A Method for Optimal Image Subtraction

We present a new method designed for optimal subtraction of two images withdifferent seeing. Using image subtraction appears to be essential for the fullanalysis of the microlensing survey images, however a perfect subtraction oftwo images is not easy as it requires the derivation of an extremely accurateconvolution kernel. Some empirical attempts to find the kernel have used theFourier transform of bright stars, but solving the statistical problem offinding the best kernel solution has never really been tackled. We demonstratethat it is possible to derive an optimal kernel solution from a simple leastsquare analysis using all the pixels of both images, and also show that it ispossible to fit the differential background variation at the same time. We alsoshow that PSF variations can also be easily handled by the method. Todemonstrate the practical efficiency of the method, we analyzed some imagesfrom a Galactic Bulge field monitored by the OGLE II project. We find that the residuals in the subtracted images are very close to thephoton noise expectations. We also present some light curves of variable stars,and show that, despite high crowding levels, we get an error distribution closeto that expected from photon noise alone. We thus demonstrate that nearlyoptimal differential photometry can be achieved even in very crowded fields. Wesuggest that this algorithm might be particularly important for microlensingsurveys, where the photometric accuracy and completeness levels could be verysignificantly improved by using this method.Comment: 8,pages, 4 Postscript figures, emulateapj.sty include