  The concepts of Fourier optics were established in France in the 1940s by
Pierre-Michel Duffieux, and laid the foundations of an extensive series of
activities in the French research community that have touched on nearly every
aspect of contemporary optics and photonics. In this paper, we review a
selection of results where applications of the Fourier transform and transfer
functions in optics have been applied to yield significant advances in
unexpected areas of optics, including the spatial shaping of complex laser
beams in amplitude and in phase, real-time ultrafast measurements, novel ghost
imaging techniques, and the development of parallel processing methodologies
for photonic artificial intelligence.
