Fourier series diffractive lens with extended depth of focus

Abstract

Angular diffractive lenses have been proven to achieve a narrow beam waist with a long depth of focus. We generalize these type of lenses by defining the angular distribution of the focal length as a Fourier series. The Fourier coefficients of the lens are optimized, using Particle Swarm Optimization algorithm, to minimize the beam width and increase its uniformity for a given depth of focus. In order to obtain a fast simulation during the optimization process, we used Chirp Z-transform algorithm. Finally, we performed an experimental verification of the results using a Spatial Light Modulator. The Fourier series diffractive lens presents a more uniform and narrower beam than previous angular lenses, in both simulations and experiments. These results may find applications in the design of contact and intraocular lenses with extended depth of focus, laser focusing and imaging systems.