4.1 WFC3 Geometric Distortion

WFC3 images exhibit significant geometric distortion, similar to that seen in ACS images. The required folding 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 producing a rhomboidal elongation of ~7%. The IR detector has a ~24 degree tilt about its x-axis, creating a rectangular elongation of ~10%. 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.

The first on-orbit measurements of the geometric distortion for the WFC3 detectors were made in 2009 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 geometric distortion, as described in WFC3 ISR 2009-33 and WFC3 ISR 2009-34, and updated in WFC3 ISR 2012-07, is presented as a fourth-order polynomial model and is accurate to a precision level of better than 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 ( WFC3 ISR 2012-07,) in the form of Instrument Distortion Coefficient Tables (IDCTABs), are used to correct for distortion in MAST drizzled data products. These reference files are also available to users who wish to reprocess their data with the DrizzlePac/AstroDrizzle software.

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 the manufacturing process. That is, the lithographic mask pattern used during the chip manufacture is imprinted on the detector. The correction for the lithographic pattern imprint 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) ( WFC3 ISR 2013-14). The look-up table is incorporated by AstroDrizzle in the pipeline, using the filename specified in the D2IMFILE keyword in the primary image header. AstroDrizzle attaches new fits extensions to the calibrated image of type 'D2IMARR' (four extensions total, two for each chip in each X and Y axis). See Table 2.5 for details on these additional image header extensions.

In addition to the pixel-grid irregularities there are fine-scale non-polynomial filter-dependent distortions that have been calibrated for a subset of 15 UVIS filters (see Table 2.5). These are specified in the NPOLFILE keyword in the primary image header and attached to the image as FITS extensions (four extensions, two for each CCD chip and each X and Y axis), WFC3 ISR 2014-12. Each element of the 64 × 32 table is bi-linearly interpolated pixel-by-pixel in UVIS images by AstroDrizzle.

Figure 4.1:Non-linear components (vectors magnified by 10) of the geometric distortion on the WFC3-UVIS detector.

4.1.1 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 tilt of the CCD around its detector diagonal with respect to the chief ray. The angle between the x- and y-axes is ~86.1 degrees. The field diagonals are tilted slightly from the V2- and V3-axes (see Figure 1.2). There is a ~1.2" 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". The principal effect is the diagonal variation of scale. At the center of UVIS1 (CCD CHIP1, top), the scale in the x-direction is 0.0396"/pixel, and 0.0393"/pixel in the y-direction. For UVIS2 (CCD CHIP2, bottom), these scales are 0.0398''/pixel, and 0.0398"/pixel, respectively. UVIS1 forms a slightly distorted rectangle 162"×81" in size, while UVIS2 subtends 163"×82". In the presence of distortion, it is not possible to flat field the image in such a way as to preserve both surface brightness and flux. The convention that has been adopted in the pipeline preserves surface brightness, therefore a correction is necessary if the goal is to measure accurate fluxes via point-source photometry. See Section 9.1.11 and WFC3 ISR 2010-08 for a discussion on the effects of the pixel area map on photometry.

4.1.2 The IR Channel

The IR detector field of view is nominally concentric with the UVIS field, but it subtends a smaller area on the sky, 138"×123". The detector tilt is about the x-axis, so the projected aperture shape is nearly a rectangle, with the angle between the x- and y-axes on the sky nearly 90 degrees as shown by the outline in Figure 4.2. At field center, the x- and y-scales are 0.135 and 0.121''/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".

Figure 4.2: Non-linear components (vectors magnified by 10) of the geometric distortion on the WFC3-IR detector.