Astronomical seeing

Astronomical seeing is the atmospheric blurring of a stellar image, conventionally expressed as the angular full width at half maximum of its long-exposure point spread function, usually in arcseconds. For a large aperture in the ideal Kolmogorov model, it is approximately $0.98\lambda /r_0$ radians, with Fried parameter $r_0$.

Calibrated Fourier statistics of short-exposure speckle patterns recover information suppressed by a long seeing-blurred exposure. A power spectrum constrains the modulus, while additional phase-sensitive statistics such as the bispectrum are needed for image reconstruction. The exposure must adequately freeze turbulence and the source must supply enough photons; noise and calibrator mismatch limit the reconstruction.

Many short frames freeze atmospheric image fluctuations. Selecting the sharpest frames, registering them and combining them can improve angular resolution. Selection discards photons and can create a read-noise penalty, so adequate reference-source photon counts are essential. It does not guarantee that every high-order wavefront error disappears.

The Fried parameter is the atmospheric coherence length for optical phase. In the standard inertial-range model, the phase structure function is $6.88(\rho /r_0{)}^{5/3}$. For unchanged atmospheric turbulence, $r_0\propto {\lambda }^{6/5}$. The NACO manual, section 3.1 describes this scaling and its role in adaptive correction.

Anisoplanatism is the loss of correlation between wavefront errors along different viewing directions. Correcting a guide star therefore leaves a larger residual for a sufficiently separated target.

The isoplanatic angle is the characteristic angular separation over which a single-direction atmospheric correction remains useful. It depends on the altitude distribution of atmospheric turbulence as well as on wavelength.