Although the built differences between the two RGS units are small, the energy resolutions of the two instruments are slightly different due to their slightly different focusing as shown in Fig. 81.
The shape of the LSF core largely determines the ability of the
spectrometer to separate closely spaced emission lines. The various
components scale differently with wavelength, giving rise to a
composite line shape which cannot easily be characterised in terms of
a simple analytical function. The telescope blur contributes a
constant term to the spectrometer line width, while misalignments and
flatness errors of the gratings contribute a term which slowly
increases with increasing wavelength. The broadening due to pointing
instability, which affects the resolving power through variations of
the angle of incidence on the gratings has proved to be negligible.
The scattering component is most significant at the shortest
wavelengths and the highest diffraction orders. This is illustrated in
Fig. 81 where the predicted resolution (the
FWHM of the LSF) for the two RGSs is shown in the second and fourth
panels. The steep rise below 7 Å is due to the scattering
component of the gratings. Also shown are the measurements, which are
deduced from narrow, bright emission lines in HR 1099 (Ly 
lines of Ne, O, N and C). Fig. 81 demonstrates
that the instrument resolving power is close to expectations.
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The ability to detect weak emission lines above the background or the
continuum is better measured by the half energy width (HEW) of the
profile. This width, especially at short wavelengths, is more
dependent on the amplitude and width of the scattering wings. Again,
the data agree with the predictions and, in the HEW sense, the
resolving power goes to 
800 at the longest wavelengths. The
first and third panels of Fig. 81 display the
HEW as a function of wavelength, for both RGS units separately.