Figure 7: Measurement of pair-wise colloidal interaction potentials from digital video data. Top: Distribution of particle separations initially at r(t) which evolved to after msec. In the absence of an interparticle interaction, the freely diffusing spheres would form a distribution of points along the dashed diagonal line. Deviations from that line indicate the presence of interactions. The density of points does not reflect the probability of finding particles at a particular separation, but rather the frequency with which initial conditions were set in that region with the blinking optical tweezers. Inset: Grey-scale histogram of the same data set normalized as a propagation matrix, . Bottom: Interaction potential in units of the thermal energy as a function of center-to-center separation measured in units of sphere radii. The solid line is a fit to the DLVO theory with corrections for charge renormalization as described in eqns. (24) and (25). Inset: modified semi-logarithmic plot to emphasize the screened-Coulomb nature of the measured interaction.