Optimization of angular diffractive lenses with extended depth of focus

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Torcal Milla, Francisco José
Hoyo Muñoz, Jesús del
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IOP Publishing, Ltd.
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Conventional refractive lenses concentrate the incident light at focal distance. A narrow beam waist can be achieved by increasing the lens numerical aperture, but strongly reduces the depth of focus. In this paper, we explore diffractive lenses designs, with fast angular variation of the focal distance, that produce both a narrow beam waist and a long depth of focus. We predict the focusing properties or the diffractive lenses with a simple analytical model based on an incoherent superposition of standard lenses with different focal distances. The histogram of the local focal distances is used to determine the weights in the superposition. Our model optimizes the shape of the diffractive lenses, in order to extend the depth of focus, which corresponds to the lotus lens. We verify our results with numerical simulations based on Rayleigh-Sommerfeld approach. Experimentally, we validate our analytical and numerical solutions with a Spatial Light Modulator are carried out and compared to the analytical and numerical results. We have found configurations for the lotus lens where the depth of focus is significantly incremented with only a slight increment of the focal width. For example, we increased the depth of focus from 7.6 mm to 37.2 mm while the beam waist varied from 35.0 microns to 51.6 microns for a lens with diameter D~=~4~mm, and focal distance f'~=~125~mm. These results may find applications in the design of contact and intraocular lenses with extended depth of focus, laser focus generators, and imaging applications where extended depth of focus is needed.
Received 5 December 2019 Revised 27 March 2020 Accepted 2 April 2020 Accepted Manuscript online 2 April 2020