When an EM wave impinges on a target, it generates surface currents on that target, and these currents radiate the scattered fields.
However, this approach, namely finding the surface currents and calculating the fields, is just a mathematical construction to make the problem easier to solve. It is either the induction equivalence, or the physical equivalence principle (see Advanced Engineering Electromagnetics, by Balanis, Sections 7.9-7.12). In other words, to make the problem easier to solve, the object is replaced by surface currents so that the background constitutive parameters (epsilon,mu) remain the same.
So it is my understanding then, that these currents really do not exist. Do surface currents really exist?