# 5.2.1Coordinate Transformations

There are three coordinate systems applicable to ACS images.

• The position of a pixel on the geometrically distorted raw image (raw.fits) or, identically, the position on the flat-fielded images (flt.fits/flc.fits) after pipeline processing through calacs.
• The pixel position on the drizzled images (drz.fits/drc.fits) created by AstroDrizzle which corresponds to an undistorted pixel position on a tangent plane projection of the sky.
• The corresponding position (RA, Dec) on the sky.

A pixel position on a drizzled image (drz.fits/drc.fits) may be transformed to a position on the celestial sphere (RA, Dec) using the task pixtosky (in the DrizzlePac package, see the for details). There is a corresponding task, skytopix, also in the DrizzlePac package, that transforms a RA, Dec position to a pixel position on a drizzled image.

# 5.2.2Absolute and Relative Astrometry

The astrometric information in the header of an ACS image comes indirectly from the positions of the guide stars used during the observations. As a result, the absolute astrometry attainable by using the image header world coordinate system directly is limited by two sources of error. First, the positions of guide stars are not known to better than about 0.3 arcseconds. Second, the mapping from the guide star to the instrument aperture introduces a smaller, but significant error.

Although absolute astrometry cannot be done to high accuracy without additional knowledge, relative astrometry with ACS 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, see the DrizzlePac website for details. With the inclusion of a time-dependent skew in the ACS distortion model1 used by AstroDrizzle, the accuracy of alignment between ACS/WFC images is ~0.05 pixels or better. (Please see ACS ISR 2015-02 and ACS ISR 2015-06).

Accurate astrometric measurements, especially for faint sources, should take into account the effects of CTE, as described in ACS ISR 2007-04. The Institute is monitoring the variations of the linear skew terms and will continue updating the corresponding astrometric reference files described in the above-mentioned ISR.

# 5.2.3Impact of Guide Star Failure

The normal guiding mode uses two guide stars that are tracked by two of HST's Fine Guidance Sensors (FGSs). On some occasions, when two suitable guide stars are not available, single-star guiding is used 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 refer to the for information about jitter files.

In single guide star guiding, typical gyro drift rates produce a roll about the guide star of 1.0–1.5 mas per 1 second exposure, which in turn introduces a translational drift of the target on the detector. This roll is not reset and continues to build over multiple orbits and reacquisitions, until the next full guide star acquisition.

The exact size of the drift of the target in an exposure depends on the exact roll drift rate, r, the distance from the single guide star to the target in the HST field of view, d, and the exposure time, t. The distance d can be estimated from the HST field of view diagram in Figure 3.1 of the ACS IHB. An estimate of the target drift in arcseconds, s, is given by: $//$. For ACS with single-star guiding, the typical and maximum drift rate of the target on the detector are shown in Table 5.5.

Table 5.5: Drift Rates for Single-Star Guiding with ACS

TYPICAL

per 1000 sec. exposure

per orbit (96 min.)

WFC

0.0041 arcsec (0.08 pix)

0.024 arcsec (0.47 pix)

HRC

0.0048 arcsec (0.19 pix)

0.028 arcsec (1.11 pix)

MAXIMUM

per 1000 sec. exposure

per orbit (96 min.)

WFC

0.0080 arcsec (0.16 pix)

0.046 arcsec (0.92 pix)

HRC

0.0092 arcsec (0.37 pix)

0.053 arcsec (2.12 pix)

The drift over an orbital visibility period can be calculated from the values in Table 5.5. The typical visibility period in an orbit (outside the Continuous Viewing Zone, CVZ) ranges from 52 to 60 minutes, depending on target declination. 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 rms (radial), 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, and will affect the AstroDrizzle products from the pipeline because it depends on the header WCS (predicted) positions to determine image offsets when combining dithered images. Therefore, the structure of sources in the image will be degraded during the cosmic ray rejection routine. This problem can, however, be addressed during post-processing by manually running AstroDrizzle, after the images have been aligned using TweakReg.

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 (TEL ISR 2005-02). So, it is generally advisable to check the image shifts, and if necessary, align the images using the TweakReg task in DrizzlePac to improve the alignment of the exposures before running AstroDrizzle.

In summary, for most scientific applications, single-star guiding will not degrade the usefulness of ACS data, provided that the images are aligned (if necessary, use TweakReg to update the image alignment) before running AstroDrizzle. However, single-star guiding is not recommended for the following applications:

• Programs that require very accurate knowledge of the PSF, including coronagraphic programs and 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.

1 Please check the ACS Distortion page for updated information about the skew component in the ACS distortion model.