The first fully-resolved, non-intrusive, experimental measurements of the spatio-temporal structure and dynamics of the full nine-component velocity gradient tensor field Vux,t in a turbulent flow are here obtained by applying the scalar imaging velocimetry technique Phys. Fluids A 4, 2191-2206 to laboratory turbulent flow scalar field data. A variational method implementing this concept is described in which weighted residuals of the conserved scalar transport equation, the continuity condition, and a derivative smoothness condition are minimized over the space of velocity fields. The technique is applied to direct numerical simulation DNS data for the limiting case of turbulent mixing of a Sc 1 passive scalar field. The spatial velocity fields ux,t obtained correlate well with the exact DNS results, as do statistics of the velocity and velocity gradient fields. The method is then applied to fully resolved four-dimensional Sc 1 scalar field imaging measurements from a laboratory turbulent flow. Results give the first fully resolved data for the time-varying u, v, w vector velocity component fields simultaneously everywhere on a regular three-dimensional spatial grid in a turbulent flow. Direct differentiation of these fields yields the spatial structure in the full velocity gradient tensor field components. From these, the vector vorticity field wix,t and tensor strain rate field epsilon-ijx,t are extracted, as are the kinetic energy density field kxt, the kinetic energy dissipation rate field phixt, and the enstrophy field Wxt. Finally, extraction of the time evolution in these fields is demonstrated by applying this scalar imaging velocimetry method to perform the inversion for the velocity field at several sequential time steps.