Errors in the predicted gain of pyramidal horns

The concepts of the geometrical theory of diffraction are used to derive the on-axis gain of two-dimensional
E
plane sectoral horns. Geometrical optics and single (noninteraction) diffraction by the aperture edges yield essentially the Kirchhoff result-a monotonic gain versus wavelength curve. Reflection of diffracted fields from the horn interior and double diffraction at the aperture add an oscillation to this curve which is not significantly altered by further diffraction for moderate to large horns. Including these results approximately in Schelkunoff's equation for the pyramidal horn explains the gain variations observed in microwave gain standards and provides an error estimate in their predicted gain.