  The population distribution within the ground-state of an atomic ensemble is
of large significance in a variety of quantum optics processes. We present a
method to reconstruct the detailed population distribution from a set of
absorption measurements with various frequencies and polarizations, by
utilizing the differences between the dipole matrix elements of the probed
transitions. The technique is experimentally implemented on a thermal rubidium
vapor, demonstrating a population-based analysis in two optical pumping
examples. The results are used to verify and calibrate an elaborated numerical
model, and the limitations of the reconstruction scheme which result from the
symmetry properties of the dipole matrix elements are discussed.
