Geodesic
Scattering of waves by a~diffraction grating with a~local default of its periodic structure
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 36, Tome 342 (2007), pp. 164-186

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Scattering of waves by an impedance strips grating with a local defect over its surface is considered. Formulation of the problem and a basic energy correlation are discussed. Integral equations for the problem at hand is studied. The leading term of the asymptotic solution for a small defect is represented. The latter depends on integral characteristics of the defect. 
@article{ZNSL_2007_342_a7,
     author = {M. A. Lyalinov},
     title = {Scattering of waves by a~diffraction grating with a~local default of its periodic structure},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {164--186},
     publisher = {mathdoc},
     volume = {342},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_342_a7/}
}
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M. A. Lyalinov. Scattering of waves by a~diffraction grating with a~local default of its periodic structure. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 36, Tome 342 (2007), pp. 164-186. http://geodesic.mathdoc.fr/item/ZNSL_2007_342_a7/