  The key features of the MATPHOT algorithm for precise and accurate stellar
photometry and astrometry using discrete Point Spread Functions are described.
A discrete Point Spread Function (PSF) is a sampled version of a continuous PSF
which describes the two-dimensional probability distribution of photons from a
point source (star) just above the detector. The shape information about the
photon scattering pattern of a discrete PSF is typically encoded using a
numerical table (matrix) or a FITS image file. Discrete PSFs are shifted within
an observational model using a 21-pixel-wide damped sinc function and position
partial derivatives are computed using a five-point numerical differentiation
formula. Precise and accurate stellar photometry and astrometry is achieved
with undersampled CCD observations by using supersampled discrete PSFs that are
sampled 2, 3, or more times more finely than the observational data. The
precision and accuracy of the MATPHOT algorithm is demonstrated by using the
C-language MPD code to analyze simulated CCD stellar observations; measured
performance is compared with a theoretical performance model. Detailed analysis
of simulated Next Generation Space Telescope observations demonstrate that
millipixel relative astrometry and millimag photometric precision is achievable
with complicated space-based discrete PSFs. For further information about
MATPHOT and MPD, including source code and documentation, see
http://www.noao.edu/staff/mighell/matphot
