  The EMCCD is a type of CCD that delivers fast readout times and negligible
readout noise, making it an ideal detector for high frame rate applications
which improve resolution, like lucky imaging or shift-and-add. This improvement
in resolution can potentially improve the photometry of faint stars in
extremely crowded fields significantly by alleviating crowding. Alleviating
crowding is a prerequisite for observing gravitational microlensing in main
sequence stars towards the galactic bulge. However, the photometric stability
of this device has not been assessed. The EMCCD has sources of noise not found
in conventional CCDs, and new methods for handling these must be developed.
  We aim to investigate how the normal photometric reduction steps from
conventional CCDs should be adjusted to be applicable to EMCCD data. One
complication is that a bias frame cannot be obtained conventionally, as the
output from an EMCCD is not normally distributed. Also, the readout process
generates spurious charges in any CCD, but in EMCCD data, these charges are
visible as opposed to the conventional CCD. Furthermore we aim to eliminate the
photon waste associated with lucky imaging by combining this method with
shift-and-add.
  A simple probabilistic model for the dark output of an EMCCD is developed.
Fitting this model with the expectation-maximization algorithm allows us to
estimate the bias, readout noise, amplification, and spurious charge rate per
pixel and thus correct for these phenomena. To investigate the stability of the
photometry, corrected frames of a crowded field are reduced with a PSF fitting
photometry package, where a lucky image is used as a reference.
  We find that it is possible to develop an algorithm that elegantly reduces
EMCCD data and produces stable photometry at the 1% level in an extremely
crowded field.
