Space Telescope Science Institute
WFC3 Data Handbook 2.1 May 2011
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WFC3 Data Handbook > Chapter 4: WFC3 Images: Distortion Correction and MultiDrizzle > 4.1 WFC3 Geometric Distortion

WFC3 images exhibit significant geometric distortion, similar to that seen in ACS images. The required folding, with powered optics, of the light paths in both channels to fit within the instrument’s optical-bench envelope results in substantial tilts of the focal surfaces with respect to the chief rays. The WFC3 UVIS detector is tilted at ~21 about one of its diagonals, producing a rhomboidal elongation of ~7%. The IR detector has a ~24 tilt about its x-axis, creating a rectangular elongation of ~10%.
If these were the only distortions, they would not present much difficulty: their impacts on photometry, mosaicking, or dithering could be computed simply. More problematic, however, is the variation of plate scale across each detector. For the WFC3 UVIS and IR channels, this variation in plate scale amounts to a change of 3.5% and 2%, respectively, over the full field. Hence the area on the sky covered by a UVIS pixel varies by about 7% from corner to corner, and about 4% for the IR channel.
Dithering and mosaicking are complicated by the fact that an integer pixel shift near the center of the detector will translate into a non-integer displacement for pixels near the edges. Even this is not a fundamental difficulty, but will imply some computational complexity in registering and correcting images. All of these considerations make it necessary to obtain accurate measurements of the distortions. The orientations of the WFC3 detector edges for both detectors are at approximately 45 with respect to the V2 and V3 coordinate axes of the telescope. Figure 2.2 of the WFC3 Instrument Handbook shows the WFC3 apertures in the telescope’s V2,V3 reference frame. For a telescope roll angle of zero this would correspond to an on-sky view with the V3-axis aligned with north and the V2-axis with east.
The first on-orbit measurements of the geometric distortion for the WFC3 detectors were made during SMOV (Servicing Mission Observatory Verification). Astrometric fields in 47 Tuc (NGC 104) and the LMC were observed with multiple offsets in programs 11444 (UVIS, filter F606W) and 11445 (IR, filter F160W). The distortion solutions have since been improved by incorporating observations taken during Cycle 17, where the globular cluster Omega Centauri (NGC 5139) was observed in multiple filters in program 11911 (UVIS) and 11928 (IR).
See WFC3 ISR 2009-33, WFC3 ISR 2009-34 to support the use of MultiDrizzle to produce distortion-corrected images (see the MultiDrizzle Handbook).
Figure 4.1 illustrates the shape of the UVIS channel field of view as projected onto the sky. As noted above, its rhomboidal shape is due primarily to the diagonal tilt of the CCD focal plane with respect to the chief ray (see Figure 1.1). The angle between the x- and y-axes is ~86.1. The field diagonals are tilted slightly from the V2- and V3-axes. There is a ~1.2 arcsec gap between the two CCD chips. The crosses in the diagram indicate where points in the image would be located without non-linear distortion, and the vectors, scaled up by a factor of 10, indicate the actual locations of the points on the sky, including the non-linear distortion components.
The corner displacements are about 140 pixels, corresponding to 5.5 arcsec. The principal effect is the diagonal variation of scale. At the center of UVIS1 (CCD CHIP1), the scale in the x-direction is 0.0396 arcsec/pixel, and 0.0393 arcsec/pixel in the y-direction. For UVIS2 (CCD CHIP2), these scales are 0.0400 arcsec/pixel, and 0.0398 arcsec/pixel, respectively. UVIS1 forms a slightly distorted rectangle 162 81 arcsec in size, while UVIS2 subtends 164 81 arcsec.
The resulting variation of the projected pixel area on the sky requires corrections to photometry of point sources using images that have not been distortion corrected. See Section 7.2.3 and WFC3 ISR 2010-08 for a discussion on the effects of the pixel area map on photometry.
Figure 4.1: Linear Components (crosses) and non-linear components (vectors, magnified by 10) of the geometric distortion on the WFC3-UVIS detector.
The IR detector field of view is nominally concentric with the UVIS field, but subtends a somewhat smaller area on the sky, 136 123 arcsec. The detector tilt is about the x-axis (USER1), so the projected aperture shape is nearly a rectangle, with the angle between the x- and y-axes on the sky nearly 90, as shown by the outline in Figure 4.2. At field center, the x- and y-scales are 0.135 and 0.121 arcsec/pixel, respectively. A vector plot of the deviation from linearity is also shown in Figure 4.2, where the deviations have been magnified by a factor of 10 for illustrative purposes. The largest deviation is 10 pixels, corresponding to about 1.4 arcsec.
Figure 4.2: Linear components (crosses) and non-linear components (vectors, magnified by 10) of the geometric distortion on the WFC3-IR detector.

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