A spectrum is a sampling of intensity as a function of wavelength (or frequency). But one does not measure the wavelength of a feature in a spectrum directly. One measures the pixel value that feature is found at. In order to determine the wavelength of the measured feature, one must also obtain a spectrum of something that has features of known wavelength. This is typically done in one (or both) of two ways. One can take spectra of atomic emission-line lamps that are obtained with the same set-up and at the same pointing as one's target objects. One can also measure atmospheric (or "telluric") features of known wavelength that appear in the spectrum of the target object. There are two advantages to the second technique. First, it does not require any additional observations. Second, the optical path from the sky to the dectector is not the same as that from the emission-line lamps to the detector. This difference can introduce systematic wavelength distorsions to the calibration from the emission-line lamps. The disadvantage to telluric line calibration is that there are often too few bright telluric lines in a spectrum for a good wavelength solution. A common approach is to make an initial calibration from the emission-line lamps, and then use telluric lines to check for any (hopefully small) systematic zero-point shifts.
If one ignores the spatial information in a 2-D spectral image, and considers a spectrum as a vector of intensities as a function of pixel values, then a wavelength calibration needs to provide a zero-point, a linear dispersion, and a measure of the important non-linear terms relating pixel value to wavelength. The quoted dispersions for our spectrograph are 4.3 Angstroms per pixel at low dispersion and 1.07 Angstroms per pixel at high-dispersion. These are approximately correct in practice, but should not be trusted for any observation that requires accurate wavelength calibration. The non-linear terms that all real spectrographs are subject to are why one needs more than one or two bright lines for good wavelength calibration. Further, as the non-linear terms are strongly affected by system flexures, one must obtain wavelength calibration exposures at the same telescope pointing as one's target exposures.
A long-slit spectrograph with a CCD detector provides spectral images with one spatial and one spectral axis. This introduces the additional complication that the spectral and spatial axes are not necessarily the same as the x and y axes of the detector. Exposures of emission-line lamps provide data on the x-axis pixel values of lines of known wavelength as a function of y-axis pixel value, and thus provide a means to correct for this spatial distortion.
Calibration from Emission-Line Lamps Calibration from Telluric Lines
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