IRE Transactions on Antennas and Propagation

Many useful applications exist for the efficient computation of Fresnel and near zone fields of large antennas. Even small antennas in beam waveguide systems must be evaluated in the Fresnel zone. Far zone fields computed from measured near zone measurements can be verified by both the measurement and the computation of the Fresnel zone fields. The authors start with the premise that the far field has been computed by a Jacobi-Bessel series. These results are used then to determine the higher order terms of a Barrar-Kay <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/R^{p}</tex> expansion of the fields. The leading term of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/R^{p}</tex> series is the far zone field. Classically, the higher order terms are found by repetitive differentiation, a laborious and often inaccurate procedure particularly since the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/R^{P}</tex> series is slowly convergent-as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D^{2}/R</tex> ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</tex> is the diameter of antenna source). The approach of the authors via the Jacobi-Bessel <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/R^{P}</tex> series determines the higher order terms by simple algebraic recursion. The only restriction on the method is that it be used within the range of validity of the Fresnel small angle (FSA) approximation. However, since the Fresnel approximation is a second order approximation in terms of ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D/R</tex> ), the range of validity is quite large. This is demonstrated in detail. The method is applicable to reflector as well as aperture field s...

A new look at Fresnel field computation using the Jacobi-Bessel series