An extremely simplified optics laboratory for teaching the fundamentals of Fourier analysis

Easy and cheap optics experiences are described to teach undergraduate students the fundamental properties of Fourier transform on an experimental basis. By exploiting the eye as the Fourier transforming device, a common magnifying lens and quasi-coherent light from a small white LED, quantitative results can be easily obtained about the fundamental theorems in Fourier analysis. The concept of coherence is also introduced in an elementary way. This approach has been successfully adopted to teach third year students in Physics, who operated in a complete autonomous way during the COVID-19 lockdown without accessing any laboratory. This proves the effectiveness of the method. Thanks to its experimental simplicity it can be easily extended to teach and show the fundamental effects to a larger audience, including high school students.