Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Electrical and Computer Engineering

First Advisor

Meir Pachter, PhD


The use of adaptive optics entails the design of a controller. This requires the development of a model of the plant to be controlled, which, in this case, Consists of the atmosphere through which light is traveling. In optics, Zemike polynornials are used as a basis set for the expansion of wavefront phase distortions. Due to the turbulence induced stochastic nature of the underlying process involved, the spatial-temporal correlation functions of the Zemike polynomial phase expansion coefficients must be evaluated if a proper stochastic model of the plant is to be developed and adaptive optics is to be employed. In this work, these correlation functions are developed using a layered atmospheile model which takes into account wind effects and analphabetism. Calculations are provided for the first flew low-order Zemike modes. Using these correlation functions, an underlying linear, stochastic, dynamical system, which represents the atmosphere and is adequate for control synthesis, is identified. Within an acceptable error bound, the correlation functions of this system are representative of the calculated functions. The deformable mirror is also toodeled, output equations are specified, and the complete system is constructed. This system, in tum, provides the basis for the employment of advanced control and estimation concepts. The control objective is to apply the estimated conjugate phase to the deformable mirror so that, at the target, the outbound wavefront distortion is minimized and the Strehl ratio is maximized.

AFIT Designator


DTIC Accession Number



The author's Vita page is omitted.

Included in

Optics Commons