Problem of describing the wave field in the near zone

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 paraboloidal wave, which, in turn, is approximated by a plane wave in the Fraunhofer approximation. Based on this, the problem of describing a wave field generated by a system of many coherently emitting 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