WFPC2 Instrument Handbook for Cycle 11
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| WFPC2 Instrument Handbook for Cycle 11 | |||
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Optical Distortion
The WFPC2 cameras have significant geometric distortion which not only affects astrometry, but also affects photometry (because it induces an apparent variation in surface brightness across the field, and hence impacts the flat fields). 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 MgF2 field flattener in front of each CCD. It is sensibly wavelength independent in the visible. (The wavelength dependence has been discussed by Trauger, et al., 1995.)
Estimates of the geometric distortion in the WFPC2 cameras have been made from observations of dense stellar fields (Holtzman et al. 1995a, PASP 107, 156; Casertano and Wiggs, 2001). In the most recent data 14 images were obtained in an "x" shaped pattern having offsets of 15" and 35" from the center; images at the center and ends of the pattern were also sub-pixel dithered. Stars appearing on more than one image were used to generate a global distortion map for the entire WFPC2 field-of-view, which was then used to derive a cubic distortion solution. The cubic distortion coefficients are of the form:
The coefficients are given in Table 5.6. 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 "/pixel in the PC, and hence 0.09961, 0.09958, and 0.09964 "/pixel in WF2, 3 and 4 respectively. An independent check on an astrometric standard field (M67) yielded 0.04555 "/pixel 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 5.6: Cubic Distortion Coefficients.
The residual maps presented in Figure 5.15 indicate the average residual at each position after using the above equations to remove the distortion. The residuals are expressed in PC pixels and scaled by a factor of 250. Each tickmark, which is 50 units, corresponds to about 9 mas. The residual length is mostly noise.
The geometric transformation of WFPC2 has a small time dependence, primarily in the interchip separation, which is probably due to small secular changes in its optical bench. The above Table is derived from data taken in 1997 and 1998, and hence is optimized for that epoch. Within each chip, changes are very small, and the new solution differs from the original Holtzman solution by a few percent of a pixel. The difference in the interchip separation, however, is as large as 150 mas. Since the interchip separation continues to change with time, the new solution is no more predictive than the original Holtzman solution.
Figure 5.15: Distortion Coefficient Residual Maps.
The cubic distortion coefficients can be used to derive effective pixel areas as presented in Figure 5.16. 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 5.16. (This correction image is also available in the HST data archive as file f1k1552bu.r9h.) This correction is necessary since the flat fields are designed to level-out a uniformly illuminated source (i.e. conserve surface brightness), and are not explicitly designed to conserve total integrated counts for a target. Since the geometric distortion conserves total counts, and merely acts to redistribute counts on the CCD, stellar photometry in flat fielded data usually will require the corrections in Figure 5.16.
Figure 5.16: Integrated Photometry Correction Induced by Camera Distortions.
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