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Astronomical Data Analysis Software and Systems VII
ASP Conference Series, Vol. 145, 1998
R. Albrecht, R. N. Hook and H. A. Bushouse, e
Ö Copyright 1998 Astronomical Society of the Pacific. All rights reserved.
ds.
The Astrometric Properties of the NOAO Mosaic Imager
L. E. Davis
National Optical Astronomy Observatories, Tucson, AZ 85719
Abstract. The astrometric properties of the NOAO Mosaic Imager are
investigated using the new IRAF MSCRED and IMMATCHX packages
and observations taken during recent engineering runs.
1. Introduction
The NOAO Mosaic Imager is an 8K by 8K pixel camera composed of 8 indi­
vidually mounted 2K by 4K CCDs separated by gaps of up to 72 pixels. Each
CCD has its own amplifier and is read into a separate image in a multi­extension
FITS file. A set of dithered exposures is required to obtain a complete obser­
vation of a given region of the sky. Reassembling an observation into a single
image requires selecting the reference coordinate system of the final combined
image, resampling each exposure to the selected reference coordinate system,
and combining the resampled images.
In this paper the new IRAF MSCRED and IMMATCHX packages and data
obtained during recent Mosaic Imager engineering runs on the NOAO 4m (FOV
36 arcminutes, scale 0.26 arcseconds per pixel) and 0.9m (FOV 59 arcminutes,
scale 0.43 arcseconds per pixel) telescopes are used to investigate the functional
form of the plate solutions, the accuracy of the plate solutions before and after
resampling and combining, and the accuracy of the flux conservation in the
resampling and combining steps. At the end of the paper some speculations are
o#ered on the feasibility or otherwise of reassembling the Mosaic Imager data in
real time at the telescope.
2. The Plate Solutions
The plate solutions were computed using published astrometry for Trumpler
37 (Marschall and van Altena 1987) and data from recent engineering runs.
Fits to both gnomonic projection (TAN) plus polynomial in x and y models
(Kovalevsky 1995), and zenithal polynomial projection (ZPN) models (Greisen
and Calabretta 1996) were performed.
2.1. 4m Plate Solutions
A theoretical 5th order ZPN model for the 4m prime focus plus corrector op­
tical system was available at the time of writing (Vaughnn 1996). This model
predicted pincushion distortion with a maximum scale change of 6.4% and max­
imum pixel area change of 8.5% across the FOV. Fits of ~400 stars in Trumpler
184

The Astrometric Properties of the NOAO Mosaic Imager 185
37 to the theoretical model produced good plate solutions for each CCD with
residuals for the 8 detectors averaging ~0.10 and ~0.07 arcseconds in # and #
respectively. Marginally better residuals of ~0.09 and ~0.06 arcseconds were ob­
tained with TAN projection plus cubic polynomial models. The residuals from
the latter fits showed no evidence for the predicted 5th order term, most prob­
ably due to a combination of the limited angular size of the individual CCDs,
and the precision of the published astrometry.
2.2. 0.9m Plate Solutions
An accurate theoretical model for the 0.9m f/7.5 Cassegrain focus plus correc­
tor system was not available at the time of writing. However TAN projection
plus cubic polynomial model fits to ~800 stars in the field produced good plate
solutions, with residuals for the 8 CCDs averaging ~0.07 arcseconds in both #
and # and no systematic trends in the residuals. The polynomial fits revealed
the presence of a 1.8% maximum scale change and 2.0% maximum pixel area
change over the FOV. These results were used to derive the equivalent ``theo­
retical'' ZPN model. Fits of the derived ZPN model to the data produced good
plate solutions with residuals of ~0.09 arcseconds in each coordinate.
3. Reassembling a Single Mosaic Observation
The TAN projection plus cubic polynomial plate solutions and bilinear interpo­
lation were used to combine the 8 pieces of the mosaic into a single 8K by 8K
image with an undistorted TAN projection coordinate system. Because the in­
dividual images were flat fielded before resampling, no additional flux correction
during resampling was required. Empirical rather than theoretical plate distor­
tion models were used in order to test the validity of the empirical approach,
and because they produced marginally better fits. Bilinear interpolation was
chosen for e#ciency, The TAN output coordinate system was chosen because it
is the standard projection for small field optical astrometry. Other options are
available.
3.1. Astrometric Accuracy
New plate solutions were computed for the resampled 4m and 0.9m data. In both
cases TAN projection plus first order polynomials in x and y produced good plate
solutions with residuals of ~0.08 / ~0.06 and ~0.10 / ~0.09 arcseconds in the #
/ # coordinates fits for the 4m and 0.9m images respectively. In all case no
discernible distortion remained, and the accuracy of the original plate solutions
was almost recovered.
3.2. Flux Conservation
Before and after resampling aperture photometry of the astrometric stars was
obtained and compared with flux correction model derived from the ZPN radial
distortion models. Agreement for the 4m data was excellent with (observed) ­ correction (predicted)> = 0.0007 +/­ 0.01 magnitudes, and no
observed trends with distance from the center of the image. The corresponding
numbers for the 0.9m data were,

186 Davis
= 0.0004 +/­ 0.018 magnitudes, and no trends with distance from the center of
the image. Therefore as long as the coordinate transformation used to resample
the image models the geometry of the optical system accurately, the resampling
code used to recombine the images will accurately conserve flux.
4. Combining Dithered Mosaic Observations
The dithered resampled observations must be combined to fill in the gaps in
the mosaic and produce a single image with complete sky coverage. Combining
the dithered observations requires precomputing the o#sets between the frames
in a dither set (before resampling), and resampling the dithered images to the
selected reference coordinate system (TAN with no distortion) in such a man­
ner that the images are separated by integer pixel o#sets, and combining the
intensities in the overlap regions. At the time of writing only a single 0.9m set
of dithered Trumpler 37 observations was available for investigation.
4.1. Astrometric Accuracy
A new plate solution was computed for the combined images. A TAN projection
plus first order polynomials in x and y model produced an excellent fit with
residuals of ~0.09 arcseconds in # and #. Therefore the combining step did
not introduce any distortion into the image geometry and the accuracy of the
original plate solutions was approximately recovered.
4.2. Flux Conservation
The image combining algorithm employed was median with no rejection. Before
and after aperture photometry of ~800 astrometric stars around the combined
frame and one of the resampled frames produced a mean value of sampled) ­ mag (combined)> = ­.008, and no trends with position in the image.
The small but real o#set appears was caused by changing observing conditions
which was not corrected for in the combining step.
5. Automatic Image Combining at the Telescope
5.1. Plate Solutions
Automating the image combining step to run in close to real time requires that
either the plate solutions are repeatable from night to night and run to run, or
a mechanism is in place to automatically compute new plate solutions at the
telescope. Thus far only the first option has been investigated, although the
second is also being considered. Preliminary tests suggest that the higher order
terms in the plate solutions are very repeatable, but that small adjustments to
the linear terms are still required. More rigorous testing with the system in a
stable condition is required to confirm this.
5.2. E#ciency
On an UltraSparc running SunOS 5.5.1, a set of nine dithered images currently
takes approximately ~2 minutes per image to read out, ~4 minutes per image

The Astrometric Properties of the NOAO Mosaic Imager 187
to reduce, and ~10 minutes per image to resample. A further ~18 minutes is
required to combine the 9 resampled dithered images. Cpu times are ~1/2 to
~1/3 of the above estimates, depending on the operation. Although a factor
of 2 improvement in e#ciency may be possible through system and software
tuning in some cases, it is obvious from the time estimates above that only some
observing programs can realistically consider combining images at the telescope
in real time and under current conditions.
5.3. Software
Much of the image combining process has already been automated, however
some more automation in the area of adjusting the plate solutions for zero point
and scale changes needs to be done.
6. Conclusions and Future Plans
The individual mosaic pieces can be recombined with high astrometric accuracy
using either the empirical TAN projection plus cubic polynomial models or the
theoretical ZPN models. The latter models have fewer parameters than the
former and are a more physically meaningful representation of the data, but the
former still produce lower formal errors.
As long as the computed plate solutions are a good match to the true geom­
etry of the instrument flux conservation during resampling is very accurate. If
this is not the case another approach must be taken, such as using a precomputed
``flat field'' correction image.
Automating image combining at the telescope is currently only feasible for
some types of observing programs. The main limitation is the computer time
required. The repeatability of the plate solutions from run to run and the issue
of computing plate solutions at the telescope are still under investigation.
Acknowledgments. The author is grateful to Frank Valdes for assistance
with the use of the MSCRED package and to Taft Armandro# and Jim Rhoades
for providing test data.
References
Greisen, E. R. & Calabretta, M. 1996, Representations of Celestial Coordinates
in FITS, fits.cv.nrao.edu fits/documents/wcs/ wcs.all.ps
Kovalevsky, J. 1995, in Modern Astrometry, Springer­Verlag, 99
Marschall, L. A. & van Altena, W. F. 1987, AJ, 94, 71
Vaughnn, D., 1996, private communication