Controlling light with freeform multifocal lens designed with supporting quadric method(SQM)

The SQM is a versatile methodology for designing freeform optics for irradiance redistribution. Recently it has often been applied in design of freeform lenses, mirrors and diffractive optical elements. Still, many questions regarding theory and performance of optics designed with the SQM are open. Here we investigate theoretically plano-freeform refractive lenses designed with the SQM when an incident collimated beam must be transformed into a beam illuminating with prescribed irradiances a large number of pixels on a flat screen. It is shown that a lens designed for such task with the SQM operates as a multifocal lens segmented into subapertures with focal lengths providing accurate control of the irradiance distribution between pixels. These subapertures are patches of hyperboloids of revolution. Two different designs are possible, one of which defines a concave lens. Eikonal function for such lenses is also derived. As a proof of concept, we numerically analyze performance of a plano-freeform lens designed with the SQM for transforming a uniform circular parallel light into an image of A. Einstein represented by gray values at ≈ 38K pixels.