It has been demonstrated that image subtraction with a space-varying kernel solution could be achieved at a cost of computing time only 20% to 30% greater than for a constant kernel solution.
We have generated a series of Monte-Carlo images of a simulated stellar
field to test the method. The ability of the method to deal with PSF
variations between images has been demonstrated. It was found that even
large relative PSF variations are very well corrected by the method,
resulting in a
very close to 1 in the subtracted image. varying
kernel solutions can also automatically correct for imperfect
registration between the images. This ability was illustrated by
generating 2 images with differential rotation with respect to each
other. While the systematic pattern due to differential rotation was
visible in the subtracted image obtained with a constant kernel
solution, it disappeared completely when fitted by a spatially varying
kernel. To complete the Monte-Carlo analysis, we tackled the problem of
under-sampling by generating 2 very under-sampled images. The 
analysis showed that even in this case an optimal result can be
achieved. Finally we applied the method to real astronomical data. Again
we achieved nearly optimal results with a spatially-varying solution,
even when the size of the sub-area used for the fit is increased.
These results are certainly useful for crowded field images, but have proved to be absolutely essential in case of fields with low density of high signal to noise objects. A good example is the case of the photometry of the 4 images of the Huchra lens (Wozniak et al. 1999, 2000).
To conclude, we can say that this new extension of the image subtraction
method will certainly prove to be very useful for the supernovae searches
that are currently underway. It may also prove useful for variability
searches in other galaxies, surveys of variables near globular
cluster cores (Olech et al. 1999), and may also become one of the
favorite methods to analyze microlensing variability in gravitational
lens systems.
Software availability:
The ISIS image subtraction package is available from a web site:
http://www.iap.fr/users/alard/package.html
This package has utilities to make image registration,
image subtraction, and
photometry of the images.
Acknowledgements
It is a pleasure to thank B. Paczynski for his support during my stay in Princeton. I thank J. Pritchard for his kind help, and especially for reading this manuscript and improving the English. I would like to acknowledge interesting discussions with B. Paczynski, P. Wozniak, and R. Lupton. I would also like to thank Dr. A. Udalski and the whole OGLE team for making their data avaiable prior to publication. It is a pleasure to thank the referee for his help with the manuscript.
Copyright The European Southern Observatory (ESO)