  We work out a simple, pulsed pump-probe measurement scheme to measure the
homogeneous linewidth of an atomic transition in an inhomogeneously broadened
spectral line in a solid state environment. We apply the theory to the I_11/2
-- I_15/2 optical transition of erbium in LiNbO_3:Er^3+ crystal. Beside
obtaining the homogeneous linewidth, we have estimated the population
relaxation time as well.
