Anisoplanatism in adaptive optics (AO) systems is a performance-degrading effect that arises whenever light from the wave-front sensor beacon and light from the object of interest sample different volumes of optical turbulence. This effect occurs if there is either a spatial separation between the object and the beacon, or a spatial separation between the wave-front sensor and phase-compensation aperture, or if both types of separation are present in the AO system. In this dissertation, anisoplanatism is characterized by the correlation of Zernike coefficients of object and beacon turbulence-induced phase. It is shown through theoretical calculations validated with experimental data, that while most Zenike modes are uncorrelated in the absence of anisoplanatism, moderate amounts of anisoplanatism result in an enhanced cross-correlation of the phase coefficients. This fact, along with a theoretical description of the performance-degradation process motivates the application of optimal estimation theory to AO compensation. In imaging systems, optimal compensation reduces the effect of anisoplanatism, increasing beacon separation limits by up to three times, and enabling estimation of wave-front tilt from a laser beacon, which cannot be measured conventionally. For beam-projection systems such as Airborne Laser, optimal compensation can decrease the AO update rate by over 70%. In interferometric systems, a fringe visibility increase of 25% is realized by applying optimal compensation, resulting in enhanced image reconstruction at large baseline separations.
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