= Solution
<Atmospheric turbulence> produces time-dependent refractive-index fluctuations and phase errors across the telescope pupil. A large aperture's long-exposure <point spread function> is broadened approximately to $0.98\lambda/r_0$, where $r_0$ is the <Fried parameter>, rather than the <diffraction> scale $\lambda/D$. For fixed turbulence, $r_0\propto\lambda^{6/5}$, so the <seeing> angle improves weakly as $\lambda^{-1/5}$. The <atmospheric coherence time> scales with $r_0$ divided by an effective wind speed. This temporal scale concerns changing turbulence, not the optical <bandwidth>'s coherence time.
\b[Reduce the disturbance.] A good high-altitude site, favourable weather, observing near the zenith, thermal control and dome ventilation reduce atmospheric and local <seeing>. They improve the uncorrected image but do not remove all high-order wavefront distortion. <Active optics> slowly maintains the main mirror's figure and alignment; it is distinct from the rapid adaptive correction of atmospheric phase errors.
\b[Correct the wavefront.] <Adaptive optics> uses a nearby natural <guide star> or artificial <laser guide star>, a <wavefront sensor>, a real-time controller and a <deformable mirror>. A Shack-Hartmann sensor estimates local wavefront slopes; mirror actuators apply the opposite optical-path distortion fast enough to track the atmosphere. A separate fast steering element or the mirror can correct image motion. In an ideal well-corrected direction this approaches <diffraction-limited resolution> and increases the concentration of light in the central image.
Finite guide-star <flux>, actuator sampling, control latency and <anisoplanatism> leave residual errors. A laser beacon samples a finite-height cone rather than the full distant-source cylinder, and a conventional laser reference does not determine absolute tip-tilt, so a natural reference remains useful. Multiple <guide stars> and multiple conjugate mirrors can widen the corrected field, with extra sensing and reconstruction complexity. These are fundamental geometry and control limits, not claims of a universal corrected sky fraction.<Adaptive Optics by European Southern Observatory>[Single Conjugate Adaptive Optics and Multi-Conjugate Adaptive Optics sections: bandwidth, fitting, anisoplanatism, laser-beacon tilt and cone limitations]{ref}
\b[Freeze and reconstruct.] Short exposures can freeze the instantaneous <speckle pattern>. <Speckle interferometry> uses calibrated Fourier statistics to recover diffraction-scale structure; power-spectrum information alone loses phase, while <bispectrum> or other phase-sensitive measurements support image reconstruction. <Lucky imaging> selects sharp short frames, registers them and combines them, trading <photon> efficiency for improved image quality. Tip-tilt alignment alone removes image motion rather than all high-order aberration. These methods require sufficiently bright sources or references and can incur substantial read-noise penalties. Deconvolving a long-exposure image is useful only where a known <point spread function> and adequate signal preserve information; it cannot recover arbitrarily lost <spatial frequencies>. Moving to space avoids atmospheric <seeing>, although it changes the observing platform and its limitations rather than correcting a ground-based telescope.
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