  In this paper, we consider the inverse scattering problem to reconstruct the
defect in an open periodic waveguide from near field data. Our first aim is to
mention that there is a mistake in the factorization method of Lechleiter 2008.
By this we can not apply it to solve this inverse problem. Our second aim is to
give ways to understand the defect from inside (Theorem 1.1) and outside
(Theorem 1.2) based on the monotonicity method.

Analysis of PDEs