We describe the advantages of using diffractive (Fresnel) lenses on thin membranes over conventional optics for, among others, future space telescope projects. Fabrication methods are presented for lenses on two types of freestanding membrane up to 50 cm in size. The first is a Fresnel lens etched into a thin (380-μm) glass sheet, and the second is an ～50-μm-thick polymer membrane containing a Fresnel lens made by replication process from a specially made fused-silica master. We show optical performance analysis of all the lenses that are fabricated, including a diffraction-limited Airy spot from a 20-m-focal-length membrane lens in a diffractive telescope system.
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