Simple analytic approximations to the integral of Bessel's J0: application to the transmittance of a circular aperture

Celso Luis Ladera; P. Martin

doi:10.1117/12.437173

14 August 2001 Simple analytic approximations to the integral of Bessel's J₀: application to the transmittance of a circular aperture

Celso Luis Ladera, P. Martin

Author Affiliations +

Proceedings Volume 4419, 4th Iberoamerican Meeting on Optics and 7th Latin American Meeting on Optics, Lasers, and Their Applications; (2001) https://doi.org/10.1117/12.437173
Event: IV Iberoamerican Meeting of Optics and the VII Latin American Meeting of Optics, Lasers and Their Applications, 2001, Tandil, Argentina

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.

Citation Download Citation

Celso Luis Ladera and P. Martin "Simple analytic approximations to the integral of Bessel's J₀: application to the transmittance of a circular aperture", Proc. SPIE 4419, 4th Iberoamerican Meeting on Optics and 7th Latin American Meeting on Optics, Lasers, and Their Applications, (14 August 2001); https://doi.org/10.1117/12.437173

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