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.
75702
Howls, C.J.
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Ring, J.
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Lindberg, J.
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Dennis, M.
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7 June 2012
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), .
(doi:10.1088/2040-8978/14/7/075702).
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
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Local EPrints ID: 338100
URI: http://eprints.soton.ac.uk/id/eprint/338100
ISSN: 1741-3567
PURE UUID: b1cff7ca-0986-4742-88c8-1f7c203e2df3
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Date deposited: 09 May 2012 14:34
Last modified: 15 Mar 2024 03:04
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Author:
J. Ring
Author:
J. Lindberg
Author:
M. Dennis
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