Abstract
Mathematical formulas are derived for predicting diffraction efficiencies of a grating made on a thick transparent parallel plate (substrate) or cemented between two plates. The formulas are applicable in two situations: (1) when the coherence length of the light source is greater than the thickness of the grating but less than that of the substrate; (2) when the thickness of the substrate is not precisely known, therefore only the average values of the diffraction efficiencies can be expected. There is no limitation on the number of propagating diffraction orders that are present in the system. The derivation uses the concept of energy scattering matrix, therefore it is simpler than a previous method that yielded limited results.
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