  This paper is concerned with the inverse problem of determining the shape of
penetrable periodic scatterers from scattered field data. We propose a sampling
method with a novel indicator function for solving this inverse problem. This
indicator functionl is very simple to implement and robust against noise in the
data. The resolution and stability analysis of the indicator function is
analyzed. Our numerical study shows that the proposed sampling method is more
stable than the factorization method and more efficient than the direct or
orthogonality sampling method in reconstructing periodic scatterers.
