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Direct minimisation of a cost function can in principle provide a versatileand highly controllable route to computational hologram generation. However, todate iterative Fourier transform algorithms have been predominantly used. Herewe show that the careful design of cost functions, combined with numericallyefficient conjugate gradient minimisation, establishes a practical method forthe generation of holograms for a wide range of target light distributions.This results in a guided optimisation process, with a crucial advantageillustrated by the ability to circumvent optical vortex formation duringhologram calculation. We demonstrate the implementation of the conjugategradient method for both discrete and continuous intensity distributions anddiscuss its applicability to optical trapping of ultracold atoms.

A conjugate gradient minimisation approach to generating holographic traps for ultracold atoms