We establish a rigorous theoretical connection between measurements of the angular distribution of atomic photofragment alignment and the underlying dynamics of molecular photodissociation. We derive laboratory and molecular-frame angular momentum state multipoles as a function of photofragment recoil angles. These state multipoles are expressed in terms of alignment anisotropy parameters, which provide information on state symmetries, coherence effects, and nonadiabatic interactions. The method is intended for analysis of experimental data obtained with two-photon spectroscopy and ion imaging techniques, although it is readily modified for treating Doppler or time-of-flight mass spectrometer peak profiles. We have applied this method to the photodissociation of Cl-2 at 355 nm, where we observe strong alignment in the ground state chlorine atom photofragments. Our analysis demonstrates that there are important contributions to the alignment from both incoherent and coherent perpendicular excitation. We also show that the existence of atomic alignment due to coherence requires that nonadiabatic transitions occur at long range.