Date of Award


Document Type


Degree Name

Master of Science


Department of Electrical and Computer Engineering

First Advisor

Byron M. Welsh, PhD


Atmospheric turbulence parameters, such as Fried's coherence diameter, the outer scale of turbulence, and the turbulence power law, are related to the wavefront slope structure function (SSF). The SSF is defined as the second moment of the wavefront slope difference as a function of both time and position. Knowledge of the SSF allows turbulence parameters to be estimated. Hartmann wavefront sensor (H-WFS) slope measurements composed of both signal and noise, allow the SSF to be estimated by computing a mean square difference of H-WFS slope measurements. The quality of the SSF estimate is quantified by the signal-to-noise ratio (SNR) of the estimator. This thesis develops a theoretical SNR expression for the SSF estimator. This SNR is a function of H-WFS geometry, the number of temporal frames included in the estimate, the outer scale, power law, and temporal properties of the turbulence. Spatial slope correlations are incorporated. Temporal slope correlations are incorporated using Taylor's frozen flow hypothesis. Results are presented for various H-WFS configurations and atmospheric turbulence properties.

AFIT Designator


DTIC Accession Number