1. Distortion in the WFC Jay Anderson Rice University jay@eeyore.rice.edu

2. Background on WFC distortion General difficulty calibrating HST –Need high-density field, accurate positions –No satisfactory fields exist –Need self-calibration ISR on HRC distortion released a year ago –WFC more complicated: Largest HST field PSF spatially variable

3. Overview of this talk 1) PSF issues –Spatial variation –Time variation –Fitting stars –A useful program 2) Distortion solution –Difficulty of calibration –Form of solution –Time variability 3) How-to Astrometry with the WFC

4. PSF Issues (1) Need a PSF to measure stars to solve for distortion –Several routines are coming out –My routine: img2xym_WFC.09x10.F Similar to the my HRC routine Operates on _flt images Uses an array of PSFs to deal with spatially dependent charge diffusion –Between 17% and 24% of a star’s light in central pixel –Affects photometry at the +/- 4% level –Affects astrometry at the 0.01 pixel level

5. Varying flux in the central pixel

6. Slices across WFC image

7. Grid of 9x10 fiducial PSFs

8. Array of WFC PSFs

9. Spatial variation of the WFC PSF (~10%)

10. PSF Issues (2): treating the PSF The base PSF model 9x10 array of PSFs 101x101 pixels 4x super-sampled Use bi-cubic interpolation Covers out to r = 12.5 pix “Effective” PSF Time variability Typically 5% in the core Treat as perturbation: PSF(dx,dy;x,y,NIM) = PSF(dx,dy;x,y) + PSF(dx,dy;NIM)

11. Variation of the PSF over a month Richer’s GO-10424 stare at NGC6397 Variation is ~ 5%

12. Zoom of month-long variation

13. PSF Issues (3): the program Operation of program: –Take _flt image –Simple finding criteria –Return (x,y,m) for sources –User collates with other observations Measurement quality (internal precision) –Photometry: 0.005 magnitude –Astrometry: 0.01 pix

14. Internal precision 0.01 pixel for each coord 0.005 mags

15. Distortion Solution (1): Why? Need for distortion solution –Image rectification –Stacking to go deep –Source identification –Spectra slit/fiber placement –Lensing analysis –Astrometry Different applications require different accuracies

18. Distortion Solution (2): Solving for Ways to solve for –Best way: calibrated reference frame None exists with density/precision useful for HST –Alternate way: self-calibration Compare two WFC images of a good-density field Hard to know where the distortion error is Hard to visualize distortion –2-d function over a 2-d surface Hard to measure distortion outright –But easier to test for errors

19. Usefulness of different types of data set

20. Distortion Solution (3): History Solution history Meurer GO-9028 F475W of 47Tuc 4 th -order polynomial Linear-term degeneracy Anderson GO-9443 Took orthogonal observation Used several filters Filter-dependent residuals Slightly different quadratic terms 68.2666-column pattern, amplitude 0.01 pixel

21. Distortion Solution (4): Form Final form of solution 1) Column correction: amplitude 0.01 pixel 2) Polynomial: amplitude 40 pixel 3) Filter-based look-up table: 0.05 pixel Software now available for 12 filters Better for some filters than others Used in the drizzle pipeline Supplementary program to improve solution for F606W and F814W: GO-10252 Use inner field in Omega Cen: 88,000 stars, even density Tables to be improved, PSFs obtained Problem: out of focus, just provides a check Other checks on solution

22. The typical residual table correction: 0.05 pixel

23. Distortion solution (4): Check #1 Checking the distortion solution –Easier to check than to solve for –Three tests: short-term, long-term, out-of-focus Short-term time variations –GO-10424 (PI Richer) –126 orbits taken over 4 weeks –Each orbit: F814W, F606W, F814W –Compare each to the average –Hard to separate distortion variation from PSF variation –Typical variation is much less than 0.02 pixel

24. Usefulness of different types of data set

25. Variation during long stare

26. Non- linear variation –Correlated with PSF variation –Only about 0.02 pixel at worst

27. Distortion Solution (5): Check #2 Long-term variation –Outer field in 47 Tuc –Observed over 300 times by WFC –Inter-compare exposures, allowing for linear transformation Examine astrometric and photometric residuals Linear variation of linear skew term: 0.1 pixel over three years Typical systematic residuals are 0.02 pixel

28. Usefulness of different types of data set

30. Initial residual errors From early solution –Typically 0.01-0.02 pix

31. Remaining errors Residuals flattened to below 0.01 pixel

32. Distortion Solution (6): Check #3 Calibration supplement program GO-10252 –1 orbit for each of F606W, F814W –Aim to improve the fine-scale solution and provide good empirical PSFs –PSF very much out of focus 10% low in central pixel Use as comparison test

33. Independent test in OMCEN

34. Distortion Solution (7): Summary Short term (weeks) –Linear and quadratic good to 0.02 pix Long term (years) –Linear has systematic trends –Quadratic stable to 0.02 pixel Out of focus –Errors up to 0.03 pixel at edges

35. Prescriptions for astrometry (1) Accessing the solution –ISR coming very soon, with FORTRAN programs for finding/measuring/correcting –Included in the drizzle pipeline Planning observations –Accuracy: 0.01 pixel per exposure, but… –Beware small systematic errors of ~0.02 pixel Planning can minimize/identify these Ideal dithering depends on goal of project –Dense field: may be able to solve for PSF –Sparse field: need large dithers to average out spatially dependent errors

36. Prescriptions for astrometry (2) Reductions –Measure _flt images only  (x,y,m) –Correct for distortion –Cross-ID stars in different images –Carefully perform transformations 6-parameter linear Go local if necessary –Combine similar things first Identify systematic errors Get a handle on random errors Lots of Astrometry left to do!