We treat gratings as arrays of lines or elements rather than as infinite periodic structures. Since we cannot calculate accurately the diffraction pattern of a single rectangular-profile line, we have constructed a simple model which assumes Fraunhofer diffraction from the various parts of the line. Three measured parameters, functions of the angle of incidence, determine the entire diffraction pattern with good accuracy except for large angles of diffraction. The radiance either of the single-line or of a grating of any number of lines is then given by the triple product of the squares of the incident amplitude, the single-line diffraction amplitude (or the effective single-line pattern) and the array factor. Spectral radiances in S polarization calculated for a set of 20-line rectangular-profile gratings are in good agreement with measured values. Even anomalous behavior is accurately predicted.
FREDERICK W. PHELPS, JR. and C. HARVEY PALMER, "Radiance of Rectangular-Profile Gratings in S Polarization," J. Opt. Soc. Am. 59, 812-817 (1969)