Fast algorithms for generating binary holograms

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.