On the scalar diffraction by a circular aperture in an infinite plane screen

Summary

If Levine and Schwinger's variational formulation of the diffraction of a plane wave by an aperture in an infinite plane screen is applied to the case where the aperture is a circular hole, the problem of finding the aperture distribution can be reduced to the solution of an infinite system of linear equations. As pointed out by Bouwkamp the most appropriate expansion of the aperture distribution is of the form

$$\Phi _1 (\varrho ) = \sum\limits_{n = 0}^\infty {b_n P_{2n + 1} } [(1 - \varrho ^2 /a^2 )^{\frac{1}{2}} ],$$

wherea = radius of the aperture. In the present paper the system of equations inb _n is investigated.