The reflection efficiencies for the various orders of diffraction produced by a grating are calculated under the following assumptions. The grating is for the most part flat, but with a fraction ε of the periodicity interval a described by a profile function z= ƒ(x). The reflection and transmission efficiencies are calculated as a series expansion in ε. Numerical calculations have been performed for the case of ultrasoft x rays incident at near grazing angles, using a complex index of refraction η = 1-δ0λ2+iβ0λ3.25 or tabulated values. No effects of shadowing by the grating profile have been considered, and the numerical work has been done for a symmetrical triangular trench incised in the flat surface.
JACK C. MILLER, "Reflection Efficiencies of a Periodic Absorbing Surface," J. Opt. Soc. Am. 54, 353-356 (1964)