Date of Award


Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy in Electrical Engineering (PhD)

Administrative Home Department

Department of Electrical and Computer Engineering

Advisor 1

Jeremy P. Bos

Committee Member 1

Michael Roggemann

Committee Member 2

Timothy Schulz

Committee Member 3

Raymond Shaw


Distributed-volume atmospheric turbulence near the ground significantly limits the performance of incoherent imaging and coherent beam projection systems operating over long horizontal paths. Defense, military and civilian surveillance, border security, and target identification systems are interested in terrestrial imaging and beam projection over very long horizontal paths, but atmospheric turbulence can blur the imagery and aberrate the laser beam such that they are beyond usefulness. While many post-processing and adaptive optics techniques have been developed to mitigate the effects of turbulence, many of these techniques do not work as expected in stronger volumetric turbulence, or in many cases don't work at all. For these techniques to be effective or next generation techniques to be developed, a better theoretical understanding of deep turbulence is necessary. In an attempt to improve understanding of deep turbulence, this work explores the saturation behavior of two features of deep turbulence; the anisoplanatic error and the branch-point density. In this work, the behavior of the anisoplanatic error over long horizontal and slant paths, where the angular extent of the scene is many times greater than the isoplanatic angle, is characterized by developing generalized expressions for the total, piston-removed, and piston-and-tilt-removed anisoplanatic error in non-Kolmogorov turbulence with a finite outer scale. As an outcome of this work it can be concluded that in many cases the anisoplanatic error saturates to a value less than 1 rad$^2$. This means that while not actually infinite, the piston-removed and piston-and-tilt-removed isoplanatic angle is often significantly larger than expected. Additionally, power law exponent, outer scale size, scene geometry, and source model play a large part in determining the effective isoplanatic angle. The limit imposed on the system by the anisoplanatic error is much less severe than predicted by classical isoplanatic angle expression, but only if we include the interplay of piston and/or global tilt removal, a finite outer scale, accurate image formation models, and realistic turbulence profiles. Additionally, in this work wave-optics simulations are used to model the branch-point density as a function of turbulence strength, sampling grid resolution, and inner scale. Another outcome of this work is that increasing grid resolution and turbulence strength cause the branch-point density to grow without bound, when no inner scale is used. When a non-zero inner scale is used, via a Hill spectrum, the growth of the branch-point density is significantly reduced as a function of increasing Rytov variance and saturates as a function of increasing inner scale.