Correcting second-order contamination in low-resolution spectra

The availability of large format CCDs with high quantum efficiency over a wide wavelength range, makes possible most modern low-resolution spectrographs to have the capability to obtain spectra that cover the whole optical range (3200–10000 Å) in a single exposure. However, it follows from the theory of diffraction gratings (see, e.g., Schroeder 2000) that different diffraction orders overlap, i.e. a photon with wavelength λ in the m-th order will be diffracted at the same direction as a photon with wavelength λ from the m+1-st order and thus both will be recorded at the same pixel on the detector. For diffraction gratings the relation between λ and λ is simple, λ = (m + 1)λ/m (but see Gutierrez-Moreno et al. (1994) for a case where this does not hold true due the a specific spectrograph design). Many spectrographs employ grisms instead of gratings, in which case the wavelength overlap relation is not that simple and is generally a non-linear function: λ = f (m+1→m)(λm+1). (1)