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Aberration-like cusped focusing in the post-paraxial Talbot effect

Aberration-like cusped focusing in the post-paraxial Talbot effect
Aberration-like cusped focusing in the post-paraxial Talbot effect
We present an analysis of the Talbot effect beyond the paraxial regime, where deviation from Fresnel propagation destroys perfect, periodic self-imaging. The resulting interference structures are examples of aberration without geometric optical rays, which we describe analytically using post-paraxial theory. They are similar to, but do not precisely replicate, a standard integral representation of a diffraction cusp (the Pearcey function). Beyond the Talbot effect, this result illustrates that aberration—as the replacement of a perfect focus with a cusp-like pattern—can occur as a consequence of improving the paraxial approximation, rather than due to imperfections in the optical system.
1741-3567
75702
Howls, C.J.
66d3f0f0-376c-4f7a-a206-093935e6c560
Ring, J.
ec066459-9d79-441f-98cc-a3a27c697420
Lindberg, J.
a531b25d-de6f-407c-9636-cf68f2372e88
Dennis, M.
06608a2d-5a02-4719-8067-08098bd38791
Howls, C.J.
66d3f0f0-376c-4f7a-a206-093935e6c560
Ring, J.
ec066459-9d79-441f-98cc-a3a27c697420
Lindberg, J.
a531b25d-de6f-407c-9636-cf68f2372e88
Dennis, M.
06608a2d-5a02-4719-8067-08098bd38791

Howls, C.J., Ring, J., Lindberg, J. and Dennis, M. (2012) Aberration-like cusped focusing in the post-paraxial Talbot effect. Journal of Optics A: Pure and Applied Optics, 14 (7), 75702. (doi:10.1088/2040-8978/14/7/075702).

Record type: Article

Abstract

We present an analysis of the Talbot effect beyond the paraxial regime, where deviation from Fresnel propagation destroys perfect, periodic self-imaging. The resulting interference structures are examples of aberration without geometric optical rays, which we describe analytically using post-paraxial theory. They are similar to, but do not precisely replicate, a standard integral representation of a diffraction cusp (the Pearcey function). Beyond the Talbot effect, this result illustrates that aberration—as the replacement of a perfect focus with a cusp-like pattern—can occur as a consequence of improving the paraxial approximation, rather than due to imperfections in the optical system.

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Submitted date: 26 April 2012
Published date: 7 June 2012
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 338100
URI: http://eprints.soton.ac.uk/id/eprint/338100
ISSN: 1741-3567
PURE UUID: b1cff7ca-0986-4742-88c8-1f7c203e2df3
ORCID for C.J. Howls: ORCID iD orcid.org/0000-0001-7989-7807

Catalogue record

Date deposited: 09 May 2012 14:34
Last modified: 15 Mar 2024 03:04

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Contributors

Author: C.J. Howls ORCID iD
Author: J. Ring
Author: J. Lindberg
Author: M. Dennis

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