HST Data Handbook for WFPC2

5.4 Astrometry

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Astrometry with WFPC2 means primarily relative astrometry. The high angular resolution and sensitivity of WFPC2 makes it possible, in principle, to measure precise positions of faint features with respect to other reference points in the WFPC2 field of view. On the other hand, the absolute astrometry that can be obtained from WFPC2 images is limited by the positions of the guide stars, usually known to about 0."5 rms in each coordinate, and by the transformation between the FGS and the WFPC2, which introduces errors of order of 0."1 (see Instrument Science Report OSG-006).

Because WFPC2 consists of four physically separate detectors, it is necessary to define a coordinate system that includes all four detectors. For convenience, sky coordinates (right ascension and declination) are often used; in this case, they must be computed and carried to a precision of a few mas, in order to maintain the precision with which the relative positions and scales of the WFPC2 detectors are known. It is important to remember that the coordinates are not known with this accuracy. The absolute accuracy of the positions obtained from WFPC2 images is typically 0."5 rms in each coordinate and is limited primarily by the accuracy of the guide star positions.

The recommended way to convert pixel coordinates into relative coordinates is to use the task, metric, which can handle both WF/PC-1 and WFPC2 images. The task xy2rd, will provide rough coordinates only and does not take geometric distortion into account.

For WFPC2 images, metric corrects the geometric distortion introduced by the camera optics, primarily the field flattening lenses, and brings the four chips into the metachip reference system, defined so as to have the same orientation and plate scale as the WF2 chip at its center. These coordinates are then converted into right ascension and declination by using the position and orientation of the WF2 chip. A related task, invmetric, can be used to effect the opposite transformation, from right ascension and declination to chip and pixel position. The final relative positions are accurate to better than 0."005 for targets contained on one chip, and 0."1 for targets on different chips. Note that both metric and invmetric include specialized information about the geometry of WFPC2 (see ISR 95-02). They do not use the header parameters that describe the world coordinate system (CRVAL1 and 2, CRPIX1 and 2, and the CDMATRIX) to relate positions in different chips. Of these parameters, only the values for WF2 are used to convert the metachip positions to and from right ascension and declination. As a side effect, neither task can work on images that do not contain WF2, for which the xy2rd task can be used.

Observers should be aware that the task xy2rd provides rough coordinates only. It uses the world coordinate system parameters in each group to determine the coordinates associated with a given pixel position. However, xy2rd does not use the most recent information on the relative chip positions, and it does not apply the geometric correction. Each can result in an error of about 0."3, especially near the edges of the chip; typical errors are closer to 0."1.

Astrometric measurements may be improved in several ways. First, the processing epoch of the images should be evaluated. Early WFPC2 images, particularly non-OTFR data, may contain header parameters with less accurate values of the plate scale and of the chip-to-chip rotations; section 4.3.3 provides detailed recommendations on updating such WFPC2 image headers. Images retrieved via OTFR will contain the most up-to-date parameters available at the time of processing. A significant improvement can be achieved by correcting the systematic errors caused by the 34th row defect, discussed in The 34-th Row Defect; this can be accomplished by using the formulae developed by Anderson & King (PASP 111, 1095). And finally, observers may wish to use the improved geometric distortion solution provided in ISR 01-10 and/or correct for any possible wavelength dependence (Trauger et al. (1995)), as discussed below.

Though the original solution, which is based upon a relatively sparse field, provides an adequate measure of the WFPC2 geometric distortion, it has significant residuals at a level of 5 mas overall and 10-15 mas in the detector corners. The improved solution is based upon multiple observations of a rich star field in Cen; the new coefficients are tabulated in table 5.8 (see ISR 01-10 for details).

Table 5.8: Parameters of the new astrometric solution (taken from WFPC2 ISR 01-10). The functional form of the solution and the coefficient nomenclature are the same as those in Holtzman et al. (1995) and Trauger et al. (1995).

	C
#	PC	WF2	WF3	WF4
1	3.543560e+2	-8.096405e+2	-8.052758e+2	7.708965e+2
2	1.000210e+0	21.667040e-3	-2.186307e+0	11.503445e-3
3	1.685097e-3	-2.186781e+0	-10.318882e-3	2.187646e+0
4	-0.476421e-6	-1.081274e-6	-0.467968e-6	1.410633e-6
5	-0.128977e-6	4.875708e-6	2.360098e-6	-3.662324e-6
6	-1.119461e-6	1.160592e-6	-1.881792e-6	-0.820634e-6
7	-38.989762e-9	-1.068123e-9	73.972588e-9	-0.388185e-9
8	0.495226e-9	75.463250e-9	0.110498e-9	-77.222274e-9
9	-36.277270e-9	0.099408e-9	76.882580e-9	-1.794536e-9
10	-0.075298e-9	72.628997e-9	0.003372e-9	-76.141940e-9

 

	D
#	PC	WF2	WF3	WF4
1	3.436460e+2	7.667990e+2	-7.692243e+2	-7.708547e+2
2	2.649830e-3	2.185899e+0	4.282145e-3	-2.186289e+0
3	0.999790e+0	16.771070e-3	-2.185173e+0	16.304679e-3
4	-0.915545e-6	-3.953135e-6	-1.588401e-6	1.692025e-6
5	-0.347576e-6	-2.815106e-6	2.574760e-6	2.596669e-6
6	0.532097e-6	0.309766e-6	0.404571e-6	-1.059466e-6
7	-2.592636e-9	-73.394946e-9	-0.208263e-9	75.750980e-9
8	-34.967762e-9	-1.715681e-9	77.114768e-9	0.528052e-9
9	-1.570711e-9	-75.104144e-9	0.162718e-9	75.946626e-9
10	-41.901809e-9	-0.423891e-9	74.483675e-9	-0.237788e-9

 

Systematic residuals in this new solution are very small, about 1.2 mas in WF and less than 4.0 mas in PC. Note, however, that neither solution addresses any possible wavelength dependence - which is predicted to be a change in overall scale rather than higher-order distortions; for this, observers should refer to the ray-tracing solution presented by Trauger et al. (1995) and the PC chip UV scale correction factors in Barstow et al. (2001).

There is also clear evidence for long-term variations in the relative detector positions, based upon an analysis of WFPC2 K-spot images (internal exposures producing eleven fixed artificial stars along the chip quadrant boundaries). The spot positions are found to vary regularly over time, in a systematic fashion. All spot images within each chip move similar amounts, implying that the changes are due to a lateral motion of the image with respect to the detector rather than a rotation. The shifts were relatively large at first, about 2-4 pixels in the first few months of WFPC2 operation, and later decreased to about 0.1-0.2 pixel/year(WFPC2 ISR 01-10). Note that these long-term variations are not accounted for in the pointing information in the headers.