  Optimal extraction is a key step in processing the raw images of spectra as
registered by two-dimensional detector arrays to a one-dimensional format.
Previously reported algorithms reconstruct models for a mean one-dimensional
spatial profile to assist a properly weighted extraction. We outline a simple
optimal extraction algorithm including error propagation, which is very
suitable for stabilised, fibre-fed spectrographs and does not model the spatial
profile shape. A high signal-to-noise, master-flat image serves as reference
image and is directly used as an extraction profile mask. Each extracted
spectral value is the scaling factor relative to the cross-section of the
unnormalised master-flat which contains all information about the spatial
profile as well as pixel-to-pixel variations, fringing, and blaze. The
extracted spectrum is measured relative to the flat spectrum. Using echelle
spectra of the HARPS spectrograph we demonstrate a competitive extraction
performance in terms of signal-to-noise and show that extracted spectra can be
used for high precision radial velocity measurement. Pre- or post-flat-fielding
of the data is not necessary, since all spectrograph inefficiencies inherent to
the extraction mask are automatically accounted for. Also the reconstruction of
the mean spatial profile by models is not needed, thereby reducing the number
of operations to extract spectra. Flat-relative optimal extraction is a simple,
efficient, and robust method that can be applied easily to stabilised,
fibre-fed spectrographs.
