Axial and focal-plane diffraction catastrophe integrals

MV Berry; CJ Howls

doi:10.1088/1751-8113/43/37/375206

Axial and focal-plane diffraction catastrophe integrals

MV Berry
, CJ Howls

School of Physics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

8 Citations (Scopus)

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 X9 diffraction catastrophes. These representations reveal unexpected relations between the integrals.

Translated title of the contribution	Axial and focal-plane diffraction catastrophe integrals
Original language	English
Pages (from-to)	1 - 13
Number of pages	13
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	43
DOIs	https://doi.org/10.1088/1751-8113/43/37/375206
Publication status	Published - Aug 2010

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@article{a37a0cf96a9a4b4c8fd56d833928b301,

title = "Axial and focal-plane diffraction catastrophe integrals",

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 X9 diffraction catastrophes. These representations reveal unexpected relations between the integrals.",

author = "MV Berry and CJ Howls",

year = "2010",

month = aug,

doi = "10.1088/1751-8113/43/37/375206",

language = "English",

volume = "43",

pages = "1 -- 13",

journal = "Journal of Physics A: Mathematical and Theoretical",

issn = "1751-8121",

publisher = "IOP Publishing",

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TY - JOUR

T1 - Axial and focal-plane diffraction catastrophe integrals

AU - Berry, MV

AU - Howls, CJ

PY - 2010/8

Y1 - 2010/8

N2 - 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 X9 diffraction catastrophes. These representations reveal unexpected relations between the integrals.

AB - 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 X9 diffraction catastrophes. These representations reveal unexpected relations between the integrals.

U2 - 10.1088/1751-8113/43/37/375206

DO - 10.1088/1751-8113/43/37/375206

M3 - Article (Academic Journal)

SN - 1751-8121

VL - 43

SP - 1

EP - 13

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

ER -

Axial and focal-plane diffraction catastrophe integrals

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