Analyzing the spectrum characteristics of a double-grating transmission scheme

In this paper, the spectral characteristics formed by a double-grating transmission scheme are discussed based on the scalar diffraction theory. First, considering two different grating periods, the angular spectrum at the back of the second grating is obtained. Then, the spectral characteristics are discussed with three different periodic conditions, while it is proved that the spatial distribution and spacing of the spectrum are absolutely determined by the grating constants and angles. The theoretical results manifest that the spatial distribution range of the spectrum becomes larger as the angle increases, unlike the spectral points, which are distributed on a single line when the grating lines of the two gratings are parallel. Finally, for the sake of proving that our theoretical analysis is correct and reasonable, three sets of experiments are conducted with three different combinations of Ronchi gratings. As expected, the experimental and theoretical results are in perfect agreement. In a word, the involved results could be useful for expanding the application of moiré deflectometry.