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Astronomical Data Analysis Software and Systems IV
ASP Conference Series, Vol. 77, 1995
R. A. Shaw, H. E. Payne, and J. J. E. Hayes, eds.
Registering, PSF­Matching and Intensity­Matching
Images in IRAF
A. C. Phillips
Lick Observatory, University of California, Santa Cruz, CA, 95064
L. E. Davis
National Optical Astronomy Observatories, P. O. Box 26732, Tucson,
AZ 85726
Abstract. We have developed a set of tasks in the IRAF environ­
ment for registering, matching the point­spread functions, and matching
the intensity scales of two or more images. This software can be ap­
plied to a wide variety of astronomical problems including searches for
transient events such as extragalactic novae and supernovae, continuum­
subtraction for emission line imaging, and the examination of small scale
color gradients. We briefly describe the algorithms and illustrate the
software with images obtained under different seeing conditions.
1. Introduction
A variety of astronomical programs involve comparing similar image data of
the same field. Examples include searches for extragalactic novae, supernovae
and variable stars; continuum­subtraction for narrow­band emission­line images;
and production of color or polarization maps, to name a few of the more obvious
cases. For these types of observations, it is usually essential that all observational
differences be eliminated before comparison. While instrumental signatures can
be removed accurately, varying conditions (e.g., seeing, transparency) are more
problematic. This is particularly crucial where the objects of interest are either
extended or are found in regions of strong background gradients.
The process of ``matching'' an image to a reference image requires: (1) ap­
plying a geometric transformation to spatially register an image to the reference
image; (2) convolving the registered image with an appropriate kernel to degrade
the point­spread function to match that of the reference image; and (3) scaling
and offsetting the intensity of the convolved image to match the intensity and
background sky level of the reference image.
We have developed a set of IRAF tasks to compute and apply the neces­
sary transformations for image matching. In this paper we briefly describe the
algorithms and tasks and illustrate the software with a pair of images obtained
under different seeing conditions. We conclude by describing the current status
and future development plans of the software.
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2. Spatial Registration
The current software performs spatial registration by supplying the registration
task with a reference and input image list, and a list of features common to both
images. Two spatial registration tasks are available: a ``polynomial warping''
procedure for general cases, and a new cross­correlation task for the special case
that only translations are required.
The polynomial warping task is an IRAF script which combines existing
IRAF object selecting, centering, and geometric transformation tasks. This
task is required for the general case that pixel scales and/or orientation differ
between the input and reference images. The user supplies this task with a set of
star positions in the reference image, and the positions of two stars in both the
reference and input images. The task computes an initial transformation using
the two specified stars, refines it using the full reference star list, and applies
the computed transformation to the input image.
If the input and reference images have identical pixel scales and orientation,
they can be registered using the cross­correlation task. The user supplies this
task with a list of rectangular image regions, each containing high signal­to­
noise features suitable for cross­correlation. The task computes the shift from
the cross­correlation function and applies it to the input image.
3. Point­Spread Function Matching
Point­spread function (PSF) variations have many sources: seeing changes, guid­
ing errors and focus variations are the most common. Removing the PSF differ­
ences is easy in principle but difficult in practice. If r is the reference image, i is
the (spatially­registered) input image, and R and I are their Fourier transforms,
then
r = i ? k;
and the Convolution Theorem gives us
R = I \Theta K;
where k is some convolution kernel describing the difference in seeing, etc., and
K is its Fourier transform. k also contains scaling information for differences in
exposure and transparency. The unknown kernel k is then given simply by
k = FTfR=Ig:
In practice, unfortunately, the high­frequency components of the images are
dominated by noise and so the ratio in Fourier space is poorly behaved. We
have found that satisfactory results can obtained by replacing the high­frequency
components with a Gaussian model fit to the lower­frequency (higher signal­to­
noise) components. This approximation, as well as many other considerations,
are discussed in Phillips (1993b).
In principle, the kernel k can be used to deconvolve an image to match
a better­seeing image, but in practice, noise is again a severe problem, and
deconvolution is a costly procedure. Degrading the better­seeing image is usually

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acceptable. The convolution smooths the noise as well as the object signal, so
only contrast---not signal­to­noise---is lost.
Two PSF­matching options are available in our IRAF task. Both require
the reference image to have lower resolution than the input image. In the first,
the user must supply the task with the reference and input image and a list
of high signal­to­noise point sources. In the second, the user must supply pre­
computed PSFs for the reference and input images. (Pre­computed PSFs may
be derived from other IRAF software such as the DAOPHOT package or be
computed by the user.) In both cases, the task computes the required kernel
and performs the convolution. The PSF­matching task also includes options for
removing the background around the input point sources, as well as control over
the replacement of the high­frequency components with the Gaussian model.
4. Intensity Matching
Many image matching problems require the final images to have the same in­
tensity scale. The current software requires the input and reference images to
be spatially­registered and PSF­matched. The user specifies a rectangular data
region which contains both object and (ideally) sky data. The task uses linear
least squares techniques (including a user­supplied noise model for both images,
and automatic deviant pixel rejection) to compute the required scale factor and
zero point offset, and applies the transformation.
5. Results: An Illustration
Figure 1 shows two B­band images of the Phoenix dwarf galaxy at different
epochs (top). Also shown are the difference image after registration and intensity
matching only (bottom left), and the same with PSF­matching (right). In the
fully­matched case, about a dozen Cepheids variables are easily seen. Note
also the high­proper motion star just below and left of the center. Additional
illustrations may be found elsewhere (Phillips 1993a,b; Margon et al. 1992; Ruiz
et al. 1987).
6. Current Status and Future Plans
A prototype version of this software is currently available from A. Phillips
(phillips@lick.ucsc.edu) on a use at your own risk basis. Prospective users should
be aware that the software is unsupported and minimally documented, although
the author welcomes comments and suggestions for improvement.
The cross­correlation task for spatial registration will be included in the next
release of IRAF, and is already available to users as add­on software. A new
version of the PSF­matching task is nearing completion and will be available as
add­on software shortly after this meeting. Contact L. Davis (davis@noao.edu)
for a status report.
Future plans include modifying the cross­correlation task to handle images
with small scale and orientation differences and adding the intensity scaling task
to IRAF itself.

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Figure 1. Searching for Cepheid variables in the Phoenix dwarf
galaxy. See text. (CTIO 4­m images courtesy of Nelson Calwell.)
Acknowledgments. ACP wishes to thank NOAO for providing him sup­
port as a Visiting Specialist during the summer of 1988, when the PSF­matching
algorithm and software were developed. He also thanks the IRAF group for their
hospitality and patient instruction during that time.
References
Margon, B., Phillips, A. C., Jacoby, G. H., & Ciardullo, R. 1992, AJ, 103, 924
Phillips, A. C. 1993a, AJ, 105, 486
Phillips, A. C. 1993b, PhD Dissertation, University of Washington, Seattle
Ruiz, M. T., Blanco, V., Maza, J., Heathcote, S., Phillips, A., Kawara, K.,
Anguita, C., Hamuy, M., & G'omez, A. 1987, ApJ, 316, L21