A periodic approach introduced previously is applied to the TM wave scattering from a finite periodic surface. A mathematical relation is proposed to estimate the scattering amplitude from the diffraction amplitude for the periodic surface, where the periodic surface is defined as a superposition of surface profiles generated by displacing the finite periodic surface by every integer multiple of the period . From numerical examples, it is concluded that the scattering cross section for the finite periodic surface can be well estimated from the diffraction amplitude for a sufficiently large .

As a method of analyzing the wave scattering from a finite periodic surface, this paper introduces a periodic approach. The approach first considers the wave diffraction by a periodic surface that is a superposition of surface profiles generated by displacing the finite periodic surface by every integer multiple of the period . It is pointed out that the Floquet solution for such a periodic case becomes an integral representation of the scattered field from the finite periodic surface when the period goes to infinity. A mathematical relation estimating the scattering amplitude for the finite periodic surface from the diffraction amplitude for the periodic surface is proposed. From some numerical examples, it is concluded that the scattering cross section for the finite periodic surface can be well estimated from the diffraction amplitude for a sufficiently large .