Abstract

It has been recognized for some time that compensation for thermal blooming by phase-conjugate adaptive optics is prone to instability. The theory of thermal-blooming phase-compensation instability is extended here to take into account the lattice geometry of real adaptive optics. A general equation for instability growth rates is derived, and approximate methods of solution are discussed. This growth-rate equation has been used elsewhere to explain observation of chain-link patterns in laboratory laser irradiance measurements. The general growth-rate equation depends on wave-front-sensor, deformable-mirror, and servo details through two structure functions, whose construction is illustrated for the specific system used in a recent laboratory experiment. It is shown that an approximate solution of the growth-rate equation leads to the following universality theorem: Instability growth rates are approximately independent of wave-front-sensor and deformable-mirror details as long as the servo coupling them is null seeking. It is also shown, through an approximate solution, that real parts of growth rates are generally reduced by wind, in contrast to the situation in which adaptive optics is modeled as a simple Fourier filter. Finally, a novel, analytically convenient, and realistic model of a deformable-mirror influence function is derived for use in illustrating the instability theory.

© 1992 Optical Society of America

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