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   This work provides the design of a multifocal display that can create a dense stack of focal planes in a single shot. We achieve this using a novel computational lens that provides spatial selectivity in its focal length, i.e, the lens appears to have different focal lengths across points on a display behind it. This enables a multifocal display via an appropriate selection of the spatially-varying focal length, thereby avoiding time multiplexing techniques that are associated with traditional focus tunable lenses. The idea central to this design is a modification of a Lohmann lens, a focus tunable lens created with two cubic phase plates that translate relative to each other. Using optical relays and a phase spatial light modulator, we replace the physical translation of the cubic plates with an optical one, while simultaneously allowing for different pixels on the display to undergo different amounts of translations and, consequently, different focal lengths. We refer to this design as a Split-Lohmann multifocal display. Split-Lohmann displays provide a large étendue as well as high spatial and depth resolutions; the absence of time multiplexing and the extremely light computational footprint for content processing makes it suitable for video and interactive experiences. Using a lab prototype, we show results over a wide range of static, dynamic, and interactive 3D scenes, showcasing high visual quality over a large working range. 

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   null (Ed.)
5. Finite generation of split-F-regular$$\text{split-}F\text{-regular}$$ monoid algebras

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   Abstract Let be a submonoid of a free Abelian group of finite rank. We show that if is a field of prime characteristic such that the monoid ‐algebra is , then is a finitely generated ‐algebra, or equivalently, that is a finitely generated monoid. Split‐‐regular rings are possibly non‐Noetherian or non‐‐finite rings that satisfy the defining property of strongly ‐regular rings from the theories of tight closure and ‐singularities. Our finite generation result provides evidence in favor of the conjecture that rings in function fields over have to be Noetherian. The key tool is Diophantine approximation from convex geometry. 

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