9.2 Astrometry

9.2.1 Coordinate Transformations

There are three coordinate systems applicable to WFC3 Images. First, there is the position of a pixel on the geometrically distorted flat-fielded images (FLT) after pipeline processing through calwf3. Second, there is the pixel position on the drizzled images (DRZ) created by AstroDrizzle, which corresponds to an undistorted pixel position on a tangent plane projection of the sky. Third, there is the corresponding world coordinate (RA, Dec) position on the sky.

There are utilities to transform between these coordinate systems that are built on the WCSLIB, a C library that implements the FITS standards for World Coordinate System (WCS) information. For transformations involving (FLT) images, the distortion information in the FITS header is used to correct for the very large effects of geometric distortion. Drizzlepac and astropy WCS are two commonly used Python interfaces to this library that implement these transformations.

For example, consider an object found at x,y pixel position (152,156) on UVIS chip 1 on an FLT image (test_flt.fits). The position on the celestial sphere, and the corresponding pixel position on a distortion-corrected DRZ file (test_drz.fits) can be found as follows.

Example #1 Pixel position on FLT to sky position using astropy wcs.all_pix2world

>>>from astropy.io import fits
>>>from astropy.wcs import wcs
>>>import numpy as np

Create wcs object containing WCS keywords from header.

>>> flt_wcs = wcs.WCS(fits.open(‘test_flt.fits’)[1].header, fits.open(‘test_flt.fits’))

Find RA and Dec corresponding to pixel position (152,156) on the FLT.

>>> pixcrd_flt = np.array([[152,156]])
>>> flt_skycoords = flt_wcs.all_pix2world(pixcrd_flt,1)

astropy.wcs.all_pix2world does all three transformations in series (table lookup distortions, SIP, and core WCS) from pixel to world coordinates.

Example #2 Pixel position on FLT to sky position using drizzlepac pixtosky

>>> from drizzlepac import pixtosky

Find RA and Dec corresponding to pixel position (152,156) on the FLT.

>>> r,d = pixtosky.xy2rd(‘test_flt.fits[sci,1]’,152.0,156.0)

The x,y pixel position in the DRZ frame corresponding to a coordinate in the FLT frame can also be found.

Example #3 Pixel position in FLT frame to DRZ frame, astropy.wcs

Continuing from the code in Example 1:

Also create wcs object from DRZ file

>>>drz_wcs = wcs.WCS(fits.open(test_drz)[1].header, fits.open(test_drz)[1])

Use all_pix2world to convert the sky position (found in Ex 1.) into DRZ pixel position.

>>>drz_pix = drz_wcs.all_world2pix(flt_skycoords, 1)

Example #4 Pixel position in FLT frame to DRZ frame, drizzlepac pixtopix

>>> from drizzlepac import pixtopix

>>> x_drz,y_drz = pixtopix.tran('test_flt.fits[sci,1]', 'test_drz.fits[sci,1]', 'forward', 152.0,156.0)

9.2.2 Absolute and Relative Astrometry

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).

9.2.3 Impact of Guide Star Failure

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 Observation Logs in the  Introduction to the HST Data Handbooks. In recent years, as gyroscopes have failed and been replaced, the typical has increased from 1.5mas/sec to ≤17 mas/sec. This drift 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, for the current drift rate, the roll about the guide star produces a translation of up to 60 mas (1.5 UVIS pixel, 0.45 IR pixel) in 1000 sec.

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 this number; 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 this section 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. Originally, for the majority of observations and scientific applications this did not degrade the data (especially if the exposures are not very long). The drift was smaller than the FWHM of the point spread function (PSF), and was comparable to the typical jitter of the telescope during an HST observation (0.003-0.005 arcsec) even when two guide stars were used. Currently, the drift on the detector could measurable affect the size and shape of the PSF.
  • There will be small shifts between consecutive exposures. These shifts can build up between orbits in the same visit. This will affect the AstroDrizzle 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 AstroDrizzle 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"/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 AstroDrizzle off-line to perform the cosmic ray rejection and image combination.

In summary, for most scientific applications, single-star guiding will not necessarily degrade the usefulness of WFC3 data, provided that the shifts are measured post-facto and AstroDrizzle is re-run offline using these shifts. However, we do not recommend single-star guiding for the following applications:

  • Programs that require very accurate knowledge of the PSF such as astrometric programs
  • 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.