WFC3/UVIS Geometric Distortion -- Time Evolution of Linear Terms w.r.t Gaia

We align more than 7,400 WFC3/UVIS exposures to the Gaia DR3 catalog to examine the time evolution of the linear terms (shift, rotation, scale and skew) of the geometric distortion solution between 2009 and 2022. We find small linear temporal changes in the scale and skew terms (less than 0.2 pixels in 13 years) which are generally dominated by intrinsic scatter (up to $\pm$ 0.3 pixels). Concurrently, a larger filter-dependent offset in the scale term is observed, with a maximum difference of 0.3 pixels between F275W and F814W images at all epochs. A small rotation offset to Gaia of 0.003 $\pm$ 0.004 degrees is measured from 2009 to mid-2017, after which the offsets are as large as 0.01 degrees, with a large scatter. MAST pipeline processing includes an additional alignment step which corrects UVIS images for any residual linear terms with respect to Gaia DR3 when there are at least 10 matched sources. In addition to any pointing offsets, this step accounts for any evolution in the distortion linear terms described here. For observers requiring high-precision astrometry, we recommend using the tweakreg routine to realign images using a 4-parameter fit (x-shift, y-shift, rotation, and scale) or a 6-parameter fit (x-shift, y-shift, x-rotation, y-rotation, x-scale, and y-scale) depending on the number of matched sources. We provide links to DrizzlePac tutorials for improving both absolute and relative astrometry in WFC3 images.

💡 Research Summary

This paper presents a comprehensive analysis of the long‑term stability of the linear components of the geometric distortion solution for the Hubble Space Telescope’s Wide Field Camera 3 UVIS channel (WFC3/UVIS) by aligning more than 7,400 full‑frame exposures taken between 2009 and 2022 to the Gaia Data Release 3 (DR3) catalog. The authors aim to quantify temporal changes in the four linear terms—shift (x‑ and y‑offset), rotation, scale, and skew—because any drift in these parameters can degrade absolute and relative astrometry, especially for high‑precision applications such as proper‑motion studies, parallax measurements, and deep drizzling of multi‑epoch data.

Data set and preprocessing
All full‑frame WFC3/UVIS exposures in the five widely used broadband filters (F275W, F336W, F438W, F606W, F814W) were retrieved. Subarray, binned, moving‑target, failed, or Gaia‑star‑poor (<50 Gaia sources) observations were discarded. After quality cuts, the final sample comprised 7,491 images (1,134 F275W, 1,945 F336W, 572 F438W, 1,381 F606W, 2,598 F814W). For each exposure, the hst1pass pipeline generated a high‑precision source catalog (positions, fluxes, PSF quality metrics). Gaia sources within the image footprint were queried via astroquery.gaia, with proper‑motion corrections applied to the Gaia epoch (2016.0). Only images with ≥10 Gaia matches proceeded to the alignment stage.

Alignment methodology
The authors employed the tweakwcs/tweakreg tools from the DrizzlePac suite. First, the XYXYMatch algorithm provided an initial guess for x‑ and y‑shifts by maximizing the number of matched sources. Then a linear (affine) transformation was solved in the tangent‑plane pixel space using a least‑squares fit to the matched pairs. The transformation equations are

U = P₀ + P₁ x′ + P₂ y′
V = Q₀ + Q₁ x′ + Q₂ y′

where (U,V) are Gaia reference positions, (x′,y′) are distortion‑corrected image positions (using the current IDCTAB, NPOLFILE, and D2IMFILE), and the coefficients encode shift (P₀,Q₀), scale, rotation, and skew (P₁,P₂,Q₁,Q₂). The authors extracted absolute scale, rotation (orient), and skew from the CD matrix of the World Coordinate System (WCS) header for both the “initial” WCS (IDCTAB‑only) and the “Gaia‑aligned” WCS (after tweakreg). Differences (or ratios for scale) between the two WCSs represent the residual linear terms in the IDCTAB solution.

Data quality control
Fits with a root‑mean‑square error (RMSE) > 0.2 pixel were rejected, as were images with very few matches or crowded fields that could produce pathological solutions. After this cut, 7,491 → 7,491 ? (the paper states 7,491 well‑fit images). Two rounds of 3σ sigma‑clipping were applied separately per filter and globally to remove outliers before fitting temporal trends.

Results – temporal evolution

Scale and Skew: Over the 13‑year baseline, the median change in pixel scale is < 0.2 pixel at the detector edge, corresponding to < 0.015 pixel yr⁻¹. The skew term shows comparable stability. However, a strong filter dependence is evident: the scale offset between the bluest filter (F275W) and the reddest (F814W) reaches up to 0.3 pixel, indicating that filter‑specific optical path differences dominate over any genuine temporal drift.

Rotation: From 2009 through mid‑2017 the global rotation offset relative to Gaia is 0.003° ± 0.004°, essentially constant within the measurement noise. After mid‑2017 the rotation offsets increase to as much as 0.01° with a larger scatter, suggesting that guide‑star acquisition errors or Fine Guidance Sensor (FGS) thermal drifts become more significant in later years.

Shift: The zero‑order shift term exhibits the largest scatter, reflecting the fact that HST pointing errors (guide‑star catalog uncertainties, FGS jitter) dominate over any systematic drift in the distortion model. The authors note that shift variations are not a property of the distortion solution itself but of the spacecraft attitude control at the time of each exposure.

Implications for pipeline processing
The MAST calibration pipeline already applies an additional alignment step when ≥10 Gaia matches are available, effectively correcting any residual linear terms on a per‑exposure basis. Therefore, standard calibrated products (e.g., *_flc.fits) already incorporate these corrections. Nonetheless, for users requiring sub‑mas relative astrometry, the authors recommend re‑running tweakreg with a 4‑parameter fit (x‑shift, y‑shift, rotation, uniform scale) when ≥10 matches exist, or a full 6‑parameter fit (x‑shift, y‑shift, x‑rotation, y‑rotation, x‑scale, y‑scale) when the match count is higher (≥20). The 6‑parameter model can capture subtle anisotropic scale changes and non‑orthogonal skew that the 4‑parameter model assumes to be negligible.

Recommendations and resources
The paper provides links to DrizzlePac tutorials that guide users through creating custom reference catalogs, performing tweakreg alignment, and generating distortion‑corrected, drizzled mosaics. By following these tutorials, investigators can achieve absolute astrometric accuracies limited only by Gaia’s own uncertainties (∼0.1 mas for bright stars) and the residual scatter reported here.

Conclusions
The analysis confirms that the linear components of the WFC3/UVIS geometric distortion model are remarkably stable over more than a decade, with only minor temporal trends well within the intrinsic scatter of the data. Filter‑dependent scale offsets dominate the observed variations, while rotation drift becomes noticeable only after 2017. The existing IDCTAB solution remains adequate for most scientific purposes, but high‑precision relative astrometry benefits from an explicit tweakreg re‑fit using the appropriate number of free parameters. This work thus provides both a quantitative validation of the current distortion calibration and practical guidance for the community to achieve the highest possible astrometric fidelity with WFC3/UVIS data.