Fresnel region fields of circular aperture antennas

Abstract

A different approach to the Fresn el r egion fi eld approxim ation i in t roduced. Instead of using t he conventional t run cated power series expansion approx im ation, thc Ne wto n's iteration formula for square root is u sed. By usin g such an app roximation for circular a pertures with tape red illumination of the form (1-12)", the Fresnel r eg ion fields can finally be expressed in terms of a new class of function s Woe') ', u). The function wg is s hown to be r elated to th e Lomm el's funcLion s of two variables, and the fun ction Wo is then obtained from the fun ction TVO -l by a simple recurre nce r elationsh ip. Fi eld di st ribu t ions for n = O, 1, 2, 3, 4 and at di sta nces}~ D2/A, ~ D2,'A, Y:l D2jA, D2/A, 2D2/A, "" have been com puted and prese nted as sets of curves. General and qu antitative properti es of the fi elds are clearl y demonstrated by t hese curves. It i~ a lso shown that the fi eld of any other nonuni form illumination with circular symm etry can be ex pressed i n term s of t he fi elds of t he basic i ll umination of the form (1 -12) ".