Analytic expressions and approximations for the on-axis, aberration-free Rayleigh and Debye integral in the case of focusing fields on a circular aperture

R.M. Aarts, J.J.M. Braat, P. Dirksen, S. Haver, van, C.M. Heesch, van, A.J.E.M. Janssen

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Uittreksel

We present a derivation of the analytic result for on-axis field values of the Rayleigh diffraction integral, a result that was originally presented in a paper by Osterberg and Smith (1961). The method on which our derivation is based is then applied to other diffraction integrals used in acoustics and optics, e.g., the far-field Rayleigh integral, the Debye integral and the separate near-field part of the Rayleigh integral. Having available our on-axis analytic or semi-analytic solutions for these various cases, we compare the various integrals for wave numbers k pertaining to low-frequency acoustic applications all the way up to high-frequency optical applications. Our analytic results are compared to numerical results presented in the literature.
Originele taal-2Engels
Pagina's (van-tot)08039-1/10
TijdschriftJournal of the European Mathematical Society
Volume3
DOI's
StatusGepubliceerd - 2008

Vingerafdruk

Aberrations
Aberration
Rayleigh
Diffraction
Acoustics
Approximation
Optics
Field of Values
Near-field
Far Field
Analytic Solution
Low Frequency
Numerical Results

Citeer dit

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title = "Analytic expressions and approximations for the on-axis, aberration-free Rayleigh and Debye integral in the case of focusing fields on a circular aperture",
abstract = "We present a derivation of the analytic result for on-axis field values of the Rayleigh diffraction integral, a result that was originally presented in a paper by Osterberg and Smith (1961). The method on which our derivation is based is then applied to other diffraction integrals used in acoustics and optics, e.g., the far-field Rayleigh integral, the Debye integral and the separate near-field part of the Rayleigh integral. Having available our on-axis analytic or semi-analytic solutions for these various cases, we compare the various integrals for wave numbers k pertaining to low-frequency acoustic applications all the way up to high-frequency optical applications. Our analytic results are compared to numerical results presented in the literature.",
author = "R.M. Aarts and J.J.M. Braat and P. Dirksen and {Haver, van}, S. and {Heesch, van}, C.M. and A.J.E.M. Janssen",
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Analytic expressions and approximations for the on-axis, aberration-free Rayleigh and Debye integral in the case of focusing fields on a circular aperture. / Aarts, R.M.; Braat, J.J.M.; Dirksen, P.; Haver, van, S.; Heesch, van, C.M.; Janssen, A.J.E.M.

In: Journal of the European Mathematical Society, Vol. 3, 2008, blz. 08039-1/10.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

TY - JOUR

T1 - Analytic expressions and approximations for the on-axis, aberration-free Rayleigh and Debye integral in the case of focusing fields on a circular aperture

AU - Aarts, R.M.

AU - Braat, J.J.M.

AU - Dirksen, P.

AU - Haver, van, S.

AU - Heesch, van, C.M.

AU - Janssen, A.J.E.M.

PY - 2008

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AB - We present a derivation of the analytic result for on-axis field values of the Rayleigh diffraction integral, a result that was originally presented in a paper by Osterberg and Smith (1961). The method on which our derivation is based is then applied to other diffraction integrals used in acoustics and optics, e.g., the far-field Rayleigh integral, the Debye integral and the separate near-field part of the Rayleigh integral. Having available our on-axis analytic or semi-analytic solutions for these various cases, we compare the various integrals for wave numbers k pertaining to low-frequency acoustic applications all the way up to high-frequency optical applications. Our analytic results are compared to numerical results presented in the literature.

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DO - 10.2971/jeos.2008.08039

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VL - 3

SP - 08039-1/10

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

SN - 1435-9855

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