Abstract

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:

E/E0=1(ejω/2)[J0(δ)J2(δ)],
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 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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