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In free-space optical communication, the intensity of a laser beam is modulated by a message, the beam propagates through free-space or atmosphere, and eventually strikes the receiver. At the receiver, an optical sensor converts the optical energy into an electrical signal, which is processed to reconstruct the original message. The promising features of this communication scheme such as high-bandwidth, power efficiency, and security, render it a viable means for high data rate point-to-point communication.

In this dissertation, we adopt a stochastic approach to address two major issues associated with free-space optics: digital communication over an atmospheric channel and maintaining optical alignment between the transmitter and the receiver, in spite of their relative motion. Associated with these issues, we consider several detection, estimation, and optimal control problems with point process observations. Although these problems are motivated by applications in free-space optics, they are also of direct relevance to the general field of estimation theory and stochastic control.

We study the detection aspect of digital communication over an atmospheric channel. This problem is formulated as an M-ary hypothesis testing problem involving a doubly stochastic marked and filtered Poisson process in white Gaussian noise. The formal solutions we obtain for this problem are hard to express in an explicit form, thus we approximate them by appropriate closed form expressions. These approximations can be implemented using finite-dimensional, nonlinear, causal filters.

Regarding the optical alignment issue, we consider two problems: active pointing and cooperative optical beam tracking. In the active pointing scheme that we develop for short range applications, the receiving station estimates the center of its incident optical beam based on the output of a position-sensitive photodetector. The transmitter receives this estimate via an independent communication link and incorporates it to accurately aim at the receiving station.

A cooperative optical beam tracking system consists of two stations in such a manner that each station points its optical beam toward the other one. The stations employ the arrival direction of the incident optical beams as a guide to precisely point their own beam toward the other station. We develop a detailed stochastic model for this system and employ it to determine a control law which maximizes the flow of optical energy between the stations. In so doing, we consider the effect of light propagation delay, which requires a point-ahead mechanism to compensate for the displacement of the receiving station during propagation time.