Gratings and holograms are patterned surfaces that tailor optical signals by diffraction. Despite the long history of such structures, further advances could exploit Fourier optics, which specifies the surface pattern that generates a desired diffracted output through its Fourier transform. The required surface profile should contain a precise sum of sinusoidal waves, each with a well-defined amplitude, spatial frequency, and phase, to shape the optical wavefront. However, because fabrication techniques typically yield profiles with at most a few depth levels, complex “wavy” surfaces cannot be obtained, limiting the straightforward mathematical design and implementation of sophisticated diffractive optics. In this presentation, we will discuss a simple yet powerful approach to eliminate this design–fabrication mismatch by demonstrating optical surfaces that contain an arbitrary number of specified sinusoids.
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