Design and Ultra-Precision Fabrication of Freeform Fresnel Lenses for Generating Rectangular Dark Hollow Beams

Freeform Fresnel lenses combine the powerful beam-shaping capability of freeform optics with the lightweight and compact characteristics of conventional Fresnel structures, leading to their increasing adoption across diverse applications. This paper proposes and experimentally validates a method for generating rectangular dark hollow beams using a freeform Fresnel lens. The lens is divided into multiple fan-shaped sectors centered on the optical axis, with each sector generating a defocused spot at a distinct spatial location. Based on geometrical optics, a freeform Fresnel lens with a 25 mm aperture is designed to produce a square hollow beam with a side length of 10 mm. A lens with a division angle of 5° was fabricated using ultra-precision diamond turning. The angular form error was measured to be below 0.1°, and the surface roughness was found to be below 10 nm. An optical testing system was established to characterize the generated beam profile. The experimental results successfully demonstrate the formation of the desired rectangular dark hollow beam. The measured results agree well with the simulations, confirming the feasibility and practical potential of the proposed method.