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