Diffracted field by an arbitrary aperture

American Journal of Physics - Tập 67 Số 1 - Trang 87-92 - 1999
Alfredo Dubra1, José A. Ferrari1
1Instituto de Fı́sica, Facultad de Ingenierı́a, J. Herrera y Reissig 565, Montevideo, Uruguay

Tóm tắt

Diffraction patterns of apertures on screens uniformly illuminated are standard calculations in undergraduate optics and acoustics courses. These calculations imply two-dimensional (2-D) integrations which are often performed in the far zone, at moderate angles of diffraction, i.e., using Fresnel and Fraunhofer approximations. In this note, the 2-D integration is reduced to a 1-D parametric integration over the perimeter of the aperture—resembling the Rubinowicz’s representation of the Kirchhoff diffraction integral—which allows numerical evaluation with few computational resources. The proposed formula allows mathematically exact calculation of the near-field, in the context of scalar wave theory. Explicit calculations for circular and elliptical apertures are shown.

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Tài liệu tham khảo

1964, Comparison of the Kirchhoff and the Rayleigh-Sommerfeld theories of diffraction at an aperture, J. Opt. Soc. Am., 54, 587, 10.1364/JOSA.54.000587

1961, Closed solutions of Rayleigh’s integral for axial points, J. Opt. Soc., 51, 1050, 10.1364/JOSA.51.001050

1989, An experiment on the physical reality of edge diffracted waves, Am. J. Phys., 57, 370, 10.1119/1.16024

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American Journal of Physics

Tập 67 Số 1

87-92

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