Resolving Power

The resolution of a spectrum at wavelength \(\lambda\) is \[R = R_{\lambda} = \frac{\lambda}{\Delta\lambda}\] We take \(R_{\lambda}\) because the resolution may change with the wavelength under consideration. \(\Delta\lambda\) is the smallest difference in wavelength at which two spectral lines can still be perceived separately. This is the same problem as with the perception of binary stars. There are therefore different definitions for \(\Delta\lambda\). We use the FWHM definition here and are aware that this is a fairly rough criterion. But it is in common use.

A long-slit spectrograph does not image a single spectral line as a uniformly bright stripe with a rectangular brightness curve, but rather as a curve with more or less broadly sloping edges. The width of this brightness function at half height is FWHM, full width at half maximum. Since the brightness curve is approximately Gaussian, the software used for wavelength calibration usually fits a Gaussian function to the spectral line.