Optical Fourier surfaces

Gratings1 and holograms2 use patterned surfaces to tailor optical signals by diffraction. Despite their long history, variants with remarkable functionalities continue to be developed3,4. Further advances could exploit Fourier optics5, which specifies the surface pattern that generates a desired diffracted output through its Fourier transform. To shape the optical wavefront, the ideal surface profile should contain a precise sum of sinusoidal...