Adaptive-optics sky coverage 2026-10-05
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.
Past exam of the mathematics course of the University of Cambridge 2019 iii Paper 338 1 d Solution Created 2026-10-03 Updated 2026-10-05
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.
Past exam of the mathematics course of the University of Cambridge 2019 iii Paper 338 2 a iv Solution Created 2026-10-03 Updated 2026-10-05
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.