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Optical Distortion

Point Spread Function

5.10 Optical Distortion

The WFPC2 cameras have significant geometric distortion which not only affects astrometry, but also affects photometry (because the extended sources used to generate flat fields have an induced change in apparent surface brightness). It can be a large effect, with "true" positions differing from observed positions by several pixels in the corners of the cameras. The distortion is wavelength dependent in the ultraviolet, because it is partially caused by the MgF_2 field flattener in front of each CCD. It is sensibly wavelength independent in the visible.

An estimate of the geometric distortion in the WFPC2 cameras was made (Holtzman et al., PASP 107, 156) from a series of 30 F555W exposures in a dense stellar field. Between each of these exposures, the telescope pointing was shifted by 16" in a 6 x 5 grid along rows and columns. On any given frame, positions of several dozens of stars were measured. Any pair of stars which appeared on three or more of the 30 frames was used to do a cubic distortion solution. The cubic distortion coefficients are of the form:

The coefficients are given in Table 5.5. The input (x,y) in the above equation are offsets from the center of each CCD in pixel units:

where (xobs, yobs) are the "observed" pixel positions on each CCD. The corrected values (xcorr, ycorr) are in a system with the origin near the pyramid apex, and the units are PC1 pixels. Hence PC1 in is quadrant 1, WF2 in quadrant 2, etc. Application of the transformation brings positions of all chips into the orientation of PC1.

The pixel scale can be estimated from the commanded offsets between the frames (relying on the FGS scale and distortion calibrations). It comes out as 0.04554 +/- 0.00001 arcseconds pixel-1 in the PC, and hence 0.09961, 0.09958, and 0.09964 arcseconds pixel-1 in WF2, 3 and 4 respectively. An independent check on an astrometric standard field (M67) yielded 0.04555 arcseconds pixel-1 in the PC. These plate scales refer to the scale at the center of the chip in filter F555W. The true scale is lower elsewhere on the chip because of distortion, and there is some wavelength dependence in the scale even for visible wavelengths.

Table 5.5: Cubic Distortion Coefficients.

The cubic distortion coefficients can be used to derive effective pixel areas as presented in Figure 5.12. Contours are shown at half percent levels. Measurements of total brightness or total counts (as opposed to measurements of surface brightness) should be corrected by multiplying the science image by Figure 5.12. This correction image is also available in the HST data archive as file f1k1552bu.r9h.

Figure 5.12: Integrated Photometry Correction Induced by Camera Distortions.

Figure 5.12: - Integrated Photometry Correction Induced by Camera Distortions.