Optimal extraction of single-object spectra from observations with two-dimensional detectors

Spectrographs on large telescopes are frequently equipped with two-dimensional detectors, able to form independent spectra in a number of contiguous spatial columns along the slit. If the projected column width is sufficiently small that a typical seeing disk illuminates several adjacent columns, a signal-to-noise ratio enhancement for observations of a stellar object is obtained by using appropriate weights in the combination of these individual column spectra, instead of using simple coadding. The enhancement is most significant for faint objects. The calculation and use of such column weights is described, covering both photon-counting detectors and CCDs. The combination of spectra from separate successive runs also benefits from the use of weights, since the quality of some runs is often better than others. A scheme for calculation of run weights is given. To illustrate the use of column and run weights, a specific spectroscopic observation of a QSO is discussed. Methods for analysis of absorption-line spectra to give wavelength, equivalent width, broadening, and asymmetry of detected absorption lines are given.