An imaging system is being developed as a possible means of screening for breast cancer using harmless doses of visible or near-infrared radiation. This system produces transmission images of highly scattering objects by recording and discriminating between the times-of-flight of transmitted photons. Experiments have been performed to evaluate the likely spatial resolution performance of such a system. This involved measuring the edge profile produced by an opaque mask embedded in a highly scattering medium, and evaluating the spatial resolution as a function of the period of time over which transmitted light was integrated. The results suggest that a resolution of a few millimeters is achievable with a system with a temporal resolution of about 10 ps.