Expanding the Realm of Microlensing Surveys with Difference Image   Photometry
  We present a new technique for monitoring microlensing activity even in highly crowded fields, 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 field, rather than spread out in a way requiring many different telescope pointings. We implement the suggestion by Crotts (1992) that crowded fields can be monitored by searching for changes in flux of variable objects by subtracting images of the same field, taken in time sequence, positionally registered, photometrically normalized, then subtracted from one another (or a sequence average). The present work tackles the most difficult part of this task, the adjustment of the point spread function among images in the sequence so that seeing variations play an insignificant 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 flux determined in this way we dub "difference 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 find the application of this method is difficult in a typical telescope and wide field 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 effects lead to complexities...(abstract continues) 
Austin B. Tomaney (Columbia U.), Arlin P.S. Crotts (Columbia U.)