  We develop an accurate finite-time scaling analysis of the angular width of
the coherent backscattering (CBS) peak for waves propagating in 3D random
media. Applying this method to ultracold atoms in optical speckle potentials,
we show how to determine both the mobility edge and the critical exponent of
the Anderson transition from the temporal behavior of the CBS width. Our method
could be used in experiments to fully characterize the 3D Anderson transition.
