1+1 LIF Doppler profile functions of photofragments in the presence of v-J correlation are derived in a formalism of density matrix. Radon transforms which are imposed by the resonance condition of Doppler spectroscopy have been implemented exactly. Independent parameters which characterize the angular momentum polarizations of photofragments in a specific state on an expanding Newton sphere have been examined carefully to compare the present treatment with the bipolar moment formalism of Dixon [R. N. Dixon, J. Chem. Phys. 85, 1866 (1986)]. To extract information on speed distributions of photofragments from a combined, isotropic Doppler profile, the proper procedure to take the linear combination of experimental profiles from various detection geometries and rotational branches of transitions has been presented. For future analyses of Doppler spectroscopic measurements of photofragmentation processes, it is recommended that the Doppler profile function in the present framework should be utilized.