Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 338 / 3 / d / ii / Solution

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.