One of the goals of astronomical image data acquisition is to infer the
pointing in an absolute coordinate system as accurately as possible,
in this case the celestial reference system. Instabilities
in telescope pointing and tracking however, can prevent us
from achieving this goal. SIRTF for instance, is expected to provide
pointing and control of at least absolute accuracy with
stability over 200 sec (
radial).
In the ICRS, the star-tracker assembly provides
an a-posteriori pointing knowledge of
.
The end-to-end pointing
accuracy is a function of the inherent star-tracker accuracy,
the spacecraft control system, how well the
star-tracker bore-sight is known in the focal plane array (instrument) frame,
and variations in the latter due to thermo-mechanical deflections.
The SIRTF observatory will have a data flow rate of
science images per day. This will require an automated, self-consistent means
of refining the celestial pointing as robustly as possible.
The conventional method to refine the pointing is to make comparisons of astrometric sources with positions known to better than a few percent of the observed positional errors. The primary motivation for pointing refinement is to enable robust coaddition of image frames in a common reference frame so that source extraction and position determination to faint flux levels can be performed. Moreover, refinement in an absolute (celestial) reference frame will enable robust cross-identification of extracted sources with other catalogs.
For these purposes, we have developed the `` pointingrefine'' stand-alone software package with a goal to generate science products with sub-arcsecond pointing accuracy in the ICRS. The software can refine the pointings and orientations of SIRTF images in either a ``relative'' sense where pointings become fixed relative to a single image of a mosaic, or, in an ``absolute'' sense (in the ICRS) when absolute point source information is known.
As part of routine pipeline operations at the SIRTF Science Center (SSC), all input images are pre-processed for instrument artifact removal and pointing data attached to raw FITS images. Following this, point source extraction is performed on individual frames for input into pointingrefine. The software expects point source lists adhering to the format produced by the SSC source extractor. The pointingrefine software performs the following:
A brief outline of the refinement algorithm (primarily steps 4, 5, and 6 above) is as follows.
Consider the simple three image mosaic in Figure 1. Image ``1'' defines the ``fiducial'' reference frame. The circles represent point sources detected from each overlapping image pair transformed into the fiducial frame. The filled circles are sources extracted from image n and the open circles are sources extracted from either image 1 or m. The correlated source pairs are slightly offset from each other to mimic the presence of pointing uncertainty in each raw input image. The Cartesian coordinates of a correlated point source common to an image pair are related by:
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|
(1) | |||
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We define a cost function , representing the sum of the squares of the
``corrected'' differences of all correlated point source positions in all
overlapping image pairs (
,
):
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(2) |
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(3) |
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(4) |
When absolute astrometric references are available,
the ``fiducial'' reference image (mosaic) frame is treated like a single input image,
which contains the absolute point source positions. When the input images
become refined relative to this fiducial image, they in reality become absolutely
refined (in the ICRS). The presence of absolute point sources also reduces the effect of ``random walks''
in offset uncertainties with distance if a single input image were chosen as the
reference instead. Once Cartesian offsets (
,
,
)
in the reference (mosaic) frame are computed, the
pointing centers (
,
) are corrected (by use of Equation 1) and
transformed back to the sky
to yield refined pointings. Image orientations are refined in a similar manner, but in this
case, we need to transform at least two fiducial points per image to uniquely determine
the orientation.
The Infrared Array Camera (IRAC) on SIRTF will perform simultaneous imaging at four
bands spanning the range
to
. Each array
consists of
pixels. We simulated a mosaic
of 800 IRAC (
) ``truth'' images (i.e., with no pointing
error) with each image containing randomly distributed point sources. Input image overlap
coverage was
. A second set of 800 images was
simulated with random errors added to the pointing keywords of
image headers. The errors were drawn from a Gaussian distribution with
mean radial error
. An absolute point source
list was also simulated by extracting the brightest sources with smallest centroiding errors
from each ``truth'' image. The average number of ``absolutes'' per input image
was 10. The SSC point source extractor was then used to extract
point sources
from each input image (with pointing error).
Figure 2 shows the results of our
simulation where we compare the distributions of radial offsets relative to ``truth''
pointings before and after refinement. The refinement is better than
for almost every image. The main limitation is full knowledge of the
Point Response Function (PRF)
to reduce centroiding errors in source extractions. However, we expect extraction centroids better
than
with better sampled PRFs. This will give us the
sub-arcsecond absolute pointing accuracy sought in SIRTF's imaging detectors.
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