Unstable-cavity sensitivity to spatially localized intracavity phase aberrations

The geometric theory of the aberration sensitivity of an unstable cavity to a spatially localized intracavity phase distortion is provided. Such a localized perturbation source could be caused by a small imperfection in some intracavity mirror (such as a deformable mirror) or by a turbulence zone in the flow field of a gas-laser gain medium. This geometric theory, first developed by Anan'ev [Sov. J. Quantum Electron. 1, 565 (1972)] for a uniformly extended intracavity aberration source completely filling the cavity, yields the cavity phase-weighting coefficients that determine the resultant phase-aberration structure outcoupled from the unstable resonator. The analysis presented here provides the dependence of these coefficients on the cavity magnification, the axial position (with respect to the feedback mirror), the transverse location (with respect to the unperturbed optic axis) of the aberration source, the transverse dimension of the source, and the aberration structure characterizing the source.