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

The backbone-residual model. Accurately characterising the instrumental profile of a fibre-fed echelle spectrograph