The “dynamical” theory of gratings originally developed by Rayleigh and Voigt is applied to derive the intensity of the light diffracted in various directions by an imperfect grating of finite area. The problem is reduced to the numerical solution of a system of linear equations by an approximation method in which “ghosts” and high order spectra are treated as perturbations of the main spectra. Current elementary theories are then seen to yield merely order of magnitude estimates of the intensity of the ghosts caused by various grating imperfections.
U. FANO, "On the Theory of Imperfect Diffraction Gratings," J. Opt. Soc. Am. 38, 921-928 (1948)