  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)
