Gratings and their well-known diffraction patterns are the basis of spectrometers to characterize light sources. Reciprocally, periodic peaks in the diffraction pattern of x-rays scattered by solids bring valuable information about the internal geometry of the crystal lattice, providing details about the arrangement of atoms in the solid. In both cases, periodic gratings are considered. What about non-periodic gratings? Is it possible to reconstruct any grating structure knowing its diffraction pattern? We answer this question by studying diffraction through the hologram hidden in a Canadian banknote. We measure the diffraction of near-infrared light to numerically reconstruct the grating structure using the Gerchberg–Saxton algorithm. We then compare this reconstructed grating structure with the picture of the grating structure observed with a phase-contrast microscope. Such an approach allows us to study diffraction from a perspective different from that usually taught at university.

中文翻译：

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加拿大纸币探索衍射现象

光栅及其众所周知的衍射图案是光谱仪表征光源的基础。相反，固体散射的 X 射线衍射图中的周期性峰带来了有关晶格内部几何形状的有价值的信息，提供了有关固体中原子排列的详细信息。在这两种情况下，都考虑周期性光栅。非周期光栅呢？是否有可能在知道其衍射图案的情况下重建任何光栅结构？我们通过研究加拿大钞票中隐藏的全息图的衍射来回答这个问题。我们测量近红外光的衍射，以使用 Gerchberg-Saxton 算法对光栅结构进行数值重建。然后，我们将这种重建的光栅结构与用相差显微镜观察到的光栅结构的图片进行比较。这种方法使我们能够从不同于大学通常教授的角度来研究衍射。