## Abstract

To implement adaptive optics compensation for propagation through deep turbulence, the concept of gradient descent tomography has been developed. Here two or more deformable mirrors are controlled by an efficient iterative algorithm that optimizes the integral ${I}^{2}$ image-sharpening metric. In this work a difficult case involving imaging over a $2\phantom{\rule{0.2em}{0ex}}\mathrm{km}$ path with a ${C}_{n}^{2}$ of $2\times {10}^{-13}\phantom{\rule{0.2em}{0ex}}{\mathrm{m}}^{-2\u22153}$ is considered. For a wavelength of $1.06\phantom{\rule{0.2em}{0ex}}\mathrm{\mu}\mathrm{m}$ and a 10-cm-diameter aperture, $\lambda \u2215D$ is seven times the isoplanatic angle $({\vartheta}_{0}=1.54\phantom{\rule{0.2em}{0ex}}\mathrm{\mu}\mathrm{rad})$, and the Rytov number is 5.5. For three points placed along a line spanning approximately 70 isoplanatic patch sizes all three points are compensated somewhat, illustrating that anisoplanatism is addressed. The fact that the corresponding performance improvement ratios are 1.20, 1.34, and 3.26 in the presence of such strong scintillation and anisoplanatism is quite significant.

© 2006 Optical Society of America

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