Wide Field and Planetary Camera 2 Instrument Handbook for Cycle 13
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| Wide Field and Planetary Camera 2 Instrument Handbook for Cycle 13 | ||||
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5.11 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, and more recently by Kozhurina-Platais, Anderson and Koekemoer, 2003, as will be discussed below.)
Estimates of the geometric distortion for the F555W filter have been made from observations of dense stellar fields (Holtzman et al. 1995a, PASP 107, 156; Casertano and Wiggs, 2001, Anderson and King, 2003). The cubic distortion coefficients are of the form:
The coefficients from Anderson and King (2003) are given in Table 5.6. The Anderson and King (2003) solution represents a major improvement over earlier distortion solutions, partly because of a much better algorithm for measuring stellar positions, and partly because of their discovery that a skew term is important to the solution.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 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.
The residual maps presented in Figure 5.16 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 5.16: Distortion Coefficient Residual Maps.
The cubic distortion coefficients can be used to derive effective pixel areas as presented in Figure 5.17. 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 5.17. (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 5.17.
Khozurina-Platais, Anderson, and Koekemoer (2003) used the methodology developed by Anderson and King (2003) to determine geometric distortion solutions for the F300W and F814W filters. They find that the amount of distortion is about 3% higher for the F300W filter than for the F555W filter, and about 1% lower for the F814W filter than for the F555W filter. Figure 5.18 shows the difference in distortion between the F300W and F555W positions for
Figure 5.17: Integrated Photometry Correction Induced by Camera Distortions.Cen data, while Figure 5.19 shows the same for the F814W compared to the F555W data. Table 5.7 shows the plate scale for the two filters relative to F555W. See Khozurina-Platais, Anderson, and Koekemoer (2003) for the distortion residual maps and further details.
Figure 5.18: Difference in distortion between F300W and F555W positions.
Figure 5.19: Difference in distortion between F814W and F555W positions.
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