformations (Mathematics)
Scientific paper
Orthogonal polynomials were used to model transformations between standards and plate coordinates as well as relations between two plate coordinates. Thanks to orthogonal functions, the estimates of model coefficients are uncorrelated and so are coefficient accuracies. We determine the standard deviation function of a given transform. This function gives a quantitative assessment of the accuracy and the significance of the relations between two coordinate systems. In the present article we shall give a general determination of the ultimate performances accessible with a given set of data. We analyze the accuracy of 4th order transform in astrometric reduction of Schmidt plates. Using PPM stars, the 4th order transform accuracy is 1 micrometer or 0.065 arcsec. We found that the 4th order polynomials did not model any significant distortions and that a 3rd order transform was sufficient at this level of accuracy. Finally, by comparing two similar Schmidt plates, we searched for plate distortions with different scale lengths. We found significant small amplitude distortions (above 1 micrometer) that could only be modelled by using a very high order transform. These distortions, reflecting image quality or performance of the measuring machine, illustrate the current limiting accuracy of Schmidt plate astrometry.
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