Expanding the Realm of Microlensing Surveys with Difference Image Photometry

We present a new technique for monitoring microlensing activity even in highly crowded elds, and use this technique to place limits on low-mass MACHOs in the haloes of M31 and the Galaxy. Unlike present Galactic microlensing surveys, we employ a technique in which a large fraction of the stellar sample is compressed into a single CCD eld, rather than spread out in a way requiring many di erent telescope pointings. We implement the suggestion by Crotts (1992) that crowded elds can be monitored by searching for changes in ux of variable objects by subtracting images of the same eld, taken in time sequence, positionally registered, photometrically normalized, then subtracted from one another (or a sequence average). The present work tackles the most di cult part of this task, the adjustment of the point spread function among images in the sequence so that seeing variations play an insigni cant role in determining the residual after subtraction. The interesting signal following this process consists of positive and negative point sources due to variable sources. The measurement of changes in ux determined in this way we dub \di erence image photometry" (also called \pixel lensing" [Gould 1996]). The matching of the image point spread function (PSF) is accomplished by a division of PSFs in Fourier space to produce a convolution kernel, in a manner explored for other reasons by Phillips & Davis (1995). In practice, we nd the application of this method is di cult in a typical telescope and wide eld imaging camera due to a subtle interplay between the spatial variation of the PSF associated with the optical design and the inevitable time variability of the telescope focus. Such e ects lead to complexities in matching the PSF