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Proceedings Paper

Simple analytic approximations to the integral of Bessel's J0: application to the transmittance of a circular aperture
Author(s): Celso Luis Ladera; P. Martin
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Paper Abstract

Two accurate, simple approximations to the integral of Bessel's function J0 are presented. The second-order approximant is practically indistinguishable from the true integral when plotted together, even for very large values of the argument. Our approximants, are in addition analytic, and can replace with significant advantages both the well- known power series of the integral and its asymptotic formula. We derive approximants to the transmittance of a plane wave through a circular aperture. Our second order approximant to the transmittance is analytic, and can be evaluated, for all values of the argument, just with a hand- calculator. Its accuracy is better than 0.0011.

Paper Details

Date Published: 14 August 2001
PDF: 4 pages
Proc. SPIE 4419, 4th Iberoamerican Meeting on Optics and 7th Latin American Meeting on Optics, Lasers, and Their Applications, (14 August 2001); doi: 10.1117/12.437173
Show Author Affiliations
Celso Luis Ladera, Univ. Simon Bolivar (Venezuela)
P. Martin, Univ. Simon Bolivar (Venezuela)


Published in SPIE Proceedings Vol. 4419:
4th Iberoamerican Meeting on Optics and 7th Latin American Meeting on Optics, Lasers, and Their Applications

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