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Adaptive-optics sky coverage is the fraction of targets for which a sufficiently bright nearby guide star allows useful correction. Anisoplanatism limits the offset, and photon statistics limit the sensing speed. A laser guide star improves coverage but does not remove all low-order and finite-distance limitations.

Atmospheric refractive-index fluctuations distort the incoming wavefront. In a Kolmogorov model, the long-exposure seeing width is approximately $0.98\lambda /r_0$, where the Fried parameter scales as $r_0\propto {\lambda }^{6/5}$. High-quality sites and longer wavelengths can improve the observing conditions, but do not eliminate the distorted phase. Short coherence times also require rapid correction or exposure.

Adaptive optics uses a guide source, wavefront sensor, deformable mirror and fast feedback loop. Tip-tilt correction removes image wander; higher-order actuators correct finer spatial distortions. Finite actuator spacing, sensor noise, delay and changing turbulence leave residual errors. A nearby natural guide star limits sky coverage, while a laser beacon supplies higher-order reference information over more directions. Conventional laser-guide-star systems still need independent image-motion information, commonly from a natural star.^[ref] Anisoplanatism limits the corrected field; laser finite-altitude sampling and variable PSFs need their own calibration.

Lucky imaging selects favorable short exposures and aligns them, trading exposure efficiency and photon statistics for reduced blur. Speckle interferometry uses short-exposure spatial-frequency information and suitable phase/statistical reconstruction instead of simply averaging away the speckles. Both need adequate time resolution, detector performance and calibration; selection cannot restore information never recorded. Interferometric methods can also recover fine structure with phase control or closure information. These approaches correct or infer wavefront effects; they do not make clouds, absorption or every atmospheric amplitude fluctuation disappear.^[ref]

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.

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.

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.^[ref]

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.

Atmospheric extinction changes the amplitude of the incoming light through absorption and scattering. Its wavelength dependence alters the measured optical spectrum and colors; clouds and aerosols introduce additional time dependence. Scattered moonlight and atmospheric emission increase sky brightness.

Atmospheric refraction changes the apparent position of the source. Its wavelength dependence, atmospheric dispersion, spreads a broadband image toward the zenith. The mean refractive index gradient therefore affects direction even in the absence of small-scale turbulence.

Atmospheric turbulence produces rapidly varying optical path lengths, distorting the phase and curvature of a nominally plane wavefront. Different pupil regions acquire different phase delays, producing astronomical seeing, image motion, and short-exposure speckle patterns. Different lines of sight sample different fluctuations, giving anisoplanatism.

Propagation through the fluctuating medium also changes the intensity through atmospheric scintillation, the familiar twinkling of stars. A phase-only adaptive optics correction can reduce atmospheric phase errors but does not remove absorption, all scintillation, or the atmospheric emission background.

Adaptive-optics sky coverage is limited by the need for a guide star bright enough to measure the wavefront error on the atmospheric evolution time. A faint guide gives noisy measurements; a guide too far from the target samples a different turbulent column. That angular mismatch is anisoplanatism, with useful separation characterized by the isoplanatic angle. Thus a conventional single-guide system cannot provide equally good correction at every target position.

A laser guide star supplies an artificial bright reference and improves coverage. However, its finite-distance beam does not sample the full stellar turbulence column, and conventional laser systems need a natural reference for absolute image motion. The required reference brightness, angular separation, and desired correction quality therefore still constrain observations.