Sound beam through a circular aperture and the far-field nonparaxial   regime
  Propagation of sound beam diffracted from a circular aperture in far-field region has been studied in this paper by the method of angular spectrum representation and stationary phase method. This nonparaxial theory is useful when beam angle is not very small and the wavelength $\lambda $ is comparable to aperture diameter $a$ unlike the situation in paraxial approximation. Here we have studied two cases, one for a Gaussian source and other for a plane piston source. 
Manas Kumar Roy