  Precise knowledge of optical lattice depths is important for a number of
areas of atomic physics, most notably in quantum simulation, atom
interferometry and for the accurate determination of transition matrix
elements. In such experiments, lattice depths are often measured by exposing an
ultracold atomic gas to a series of off-resonant laser-standing-wave pulses,
and fitting theoretical predictions for the fraction of atoms found in each of
the allowed momentum states by time of flight measurement, after some number of
pulses. We present a full analytic model for the time evolution of the atomic
populations of the lowest momentum-states, which is sufficient for a "weak"
lattice, as well as numerical simulations incorporating higher momentum states
for both relatively strong and weak lattices. Finally, we consider the
situation where the initial gas is explicitly assumed to be at a finite
temperature.
