Invited Paper Optimal Simulation of Volume Turbulence with Phase Screens Richard G. Paxman1 , Brian J. Thelen, and Jason J. Miller ERIM International, P.O. Box 134008, Ann Arbor, Michigan 48113-4008 ABSTRACT Imaging through volume turbulence gives rise to anisoplanatism (space-variant blur). The effects of volume turbulence on imaging are often modeled through the use of a sequence of phase screens distributed along the optical path. Wallner [1] recently derived a prescription for the optimal functional form and location of multiple phase screens for use in simulating the effects of volume turbulence in infinite-range imaging geometries. We generalize Waliner's method to accommodate the finite range case and to have a more optimal functional form for the phase screens. These methods can also be used for designing a multi- conjugate AO system. Examples of optimal solutions are given for horizontal-path finite-range imaging cases. Keywords: turbulence, phase screen, multi-conjugate, phase aberration, adaptive optics. 1. Introduction We are investigating the problem of imaging through volume turbulence, which gives rise to aniso- planatism (space-variant blur). To date, our experience with volume-turbulence imaging has been with upward-looking geometries for which objects can be taken to reside at infinity [2]. Under a weak-scattering, geometric-optics model, rays emanating from an unresolved source at infinity will be parallel when they arrive at the pupil. Accordingly, the aberrated wavefront is found from a parallel projection of the index of refraction variation associated with the intervening atmosphere. This imaging geometry is routinely simu- lated using a finite number of phase screens. Waliner [1] has recently derived a prescription for the optimal functional form and location of multiple phase screens for use in simulating infinite-range geometries. The method can also be used to design a multi-conjugate adaptive-optics (AO) system in such geometries. There are many problems of interest that require horizontal or slant-range imaging geometries. Typ- ically, the space-variant blur associated with such geometries is significantly more challenging than for upward-looking geometries. These cases involve objects that are located at finite ranges. With finite-range geometries, rays emanating from a single point in the object are not parallel when they arrive at the pupil. It follows that the aberrated wavefront is found with a cone-beam projection of the index of refraction variation. A sequence of phase screens can also be effectively used to simulate the effects of volume turbu- lence in finite-range geometries. In this paper we generalize Waliner's result to accommodate finite-range geometries and provide a prescription for optimally simulating the effects of volume turbulence with phase screens. As before, the method can also be used to design a multi-conjugate AO system for problems involving such geometries. We are motivated by recent and promising results suggesting the use of phase- diverse speckle (PDS) to overcome space-variant blur encountered in finite-range imaging geometries [3, 4]. 'email: paxman©erim-int.com, phone: (313) 994-1200 ext. 2710 2 Part of the SPIE Conference on Propagation and Imaging through the Atmosphere III. Denver, Colorado • July 1999 SPIE Vol. 3763 • 0277-786X/99/$1 0.00