In a previous work [J. Opt. Soc. Am. A24, 753 (2007)], we developed a theory describing the space-time statistics of the scintillation and displacement fields of the turbulent point-spread function (PSF), which we validated using imaging data. We now expand on that work by deriving the theoretical expression for the spread fields of the PSF. We also show how the displacement and spread fields are derivable from a set of potentials, and we discuss some of the properties of those potentials.