A conjugate gradient minimisation approach to generating holographic   traps for ultracold atoms
  Direct minimisation of a cost function can in principle provide a versatile and highly controllable route to computational hologram generation. However, to date iterative Fourier transform algorithms have been predominantly used. Here we show that the careful design of cost functions, combined with numerically efficient conjugate gradient minimisation, establishes a practical method for the generation of holograms for a wide range of target light distributions. This results in a guided optimisation process, with a crucial advantage illustrated by the ability to circumvent optical vortex formation during hologram calculation. We demonstrate the implementation of the conjugate gradient method for both discrete and continuous intensity distributions and discuss its applicability to optical trapping of ultracold atoms. 
Tiffany Harte, Graham D. Bruce, Jonathan Keeling and Donatella   Cassettari
cond-mat.quant-gas physics.atom-ph physics.optics