Fiber-fed spectrograph 2026-10-05
A fiber-fed spectrograph places optical fibers on selected targets and reformats their output into a common entrance slit. Dedicated sky fibers sample sky brightness. Fiber coupling, transmission, and output beam spreading affect throughput and resolution.
Infrared photometric band 2026-10-05
The traditional near- and thermal-infrared photometric bands in the 1–5 micrometre region are , with approximate centers micrometres. Variants such as , and have different detailed responses. They largely follow atmospheric windows; transmission, sky brightness, and detector response determine practical band edges. The ISAAC filter documentation records instrument-specific variants, including an filter closer to near 3.8 micrometres.
Past exam of the mathematics course of the University of Cambridge 2019 iii Paper 338 1 c ii Solution Created 2026-10-03 Updated 2026-10-05
The traditional infrared photometric bands extending the optical photometric system into this range are approximatelyTheir photometric passbands lie mainly in atmospheric windows between strong molecular absorption bands. This makes ground-based observations practical. The exact centers depend on the system: is near , and shortened and bands reduce unwanted background or absorption. At the longest wavelengths, atmospheric and instrumental thermal radiation make sky brightness especially important. A modern band near is an additional choice, rather than one of the traditional extensions.
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 3 d ii Solution Created 2026-10-03 Updated 2026-10-05
A multi-slit spectrograph uses a focal-plane mask containing slitlets at the target positions, or movable slitlets placed there. Each transmits its target and nearby sky into the collimator; a diffraction grating or other disperser produces a separate optical spectrum on the detector. The layout must avoid overlap between spectra, and the length of a slit allows local sampling of sky brightness and sometimes spatial information within the target.
A fiber-fed spectrograph places optical fibers at target positions in the telescope focal plane. The fibers carry the selected light to a spectrograph and their outputs are lined up as a pseudo-slit. The spectrograph can be mechanically stable and separate from the telescope's focal plane. Additional fibers aimed at blank sky provide a simultaneous estimate of sky brightness; fiber positioning, coupling losses, transmission, and focal-ratio degradation must be accounted for.