Two-dimensional analysis of generalized grating imaging in the Talbot-Lau arrangement

The Talbot-Lau arrangement is an optical system using two gratings of different pitches. The gratings are placed parallel with some distance separated. By illuminating them with a broad incoherent source, we obtain high contrast grating images formed on a plane at a distance determined by the pitches. The phenomenon is called generalized grating imaging. It is used, for example, in pattern projection profilometer and as a shearing interferometer for light, X-ray and matter waves. There are many analyses on the Talbot-Lau arrangement. However, almost all of them are related to onedimensional gratings. This paper presents a rigorous analysis on the phenomenon with two-dimensional gratings using wave optics. The analytical result is applied to hexagonal gratings and the contrast is calculated by numerical calculation. The numerical results agree with experimental results. The analysis can be used to design a Talbot-Lau arrangement with two-dimensional gratings in broad fields.

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