We consider the point-spread function (PSF) of an imaging system looking through weak optical turbulence along a horizontal path through the atmospheric surface layer. From this PSF we derive a scalar total irradiance field and a center-of-mass vector field. Theoretical values are found for the space-time autocorrelation and cross-correlation functions for these fields, which are then compared with the observed correlation functions obtained from data taken at the Validation Measurements on Propagation in the Infrared and Radar (VAMPIRA) measurement trial. We discuss the meaning of these results and possible directions for future work.