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 th
e 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.
We present a laser beam shaping method using acousto-optic deflection of light and discuss its application to dipole trapping of ultracold atoms. By driving the acousto-optic deflector with multiple frequencies, we generate an array of overlapping di
ffraction-limited beams that combine to form an arbitrary-shaped smooth and continuous trapping potential. Confinement of atoms in a flat-bottomed potential formed by a laser beam with uniform intensity over its central region confers numerous advantages over the harmonic confinement intrinsic to Gaussian beam dipole traps and many other trapping schemes.We demonstrate the versatility of this beam shaping method by generating potentials with large flat-topped regions as well as intensity patterns compensating for residual external potentials to create a uniform background to which the trapping potential of experimental interest can be added.
