Pointing, acquisition, and tracking (PAT) systems have been widely applied in many applications, from short-range (e.g. human motion tracking) to long-haul (e.g. missile guidance) systems. This dissertation extends the PAT system into new territory: free space optical (FSO) communication system alignment, the most important missing ingredient for practical deployment.

Exploring embedded geometric invariances intrinsic to the rigidity of actuators and sensors is a key design feature. Once the configuration of the actuator and sensor is determined, the geometric invariance is fixed, which can therefore be calibrated in advance. This calibrated invariance further serves as a transformation for converting

the sensor measurement to actuator action.

The challenge of the FSO alignment problem lies in how to point to a 3D target by only using a 2D sensor. Two solutions are proposed: the first one exploits the invariance, known as the linear homography, embedded in the FSO applications which involve long link length between transceivers or have planar trajectories. The second one employs either an additional 2D or 1D sensor, which results in invariances known as the trifocal tensor and radial trifocal tensor, respectively. Since these invariances have been developed upon an assumption that the measurements from sensors are free from noise, including the uncertainty resulting from aberrations, a robust calibrate algorithm is required to retrieve the optimal invariance from noisy measurements.

The first solution is suffcient for most of the PAT systems used for FSO alignment since a long link length constraint is generally the case. Although PAT systems are normally categorized into coarse and fine subsystems to deal with different requirements, they are proven to be governed by a linear homography. Robust calibration algorithms have been developed during this work and further verified by simulations. Two prototype systems have been developed: one serves as a fine pointing subsystem, which consists of a beam steerer and an angular resolver; while the other serves as a coarse pointing subsystem, which consists of a rotary gimbal and a camera. The average pointing errors in both prototypes were less than 170 and 700 micro-rads, respectively.

PAT systems based on the second solution are capable of pointing to any target within the intersected field-of-view from both sensors because two sensors provide stereo vision to determine the depth of the target, the missing information that cannot be determined by a 2D sensor. They are only required when short-distance FSO communication links must be established. Two simulations were conducted to show the robustness of the calibration procedures and the pointing accuracy with respect to random noise.