We describe a new and distinctive interferometry in which a probe particle scatters off a superposition of locations of a single free target particle. Probe particles scattering off a single free "mirror" (in one dimension) or a single free "slit" (in two dimensions) can "swap" interference with the superposed target states. The condition for interference is loss of orthogonality of the target states and reduces, in simple examples, to transfer of orthogonality from target to probe states. We analyze experimental parameters and conditions necessary for interference to be observed.