Free-form broadband flat lenses for visible imaging

Abstract

The resolution of a conventional lens is governed by its numerical aperture (NA) while its light-concentration ability is governed by its f-number (f/#), both of which are dependent on the diameter and focal length of the lens. Hence, these properties for a conventional lens are inherently coupled. Here, we show that by utilizing the principle of free-form broadband diffractive optical elements (BDOEs), we can create ultra-flat optical elements that are able to concentrate incoming light over a fixed aperture to different sized focal spots engineered in the shape of a square. Hence, we are able to decouple the NA and f/# of a lens by being able to independently control the size of the input aperture and the resolution of these devices. Specifically, we designed, fabricated, and characterized three BDOE lenses operating in the visible band (450nm–750nm), each having f/# of 11.25, but with NAs of 0.00075, 0.0067, and 0.054, respectively. We further use simulations to emphasize that such decoupling is possible even at much higher NAs. Experiments confirm achromatic focusing and broadband imaging. One of the lenses exhibited a depth-of-focus almost 2 orders of magnitude larger than the diffraction limit. Such BDOE lenses can eliminate the need for anti-aliasing filters and could also be very useful in focal-plane arrays with large pixel sizes, where light collection efficiency needs to be maintained. Furthermore, by abandoning rotational symmetry, one can achieve free-form geometries in the focal spot, such as a square that can more closely match the geometry of the sensor pixel.