  We have formulated and experimentally demonstrated an improved algorithm for
design of arbitrary two-dimensional holographic traps for ultracold atoms. Our
method builds on the best previously available algorithm, MRAF, and improves on
it in two ways. First, it allows for creation of holographic atom traps with a
well defined background potential. Second, we experimentally show that for
creating trapping potentials free of fringing artifacts it is important to go
beyond the Fourier approximation in modelling light propagation. To this end,
we incorporate full Helmholtz propagation into our calculations.
