  We describe three algorithms for generating binary-valued holograms. Our
methods are optimised for producing large arrays of tightly focussed optical
tweezers for trapping particles. Binary-valued holograms allow us to use a
digital mirror device (DMD) as the display element, which is much faster than
other alternatives. We describe how our binary amplitude holograms can be used
to correct for phase errors caused by optical aberrations. Furthermore, we
compare the speed and accuracy of the algorithms for both periodic and
arbitrary arrangements of traps, which allows one to choose the ideal scheme
depending on the circumstances.
