  In the absence of separate apertures, the size and focal length of a lens
determines both its resolution and light-collection ability defined by
numerical-aperture (NA) and f/#, respectively. We utilize free-form
broadband-diffractive-optical elements (BDOEs) to create flat lenses that
decouple NA from f#, whereby the resolution of the lens may be chosen
independently from its light-collection ability. Specifically, we designed,
fabricated and characterized three BDOE lenses operating in the visible band
(450nm-750nm), each with f/11.25, but with NAs of 0.00075, 0.0067 and 0.054,
respectively. Simulations confirm 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 could 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.

Optics