B.S.T.J. Briefs: On The Computation of the Far Field of Open CassegrainAntennas

The far field radiation patterns of open cassegrain antennas have been previously computed by a double integration 1 . Recently one integration has been eliminated by using a modified stationary phase approximation". The rather remarkable accuracy thus obtained motivated an investigation to estimate the error in this approximation. In this note we present an alternate formulation for the computation of the far field and provide an additional estimate for the error in the modified stationary phase approximation. It is also shown that for certain illuminations, there exists a closed form solution to the azimuthal integration. For illuminations derived from a linear combination of TE°,, and TM?,, waveguide modes, the integrals can be expressed in terms of convergent series of Bessel functions. Based 011 the aperture field method, the far field electric Ef of an open cassegrain antenna is related to the reflected field at the aperture, E r , by the following double integral 1 / ? / = . e x p f s x e , * ) · exp [jk sin 6a(xv c °s
(1)