3. Astrometry of the ground based images
The absolute astrometry of both plates and CCD frames is done utilizing reference stars. The insufficient density and the relatively bright magnitudes of the fundamental catalogs require the creation of a list of secondary reference stars within a suitable magnitude range and sufficiently close to the fainter target to be visible on larger scale, small field, plates or CCD frames (de Vegt 1979, Clements 1981). In our case, the absolute positions of the secondary references are established using the large-field refractor plates and a set of CAMC fundamental stars (Helmer & Morrison 1985, Carlsberg Meridian Catalog 1989, 1992, and 1993), which materialize the FK5 optical reference frame on the sky. Six CAMC stars were available for the primary calibration of the refractor plates. The metric properties of the focal plane of the refractor are such that a linear 3-constant polynomial model (for each coordinate) is adequate for an accurate transformation to the tangent plane, and therefore to the sky; magnitude and color terms are both negligible (Chiumiento et al. 1991 and references therein). The relevant errors characterizing the accuracy of the realization of the fundamental frame on the refractor plates are listed in Table 2.
Table 2. Astrometry error budget of ground based images. is the mean error (per coordinate) as calculated from the residuals of the reference stars, is the estimated mean error of the primary reference catalog, the measuring (or centering) error, and the error of the transformation plate-to-sky, as defined in the text. A good calibration is such that . Measuring errors are estimated at 30 mas (i.e., 1/15 pixel) for plate images, and 9 mas ( 1/50 pixel) for CCD images
Right ascensions and declinations on the FK5 system (equinox J2000 and epoch of plate) of 7 faint secondary astrometric standards within the CCD field-of-view were produced using the calibration just discussed. This same procedure, applied to the secondary standards, yields the plane-to-sky calibration for the CCD frame. The epoch difference among plates and CCD frames is less than two months; therefore, errors induced by undetected proper motions of the secondary reference stars are minimized. This is confirmed by the good agreement in Table 2 between the estimates in the third column of the first and second lines, and the residuals-derived values in the first column of lines three and four.
From the values in Table 2, it is evident that limitations to the astrometric calibrations come from both the image measuring errors (especially for the plates) and from the primary reference catalog, for which the contribution from the proper motions error becomes dominant for differences between catalog mean epoch and plate epoch on the order of 10 years.
Important for this work is to estimate the precision with which we can "position" any given measured images (either on the plates or on the CCD frames) within the FK5 frame. This error is the sum in quadrature of the centering error and the error of the transformation which can be evaluated as , where is the error in the primary reference catalog, n is the number of free parameters in the plate-to-field transformation used, and m is the number of primary reference stars; in our case, n = 3 and m = 6, 55 mas. The use of better catalogs (as with Hipparcos) would definitively improve on the 55 mas above. For example, with six Hipparcos stars the expected error on the transformation would be (including the proper motion error for an epoch difference of about 3 years) 5 mas! Therefore, with Hipparcos the expectation is that these calibrations will be limited, primarily, by the measuring errors, at least until the degradation induced by the proper motion error settles in.
It is important to notice that is systematic, in the sense that all measured images of the secondary reference stars will be affected by the same error (Eichhorn 1974). This explains why the of the two least squares adjustments of the 600sec CCD frame reflects just the plate measuring errors (the CCD measuring error being negligible). Using the same argument as before, the error of a given CCD position relative to the secondary frame is 20 mas 1. Therefore, the precision with which we can "position" one of our ground based CCD images within the local FK5 frame is 58 mas; this reduces to 41 mas (total positional error) combining the two independent calibrations of the 600sec CCD frame. This error does not include yet any local systematic deviation of the optical frame from the radio one. This is discussed in Section 5 below. Finally, we need a procedure to transform the HST WF/PC-I pixels into pixels consistent with the ground based CCD image. This transformation introduces another term in the total error budget, which must be added in quadrature to the value above.
Once this is accomplished, any given pixel of the WF/PC-I image can be mapped, thanks to the absolute calibration of the ground based CCD frame, onto the FK5 optical frame, i.e., the HST image can be registered onto such a frame. The HST-to-ground-based registration procedure is the subject of the next section.
© European Southern Observatory (ESO) 1997
Online publication: July 3, 1998