Solution to the bundle-to-bundle mapping problem of geometric optics using four freeform reflectors

Croke, Christopher B.; Hicks, R. Andrew

doi:10.1364/josaa.31.002097

Cited by 7 publications

(3 citation statements)

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“…A first strategy involves the so-called direct design methods. They rely on solving geometrical or differential equations describing the freeform optical system under study to achieve a wellperforming initial design [23][24][25][26][27][28][29][30][31] . Although these methods show clear merits, so far, they lack a straightforward path to increase the number of optical surfaces that can be calculated 25,29,31 .…”

Section: Freeform Optical Design Strategiesmentioning

confidence: 99%

“…They rely on solving geometrical or differential equations describing the freeform optical system under study to achieve a wellperforming initial design [23][24][25][26][27][28][29][30][31] . Although these methods show clear merits, so far, they lack a straightforward path to increase the number of optical surfaces that can be calculated 25,29,31 . Because of this limitation in scalability, their applicability remained limited until today.…”

Section: Freeform Optical Design Strategiesmentioning

confidence: 99%

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Freeform imaging systems: Fermat’s principle unlocks “first time right” design

Duerr

Thienpont

2021

Light Sci Appl

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For more than 150 years, scientists have advanced aberration theory to describe, analyze and eliminate imperfections that disturb the imaging quality of optical components and systems. Simultaneously, they have developed optical design methods for and manufacturing techniques of imaging systems with ever-increasing complexity and performance up to the point where they are now including optical elements that are unrestricted in their surface shape. These so-called optical freeform elements offer degrees of freedom that can greatly extend the functionalities and further boost the specifications of state-of-the-art imaging systems. However, the drastically increased number of surface coefficients of these freeform surfaces poses severe challenges for the optical design process, such that the deployment of freeform optics remained limited until today. In this paper, we present a deterministic direct optical design method for freeform imaging systems based on differential equations derived from Fermat’s principle and solved using power series. The method allows calculating the optical surface coefficients that ensure minimal image blurring for each individual order of aberrations. We demonstrate the systematic, deterministic, scalable, and holistic character of our method with catoptric and catadioptric design examples. As such we introduce a disruptive methodology to design optical imaging systems from scratch, we largely reduce the “trial-and-error” approach in present-day optical design, and we pave the way to a fast-track uptake of freeform elements to create the next-generation high-end optics. We include a user application that allows users to experience this unique design method hands-on.

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Section: Freeform Optical Design Strategiesmentioning

confidence: 99%

Section: Freeform Optical Design Strategiesmentioning

confidence: 99%

Freeform imaging systems: Fermat’s principle unlocks “first time right” design

Duerr

Thienpont

2021

Light Sci Appl

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“…The paper [3] concerns mirror realizations of a mapping of a 2-parameter family of rays in R 3 to another such family; the families are not necessarily normal. Using the Cartan-Kähler theorem in the theory of exterior differential systems, a numerical method is described for constructing four mirrors that realize the mapping (the presented examples involve only normal families of rays).…”

Section: Introductionmentioning

confidence: 99%

Billiard transformations of parallel flows: A periscope theorem

Plakhov

Tabachnikov

Treschev

2017

Journal of Geometry and Physics

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We consider the following problem: given two parallel and identically oriented bundles of light rays in R n+1 and given a diffeomorphism between the rays of the former bundle and the rays of the latter one, is it possible to realize this diffeomorphism by means of several mirror reflections? We prove that a 2-mirror realization is possible if and only if the diffeomorphism is the gradient of a function. We further prove that any orientation reversing diffeomorphism of domains in R 2 is locally the composition of two gradient diffeomorphisms, and therefore can be realized by 4 mirror reflections of light rays in R 3 , while an orientation preserving diffeomorphism can be realized by 6 reflections. In general, we prove that an (orientation reversing or preserving) diffeomorphism of wave fronts of two normal families of light rays in R 3 can be realized by 6 or 7 reflections.Mathematics subject classifications: Primary 49Q10, 49K30

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