  We discuss and compare three algorithms for generating holograms: simple
rounding, Floyd-Steinberg error diffusion dithering, and mixed region amplitude
freedom (MRAF). The methods are optimised for producing large arrays of tightly
focused optical tweezers for trapping particles. The algorithms are compared in
terms of their speed, efficiency, and accuracy, for periodic arrangements of
traps; an arrangement of particular interest in the field of quantum computing.
We simulate the image formation using each of a binary amplitude modulating
digital mirror device (DMD) and a phase modulating spatial light modulator
(PSLM) as the display element. While a DMD allows for fast frame rates, the
slower PSLM is more efficient and provides higher accuracy with a
quasi-continuous variation of phase. We discuss the relative merits of each
algorithm for use with both a DMD and a PSLM, allowing one to choose the ideal
approach depending on the circumstances.
