Geometrical transformations in optics*

Bryngdahl, Olof

doi:10.1364/josa.64.001092

Cited by 257 publications

(70 citation statements)

References 9 publications

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“…The transforming system therefore comprises two custom optical elements, one to transform the image and a second, positioned in the Fourier plane of the first, to correct for the phase distortion. This transformation is an example of an optical geometric transformation which has been previously studied in the context of optical image processing [19]. It was shown that a geometric transformation can only be implemented by a single optical element if the mapping is conformal.…”

mentioning

confidence: 99%

Efficient Sorting of Orbital Angular Momentum States of Light

et al. 2010

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We present a method to efficiently sort orbital angular momentum (OAM) states of light using two static optical elements. The optical elements perform a Cartesian to log-polar coordinate transformation, converting the helically phased light beam corresponding to OAM states into a beam with a transverse phase gradient. A subsequent lens then focuses each input OAM state to a different lateral position. We demonstrate the concept experimentally by using two spatial light modulators to create the desired optical elements, applying it to the separation of eleven OAM states.

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confidence: 99%

Efficient Sorting of Orbital Angular Momentum States of Light

et al. 2010

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“…This was achieved through the use of mapping of a position (x, y) in the input plane to a position (u, v) in the output plane, where u = −a ln( x 2 + y 2 /b) and v = a arctan(y/x) [15][16][17]. A mapping of this type transforms a set of concentric rings at the input plane into a set of parallel lines in the output plane.…”

mentioning

confidence: 99%

Refractive elements for the measurement of the orbital angular momentum of a single photon

Lavery¹,

Robertson²,

Berkhout³

et al. 2012

Opt. Express

231

184

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“…Sometimes it is desirable to create an image that is distorted according to a specific mapping between the coordinates in the object and image planes. This is called a geometrical optical transformation, and it can be approximated holographically [7]. Our own interest in geometrical optical transformations stems from the application of a polar-to-Cartesian transformation between two planes to the detection of optical angular momentum [8].…”

Section: Teleporting Surface Propertymentioning

confidence: 99%

TIM, a ray-tracing program for METATOY research and its dissemination

Lambert

Hamilton

Constable

et al. 2012

Computer Physics Communications

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TIM (The Interactive METATOY) is a ray-tracing program specifically tailored towards our research in METATOYs, which are optical components that appear to be able to create wave-optically forbidden light-ray fields. For this reason, TIM possesses features not found in other ray-tracing programs. TIM can either be used interactively or by modifying the openly available source code; in both cases, it can easily be run as an applet embedded in a web page. Here we describe the basic structure of TIM's source code and how to extend it, and we give examples of how we have used TIM in our own research.

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Geometrical transformations in optics*

Cited by 257 publications

References 9 publications

Efficient Sorting of Orbital Angular Momentum States of Light

Efficient Sorting of Orbital Angular Momentum States of Light

Refractive elements for the measurement of the orbital angular momentum of a single photon

TIM, a ray-tracing program for METATOY research and its dissemination

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