Past exam of the frontiers of Observational Astrophysics course of the University of Cambridge / 2012 / Paper 1 / 3 / d / Solution

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]