Numerical simulation of long-path spherical wave propagation in three-dimensional random media

A new method to overcome some limitations in the simulation of the propagat ion of waves originating from a point source through a very long path in a turbulent medium is presented. Existing propagation simulation algorithms s uffer from either windowing or lack of resolution when applied to long path s. If Cartesian coordinates are used, the limited size of the numerical mes h eventually leads to windowing errors. Casting the classical split-step Fo urier algorithm in a spherically diverging coordinate system allows one to get around this problem. In this way an angular mesh matching the source an d the propagation algorithm to the problem geometry is used. But for long-p ath propagation, this spherical divergent mesh causes a loss of resolution that can become a serious problem in the evaluation of the field statistica l moments. The method discussed in this paper overcomes both the windowing effect associated with Cartesian coordinates and the loss of resolution acc ompanying spherical coordinates by using a spherical-coordinate algorithm a nd performing repeated interpolations of the numerically propagated field b efore the mesh grows too large to sample the field accurately. Each time an interpolation is done, the angular window is decreased to maintain the mat rix size. (C) 1999 Society of Photo-Optical instrumentation Engineers. [S00 91-3286(99)00309-8].