Space Telescope Science Institute
WFC3 Data Handbook 2.1 May 2011
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WFC3 Data Handbook > Chapter 7: WFC3 Data Analysis > 7.3 Astrometry

There are three coordinate systems applicable to WFC3 images. First, there is the position of a pixel on the geometrically distorted raw image (RAW) or, identically, the position on the flat-fielded images (FLT) after pipeline processing through calwf3. Second, there is the pixel position on the drizzled images (DRZ) created by MultiDrizzle which corresponds to an undistorted pixel position on a tangent plane projection of the sky. Third, there is the corresponding position (RA, Dec) on the sky.
A position measured on a drizzled output image (DRZ) from MultiDrizzle may be transformed to a position on the celestial sphere using the utility xy2rd in the stsdas.toolbox.imgtools package within STSDAS. There is also a corresponding rd2xy task to go from the sky to the pixel position on a drizzled frame. These tools cannot be used for RAW/FLT files as they do not include the very large effects of geometric distortion.
The transformation between the pixel position on a distorted (RAW or FLT) and drizzled (DRZ) image may be performed using utilities in the dither package in STSDAS. The tasks traxy and tranback implement the same geometric mapping as drizzle and blot except applied to X,Y pixel positions rather than images. For more details on how to use these the IRAF help files should be consulted. As a more convenient high-level wrapper, the tran task, which was released as part of the late-2004 version of STSDAS, allows the mapping of X,Y positions between FLT and DRZ images. This task uses information in the image headers to define the necessary geometrical transformation and requires that the drizzle-style “coeff” geometric distortion coefficients files are also available. These files are not provided by the STSDAS archive and must be recreated by running MultiDrizzle on the FLT file on the local machine. Please note that to run MultiDrizzle you also need the IDCTAB distortion file, along with the DGEO files appropriate for the particular filter used in the observations. If DGEO files were used when the drizzled products were produced, then these files are also needed when tran is run. The DGEO are standard calibration reference files that will be available from the archive for WFC3 in 2011.
For example, if an object was found to be at (123,234) on an FLT image (test_flt.fits[sci,1]) the position on the drizzled DRZ product (test_drz.fits) can be found as follows:
The last number refers to the pixel-area map value at this point (see Section 7.2.3).
The reverse operation, DRZ to FLT, can be applied as follows:
Finally the xytosky task, which forms part of the current dither package, will convert a pixel position on a distorted FLT file directly to a sky position, by applying the distortion correction from the IDCTAB and using the world coordinate information from the header. It may be used as follows:
This task doesn’t require the coefficient files but, like MultiDrizzle, requires a copy of the IDCTAB to be available. Both tran and xytosky have options for lists of positions to be supplied as text files to allow multiple positions to be efficiently transformed. The task xytosky does not currently support DGEO files. If accuracy at a level better than 0.1 pixels is needed, then we recommend either of the following: (a) run tran to get the corresponding X, Y pixel position on the drizzled (DRZ) image, followed by xy2rd; or (b) use other tasks in the dither package, such as wtraxy.
The astrometric information in the header of a WFC3 image is derived, in part, from the measured and catalog positions of the particular guide stars used. As a result, the absolute astrometry attainable by using the image header world coordinate system is limited by two sources of error. First, the positions of guide stars are not known to better than about 200 mas. Second, the calibration of the FGS to the instrument aperture introduces a smaller, but significant error – approximately 15 mas.
Although absolute astrometry cannot be done to high accuracy without additional knowledge, relative astrometry with WFC3 is possible to a much higher accuracy. In this case the limitations are primarily the accuracy with which the geometric distortion of the camera has been characterized. Typical accuracy of the distortion correction in the pipeline with the standard fourth order polynomial solutions is 0.1 pixels (4 mas for the UVIS and 10 mas for the IR).
The guiding performance and pointing stability of HST are described in the HST Primer. The normal guiding mode uses two guide stars that are tracked by two of HST’s Fine Guidance Sensors (FGSs). However, sometimes two suitable guide stars are not available and single-star guiding is used instead with the telescope roll controlled by the gyros. These observations will suffer from small drift rates. To determine the quality of tracking during these observations please review Chapter 6 of the Introduction to the HST Data Handbooks.
The gyros have a typical drift rate of 1.5 mas/sec. This causes a rotation of the target around the single guide star, which in turn introduces a small translational drift of the target on the detector. The exact size of the drift depends on the exact roll drift rate and distance from the single guide star to the target in the HST field of view. For WFC3, the roll about the guide star produces a translation of 7 mas (0.2 UVIS pixel, 0.05 IR pixel) in 1000 sec and 38 mas (1.0 UVIS pixel, 0.3 IR pixel) per orbit.  The Tweakshifts task may be used to measure and correct for such shifts between successive exposures.
The drift over an orbital visibility period can be calculated from these numbers; the typical visibility period in an orbit (outside the Continuous Viewing Zone [CVZ]) is in the range 52-60 minutes, depending on target declination (see Section 6.3 of the HST Primer). The drifts inherent to single-star guiding are not represented in the image header astrometric information, and have two important consequences:
There will be a slight drift of the target on the detector within a given exposure. For the majority of observations and scientific applications this will not degrade the data (especially if the exposures are not very long). The drift is smaller than the FWHM of the point spread function (PSF). Also, the typical jitter of the telescope during an HST observation is 0.003-0.005 arcsec, even when two guide stars are used.
There will be small shifts between consecutive exposures. These shifts can build up between orbits in the same visit. This will affect the MultiDrizzle products from the pipeline, since these rely on the header astrometry, hence the structure of sources in the image will be degraded during the cosmic ray rejection routine. This can however be addressed during post-processing if the user first measures the shifts and then runs MultiDrizzle off-line, using the measured shifts.
Also, even when two guide stars are used, there is often a slow drift of the telescope up to 0.01 arcsec/orbit due to thermal effects. So, it is generally advisable to check the image shifts, and if necessary measure them to improve the alignment of exposures before running MultiDrizzle off-line to perform the cosmic ray rejection and image combination.
In summary, for most scientific applications single-star guiding will not degrade the usefulness of WFC3 data, provided that the shifts are measured post-facto and MultiDrizzle is re-run offline using these shifts. However, we do not recommend single-star guiding for the following applications:
Programs that rely critically on achieving a dithering pattern that is accurate on the sub-pixel scale. (However, note that even with two-star guiding this can often not be achieved).
Observers who are particularly concerned about the effect of pointing accuracy on the PSF can obtain quantitative insight using the TinyTim software package. While this does not have an option to simulate the effect of a linear drift, it can calculate the effect of jitter of a specified RMS value.

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