  We analyze the factorization method (introduced by Kirsch in 1998 to solve
inverse scattering problems at fixed frequency from the far field operator) for
a general class of boundary conditions that generalizes impedance boundary
conditions. For instance, when the surface impedance operator is of
pseudo-differential type, our main result stipulates that the factorization
method works if the order of this operator is different from one and the
operator is Fredholm of index zero with non negative imaginary part. We also
provide some validating numerical examples for boundary operators of second
order with discussion on the choice of the test function.
