  Using the transfer matrix method, we numerically compute the precise position
of the mobility edge of atoms exposed to a laser speckle potential, and study
its dependence vs. the disorder strength and correlation function. Our results
deviate significantly from previous theoretical estimates using an approximate
self-consistent approach of localization. In particular we find that the
position of the mobility edge in blue-detuned speckles is much lower than in
the red-detuned counterpart, pointing out the crucial role played by the
asymmetric on-site distribution of speckle patterns.
