FIELD ASTROMETRY USING ORTHOGONAL FUNCTIONS

Orthogonal polynomials were used to model transformations between stan dards and plate coordinates as well as relations between two plate coo rdinates. Thanks to orthogonal functions, the estimates of model coeff icients are uncorrelated and so are coefficient accuracies. We determi ne 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 articl e we shall give a general determination of the ultimate performances a ccessible with a given set of data. We analyse the accuracy of 4th ord er transform in astrometric reduction of Schmidt plates. Using PPM sta rs, the 4th order transform accuracy is 1 mum or 0.065 arcsec. We foun d that the 4th order polynomials did not model any significant distort ions and that a 3rd order transform was sufficient at this level of ac curacy. Finally, by comparing two similar Schmidt plates, we searched for plate distortions with different scale lengths. We found significa nt small amplitude distortions (above 1 mum) that could only be modell ed 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.