Axial and focal-plane diffraction catastrophe integrals
Axial and focal-plane diffraction catastrophe integrals
Exact expressions in terms of Bessel functions are found for some of the diffraction catastrophe integrals that decorate caustics in optics and mechanics. These are the axial and focal-plane sections of the elliptic and hyperbolic umbilic diffraction catastrophes, and symmetric elliptic and hyperbolic unfoldings of the X_9 diffraction catastrophes. These representations reveal unexpected relations between the integrals.
375206-[13pp]
Berry, M.V.
ab44fe7c-0c8c-4c7a-981f-50fe4a5bc6ad
Howls, C.J.
66d3f0f0-376c-4f7a-a206-093935e6c560
7 July 2010
Berry, M.V.
ab44fe7c-0c8c-4c7a-981f-50fe4a5bc6ad
Howls, C.J.
66d3f0f0-376c-4f7a-a206-093935e6c560
Berry, M.V. and Howls, C.J.
(2010)
Axial and focal-plane diffraction catastrophe integrals.
Journal of Physics A: Mathematical and Theoretical, 43 (37), .
(doi:10.1088/1751-8113/43/37/375206).
Abstract
Exact expressions in terms of Bessel functions are found for some of the diffraction catastrophe integrals that decorate caustics in optics and mechanics. These are the axial and focal-plane sections of the elliptic and hyperbolic umbilic diffraction catastrophes, and symmetric elliptic and hyperbolic unfoldings of the X_9 diffraction catastrophes. These representations reveal unexpected relations between the integrals.
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Submitted date: 22 April 2010
Published date: 7 July 2010
Organisations:
Applied Mathematics
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Local EPrints ID: 142733
URI: http://eprints.soton.ac.uk/id/eprint/142733
ISSN: 1751-8113
PURE UUID: a60bbf7f-d63f-4671-9906-ee7b64c49c31
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Date deposited: 22 Apr 2010 13:29
Last modified: 14 Mar 2024 02:44
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Author:
M.V. Berry
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