calibration source either before or after your science observation. At optical wavelengths, this is typically a thorium–argon (Th–Ar) hollow cathode lamp (see below). In the data reduction process, you identify emission lines with wavelengths that have been measured in the laboratory. A fit to the pixel versus wavelengths of these lines using a high-order polynomial provides the mapping between pixel and wavelength space. This function is then applied to the stellar spectrum.
The problem is that the stellar spectrum is taken at a different time to that of the calibration source. Mechanical shifts of the spectrograph and detector or temperature and pressure changes in the spectrograph room can occur between the time you take your calibration and that of the stellar observations. Table 3.1 shows that for an R = 100,000 spectrograph, a Doppler shift of 1 m s−1 will cause a physical shift at 10−5 cm at the detector, or about one-fifth of the wavelength of the incoming light. It does not take much of an instrumental shift of the spectrograph or detector to obliterate this signal. These instrumental shifts can dominate the measurement error due to simple photon statistics.
Let’s look into the instrumental shifts for modern spectrographs using measurements taken with the Tautenburg Coudé Echelle spectrograph (TCES). The TCES is an example of a modern, well-designed echelle spectrograph with good stability for standard spectroscopic work. The spectrograph has a resolving power of R
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