Excerpt from Diffraction by an Aperture I

The diffraction of a wave by an aperture of any shape in a thin screen is treated by a new method. This method is called "the geometrical theory of diffraction", because it is an extension of geometrical optics which accounts for diffraction. In this method new rays - called diffracted rays - are introduced. They are produced when an incident ray hits the edge of the aperture, and they satisfy the "law of diffraction". A field is associated with each ray in a quantitative way, by means of the optical principles of phase variation and energy conservation. In addition "diffraction coefficients" are introduced to relate the field on a diffracted ray to that on the corresponding incident ray.

By this method a simple formula is field in the aperture or the far by any aperture. By means of this formula the field in the aperture or the far field diffraction pattern can be found. In addition the transmission cross section of the aperture can be determined. Explicit formulas and numerical results are given for slits and circular apertures. The accuracy of the results increases as the wavelength decreases, but they are even useful for wavelengths as large as the aperture dimensions.

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