EXPERIMENTAL VISUALIZATION AND NUMERICAL SIMULATION OF FRAUNHOFER DIFFRACTION FROM ORDERED AND DISORDERED OPAQUE MICROSTRUCTURES FOR EDUCATION PRACTICE: ЕКСПЕРИМЕНТАЛЬНА ВІЗУАЛІЗАЦІЯ ТА ЧИСЕЛЬНЕ МОДЕЛЮВАННЯ ДИФРАКЦІЇ ФРАУНГОФЕРА ВІД ВПОРЯДКОВАНИХ І НЕВПОРЯДКОВАНИХ НЕПРОЗОРИХ МІКРОСТРУКТУР ДЛЯ ОСВІТНЬОЇ ПРАКТИКИ

Formulation of the Problem. In teaching Fraunhofer diffraction, experimental approaches that clearly reveal the relationship between real-space structures and their Fourier-space representation remain limited in accessibility and scope. This work presents a simple, low-cost, and visually effective method that enables students to observe diffraction patterns and systematically investigate the influence of fabrication-induced imperfections in printed optical masks.


Materials and Methods. The approach combines experimental visualization using binary amplitude masks printed on transparent film with a standard office laser printer and illumination by a low-power semiconductor laser pointer, with numerical simulations based on two-dimensional fast Fourier transforms implemented in Python. Microstructures ranging from one-dimensional gratings to two-dimensional periodic lattices and structures with a basis (centered and honeycomb), as well as disordered ensembles and quasi-hyperuniform configurations, are directly compared between experiment and simulation. This comparison allows detailed analysis of how printer-induced deviations – including local distortions, positioning errors, toner spreading, and partial merging of elements – affect the resulting diffraction features.


Results. The results demonstrate that in periodic structures the positions of diffraction maxima closely follow the designed geometry, while fabrication-induced imperfections primarily modulate intensities, partially restore nominally forbidden orders, and generate weak additional maxima. In disordered arrays of printed disks, the increased effective feature size and polydispersity in the printed geometry lead to strong smoothing and suppression of the higher-order diffraction rings, whereas imposed short-range correlations produce characteristic features such as a central dark ring. These findings illustrate how subtle systematic and stochastic deviations from idealized binary amplitude masks influence Fraunhofer diffraction patterns, thereby transforming typical printing artefacts into a valuable pedagogical tool.


Conclusion. From an educational perspective, the method provides an affordable, hands-on platform for exploring Fraunhofer diffraction, Fourier optics, reciprocal-space concepts, and statistical correlations. By bridging idealized theoretical models, realistic fabrication limitations, and numerical simulation, it is particularly well suited for undergraduate laboratory courses in wave optics.