Canadian banknotes to explore the phenomenon of diffraction

Abstract

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.