It is a good idea to include an estimation of the spectral resolution of your observations when describing them in a paper. There are several different quantities related to spectral resolution:

- The dispersion of a spectrum is the number of resolution elements per wavelength unit (usually given in pixels per Ångstrom)
- The reciprocal dispersion is the number of wavelength units per resolution element (usually Ångstroms per pixel)
- The resolution is the smallest wavelength interval which can be fully resolved (usually given in Ångstroms)
- The resolving power of a spectrograph, R, is the resolution divided by the wavelength (lambda over delta lambda)

Most of these quantities vary slightly over a spectrum and depend on the precise design of the spectrograph. Older observations (mainly those using photographic plates) may use millimetres rather than pixels as their spatial unit.

I prefer to quote the reciprocal dispersion (Ångstroms per pixel) and the resolution (Ångstroms). These two quantities are related by the amount of instrumental broadening affecting your observations, which usually depends mainly on the size of the slit used when the observations were obtained.

The reciprocal dispersion is easily obtained from `molly` (read in your spectra and wavelength-bin them to get `molly` to report the average dispersion per pixel) or from the information about the spectrograph (if you trust it). The resolution should be measured from your observations.

Arc lamp and night sky emission lines are very sharp and can be assumed to have no intrinsic broadening. Therefore measuring their width in your extracted spectra gives a good idea of your resolution. This can be done using the `mgfit` command in `molly`, which fits combinations of Gaussians and polynomials by least squares.

Choose a stong line which is single (i.e. is not composed of two close and blended lines). `mgfit` is a powerful tool which requires an input file defining your fitting function:

poly: 6300. $const $grad gaussian: 6300.3 $rv $fwhm $height $const = 200.0 $grad = 0.0 $rv = 0.0 $fwhm = 2.0 $height = 1000.0

In this input file, there is a polynomial (with a pivot wavelength at 6300Å) to fit the continuum with two adjustable terms (the constant and the gradient). There is also a Gaussian function with a fixed reference wavelength of 6300Å and three adjustable terms: offset from the reference wavelength (expressed in km/s), FWHM (km/s) and height. Running `mgfit` causes the quantities `const`, `grad`, `rv`, `fwhm` and `height` to be adjusted to best fit your spectrum. Open `molly`, read in a sky spectrum and `mgfit` it:

molly load skyo.mol 1 1 1 mgfit 1 1 2 [inputfile] [outputfile] -3 3 n

The output from `mgfit` with the input file above should be something like this:

Fitted variable values along with their 1-sigma 1-param uncertainties are: Variable: const = 221.281885 +/- 0.554194484 Variable: grad = 0.06869064 +/- 0.001065056 Variable: rv = 14.6813215 +/- 0.648808218 Variable: fwhm = 2.14673494 +/- 0.027358821 Variable: height = 2268.01881 +/- 33.96894534

In this case the resolution is the FWHM of the Gaussian and is 2.15Å (remember that this assumes that the instrumental broadening profile can be well represented by a Gaussian). Set the plot limits, plot the spectral line in white and overplot the fit in green:

xyrange 6295 6305 0 0 pclose plot 1 1 dcolour 3 plot 2 2 dcolour 1 pclose