Invisibility cloaking in weak scattering

We consider invisibility cloaking of a slab object in scalar wave theory within the first-order Born approximation. We show that in the forward direction cloaking is achieved for any object slab and incident field, whereas in the backward direction cloaking is possible at least for self-imaging fields. In both cases the scattering potential of the cloak slab depends on that of the object slab. The method of object-dependent cloaking using weak slab scatterers can be a useful addition to existing cloaking methods, for instance, in atmospheric optics and biophotonics.