On the Problem of Describing the Wave Field in the Near Zone

Abstract

Expressions for the phase of a spherical wave in the near, middle, and far zones of observation are obtained. It is proved that in the Fresnel approximation a spherical wave is approximated by a paraboloid wave, which in its turn is approximated by a plane wave in the Fraunhofer approximation. Based on this, the problem of the description of a wave field generated by a system of many coherently radiating point sources is considered. An expression is obtained for the intensity distribution in the interference problem for the near-field approximation. It is shown that the distribution of intensity maxima is determined by solving a cubic equation, which, in the Fresnel approximation, transforms into a linear equation expressing the classical result on a uniform distribution of intensity maxima.