Optimal Techniques in Spectroscopy: The Extraction of Multiple Spectra from Single and Multiple Exposures using Moments and B-Splines (Kelson 2005)

Spectrograms are distorted in both the spatial and dispersion directions. As a result the data are not generally sampled on a uniform rectilinear grid of physically useful coordinates. Observers have often been required to resample their data onto rectilinear coordinate systems in order to continue with standard methods of analysis. The rebinning process involves replacing the data with an interpolating function, followed by sampling of that function at desired regular intervals of physically useful coordinates. These interpolating functions usually do not make full use of the information available in the data, and tend to degrade the resolution of spectra. With modern computing resources and knowledge of the distortions, one can construct interpolating functions that optimally reproduce the data. The information content of the data is preserved, without, for example, degradation of the resolution in the spectra. This working document discusses how to construct such interpolating functions for use in rebinning and extracting spectra. While the discussion is focused on the specific application for echellograms obtained with the MIKE spectrograph at Magellan, the method has been successfully applied to data obtained with other instruments, including MaGE, FIRE, LDSS3, IMACS, DEIMOS, FORS, and FORS2.