Conclusion

This first article established a model, called "Fourier optics", between the physical foundations of diffraction and mathematical concepts used in signal processing. Its construction required starting with the notion of the electromagnetic field and, step by step, legitimate simplifications, depending on the distance from the field of observation, showed that the Fourier transform was an effective tool for interpreting undulatory light phenomena. Finally, two families of experimental set-ups enable Fourier optics to be used: sufficient distance from the field of observation, known as the "far field", and the use of a converging lens, which allows optical devices to be miniaturized.

The end of the paper introduces analog Fourier optics, with classic one-dimensional examples, as well as digital Fourier optics, which are playing an increasingly important role in today's...