WFC3 Data Handbook V. 4.0

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4.1	WFC3 Geometric Distortion

4.1.1 The IR Channel

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 degrees about one of its diagonals, producing a rhomboidal elongation of ~7%. The IR detector has a ~24 degree 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, mosaics, 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 mosaics 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 implies 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 degrees 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 derived WFC3-UVIS geometric distortion, as described in detail by Kozhurina-Platais et al., (WFC3-ISR-2009-33 and WFC3-ISR-2009-34, and updated in WFC3-ISR-2014-12), is presented as a fourth-order polynomial model and is accurate to a precision level of 0.1 pixel in the UVIS and IR or 4 mas and 10 mas, respectively.

In Cycles 18, 19, 20, the globular cluster Omega Centauri was observed through 14 UVIS and 5 IR filters (WFC3 Calibration Programs 11911, 11928, 12353 and 13100). Therefore, for each of the 14 calibrated UVIS and 5 calibrated IR filters, unique polynomial coefficients of the geometric distortion (Kozhurina-Platais et.al, WFC3-ISR-2012-07,) in the form of Instrument Distortion Correction Tables (IDCTAB), are available for use in ST software DrizzlePac/AstroDrizzle and in the STScI on-the-fly pipeline (OTFR).

For the UVIS CCDs, on top of this large-scale geometric distortion, there is a micro-distortion, which consists of fine-scale systematics in the residuals from the best-fit polynomial solutions. These systematic residuals typically extend to ~0.15 pixel and vary in amplitude depending on the location within a CCD chip. Such residuals cannot be removed by a polynomial model. These fine scale and low amplitude distortions are the result of a detector defect caused by the manufacturing process. The WFC3-UVIS detector defect due to lithographic-mask pattern is imprinted onto the detector itself.

The correction for these defects is implemented in DrizzlePac/AstroDrizzle as a 2-D bilinear interpolation (D2IMFILE,Detector to Image distortion correction reference file) which is applied, prior to the large-scale distortion (polynomial model) correction (IDCTAB) (Kozhurina-Platais, et.al. WFC3-ISR-2013-14). The look-up table is incorporated by running updatewcs (via AstroDrizzle) with the filename specified in the D2IMFILE keyword in the primary image header, which will then be attached to the image as a fits extension of type 'D2IMARR' (four extensions total, two for each chip and dimension). Each element of the 32x17 table gives the astrometric xy shift in pixels to apply at a particular location on the detector. SSBX allows AstroDrizzle to interpolate across a 2-D table grid, hence only SSBX versions after May 2012 can apply the D2IMFILE corrections. The current D2IMFILE file is available here:

http://www.stsci.edu/hst/wfc3/lbn_archive/2013_06_11_new_d2im

The knowledge of geometric distortion of the WFC3-UVIS and IR is the backbone of the STSDAS software DrizzlePac/AstroDrizzle software (Gonzaga, et al., 2012), which is currently installed in the STScI on-the-fly pipeline (OTFR). This software requires accurate distortion correction in order to combine dithered WFC3 images, and thus enhance the spatial resolution and deepen the detection limit.

Users can find information on DrizzlePac and AstroDrizzle at http://www.stsci.edu/hst/HST_overview/drizzlepac

The UVIS Channel

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 degrees. 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 dots 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 x 81 arcsec in size, while UVIS2 subtends 164 x 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 9.2.3 and WFC3 ISR 2010-08 for a discussion on the effects of the pixel area map on photometry.

Figure 4.1: Linear Components (dots) and non-linear components (vectors, magnified by 10) of the geometric distortion on the WFC3-UVIS detector.

4.1.1 The IR Channel

The IR detector field of view is nominally concentric with the UVIS field, but subtends a somewhat smaller area on the sky, 136 x 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 degree 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: F Linear components (dots) and non-linear components (vectors, magnified by 10) of the geometric distortion on the WFC3-IR detector.