Towards digital Fourier optics - From the Fourier’s space to the imagery

The article "Vers l'optique de Fourier digitale - De la diffraction au plan de Fourier..." (Towards digital Fourier optics - From diffraction to the Fourier plane) [E 4 150] sets out the background to Fourier optics, on the basis of which several aperture interference devices have been studied.

After a brief reminder of the basic concepts of Fourier optics, this article brings together potential applications of Fourier optics in the form of how to write and read them, in order to better identify them. In particular, it discusses the notion of frequency components (from low to high frequencies) in the Fourier plane and notions of filtering these spatial frequencies.

Single-exposure analog Fourier optics applications are then naturally described, along with the various existing classical filtering techniques, such as low-pass, band-pass and high-pass amplitude filtering, and phase filtering such as phase contrast. This is followed by a number of interferometric applications in so-called multiple exposures, such as speckle-based double star distance measurement and analog Fourier holography, to make the link with Fresnel holography.

Following the same logic, digital Fourier optics is introduced as a single exposure for the independently oriented differential phase contrast microscope. Digital holography is then presented through Fresnel optics for multiple-exposure applications, such as the design of digital holograms, the rendering of virtual objects in three dimensions, or interferometry enhanced by current computing resources. Opening up to the digital world of optics is certainly a major challenge.

At the end of the article, readers will find a glossary and a table of acronyms.