Absolute instruments and perfect imaging in geometrical optics

Tyc, Tomáš; Herzanova, Lenka; Šarbort, Martin; Беринг, Клаус

doi:10.1088/1367-2630/13/11/115004

Cited by 77 publications

(104 citation statements)

References 20 publications

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“…Our argument about direct imaging with curved surfaces shows that there can be no images after a single passage through the surface. However, after two passages through the surface, such a sphere would look identical to an Eaton lens [16], which images each point P to a point P on the opposite side of the lens centre [17] ( Fig. 2(c)).…”

Section: Indirect Imagingmentioning

confidence: 99%

Direct stigmatic imaging with curved surfaces

2015

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We study the possibilities of direct (using one intersection with each light ray) stigmatic imaging with a curved surface that can change ray directions in an arbitrary way. By purely geometric arguments we show that the only possible case of such imaging is the trivial one where the image of any point is identical to the point itself and the surface does not perform any change of the ray direction at all. We also discuss an example of a curved surface which performs indirect stigmatic imaging after twice intersecting each light ray.

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Section: Indirect Imagingmentioning

confidence: 99%

Direct stigmatic imaging with curved surfaces

2015

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“…The final family of transmuted graded index devices that we will consider we will refer to as "multipole" lenses due to the fact that their ray trajectories mimic the field lines of multipolar line-charge distributions (dipolar, quadrupolar etc). The refractive index profile of such a lens is given by (14)) for arbitrary real l is known as the generalized Maxwell fish-eye [38,39], and for 1 l = this becomes the more well-known form of the Maxwell fish-eye lens in which each point on the radius of the device is refocused to the opposite point on the same surface [17]. It was noted in [40] that the ray trajectories of the fish-eye in one plane (see Fig.…”

Section: Other Transmuted Devicesmentioning

confidence: 99%

Transmutation of singularities and zeros in graded index optical instruments: a methodology for designing practical devices

Hooper¹,

Philbin²

2013

Opt. Express

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Abstract:We describe a design methodology for modifying the refractive index profile of graded-index optical instruments that incorporate singularities or zeros in their refractive index. The process maintains the device performance whilst resulting in graded profiles that are all-dielectric, do not require materials with unrealistic values, and that are impedance matched to the bounding medium. This is achieved by transmuting the singularities (or zeros) using the formalism of transformation optics, but with an additional boundary condition requiring the gradient of the coordinate transformation be continuous. This additional boundary condition ensures that the device is impedance matched to the bounding medium when the spatially varying permittivity and permeability profiles are scaled to realizable values. We demonstrate the method in some detail for an Eaton lens, before describing the profiles for an "invisible disc" and "multipole" lenses.

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“…Tyc at al also prove that there is no exact solution with positive refractive index distribution in ref. [12]. Also we present a novel numerical design method for Type B GRIN lenses based on the Singular Value Decomposition.…”

Section: Examples Of Type B Grin Lensmentioning

confidence: 99%

On the design of spherical gradient index lenses

Miñano¹,

Grabovičkić²,

Benı́tez³

et al. 2012

SPIE Proceedings

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Classical spherical gradient index (GRIN) lenses (such as Maxwell Fish Eye lens, Eaton lens, Luneburg lens, etc.) design procedure using the Abel integral equation is reviewed and reorganized. Each lens is fully defined by a function called the angle of flight which describes the ray deflection through the lens. The radial refractive index distribution is obtained by applying a linear integral transformation to the angle of flight. The interest of this formulation is in the linearity of the integral transformation which allows us to derive new solutions from linear combinations of known lenses. Beside the review of the classical GRIN designs, we present a numerical method for GRIN lenses defined by the Abel integral equation with fixed limits, which is an ill-posed problem.

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Absolute instruments and perfect imaging in geometrical optics

Cited by 77 publications

References 20 publications

Direct stigmatic imaging with curved surfaces

Direct stigmatic imaging with curved surfaces

Transmutation of singularities and zeros in graded index optical instruments: a methodology for designing practical devices

On the design of spherical gradient index lenses

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