The elements of the Jones matrices for an optically pumped sample have been derived and used to predict four-level double resonance absorption coefficients that are functions of the velocity component of the molecules in the direction of the pump beam for different polarizations of the probe beam. When a saturating pump and weak probe are used in four-level double resonance experiments under population modulation conditions, these absorption coefficients are found to depend only on the first three statistical tensor ranks: n = 0 (population), 1 (orientation), and 2 (alignment). It is also found that for polarization modulation experiments with plane-polarized radiation, the absorption coefficient depends only on the alignment of the m-state populations. Similarly, for polarization modulation with circularly polarized radiation, the absorption coefficient depends only on the orientation. The theory was used to interpret double-resonance polarization modulation experiments in 13CH3F and 15NH3 in order to examine the effects of collisions on the initial anisotropy of the projection of J on a space-fixed Z axis. The four-level double-resonance lineshapes were fit by least squares to absorption coefficients predicted by the theory. The collisional effects were modeled by a sum of Keilson-Storer collision kernels. The results of the fits were much improved when the value of the effective rate constant for the transfer of the n = 0 tensor from the upper level of the pump to the lower level of the probe was larger than the values of the effective rate constants for the transfer of the n = 1 and 2 populations. The best ratio of the rate constant for n > 0 to that for n = 0 is about 2/3 for 13CH3F and 1/3 for 15NH3. Additional analysis of the lineshapes showed the importance of long-range dipole-dipole interactions, elastic realignment and reorientation, and V-V mechanisms for collision-induced rotational energy transfer in 13CH3F and 15NH3. Copyright 1998 Academic Press.