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This paper deals with approximations to Andrews’ semi-empirical expression for the relative electric amplitude along the magnetic diameter in the plane of a circular aperture. These approximations yield analytic solutions in the form of zeroth- and second-order cylindrical Bessel functions:
where ω = πD/λ, δ = 2πx/λ, D is diameter of aperture, x is the distance from the center of the aperture, and λ is the wavelength of the incident plane wave. Of special interest are the cases of integral D/λ in which e−jω becomes plus and minus one as D/λ is even and odd, respectively. For cases of D/λ = 20 and D/λ = 4, the approximation is good over half the aperture. The results give a physical picture of interference among three traveling waves, the incident plane wave and two waves from the edge that are essentially cylindrical in nature.A treatment of multiple reradiation based on the above physical picture led to the conclusion that it was not significant for apertures with diameters greater than one wavelength.
© 1964 Optical Society of America
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