  We present efficient theoretical tools for describing the optical pumping of
atoms by light propagating at arbitrary directions with respect to an external
magnetic field, at buffer-gas pressures that are small enough for
velocity-selective optical pumping (VSOP) but large enough to cause substantial
collisional relaxation of the velocities and the spin. These are the conditions
for the sodium atoms at an altitude of about 100 km that are used as guidestars
for adaptive optics in modern ground-based telescopes to correct for
aberrations due to atmospheric turbulence. We use spin and velocity relaxation
modes to describe the distribution of atoms in spin space (including both
populations and coherences) and velocity space. Cusp kernels are used to
describe velocity-changing collisions. Optical pumping operators are
represented as a sum of poles in the complex velocity plane. Signals simulated
with these methods are in excellent agreement with previous experiments and
with preliminary experiments in our laboratory.
