  Context: Instrumental profile (IP) is the basic property of a spectrograph.
Accurate IP characterisation is the prerequisite of accurate wavelength
solution. It also facilitates new spectral acquisition methods such as the
forward modeling and deconvolution. Aims: We investigate an IP modeling method
for the fibre-fed echelle spectrograph with the emission lines of the ThAr
lamp, and explore the method to evaluate the accuracy of IP characterisation.
Methods: The backbone-residual (BR) model is put forward and tested on the
fibre-fed High Resolution Spectrograph (HRS) at the Chinese Xinglong 2.16-m
Telescope, which is the sum of the backbone function and the residual function.
The backbone function is a bell-shaped function to describe the main component
and the spatial variation of IP. The residual function, which is expressed as
the cubic spline function, accounts for the difference between the bell-shaped
function and the actual IP. The method of evaluating the accuracy of IP
characterisation is based on the spectral reconstruction and Monte Carlo
simulation. Results: The IP of HRS is characterised with the BR model, and the
accuracy of the characterised IP reaches 0.006 of the peak value of the
backbone function. This result demonstrates that the accurate IP
characterisation has been achieved on HRS with the BR model, and the BR model
is an excellent choice for accurate IP characterisation of fibre-fed echelle
spectrographs.
