Intracavity adaptive optic compensation of phase aberrations I: Analysis

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Abstract
The analytical treatment of linear intracavity phase aberrations and their compensation by an appropriately configured intracavity adaptive optic element is presented in this paper. The approximate geometrical treatment of the effects of intracavity phase aberrations is first treated, followed by a complete exact diffraction integral formulation of the adaptive compensation of linear phase-tilt and phase-curvature aberrations. This new analysis yields the exact intracavity phase compensation for phase tilt, curvature-of-field, and astigmatism-phase aberrations in positive branch, confocal unstable resonator cavities.