observational frame are incorporated into sensitivity analysis. The nominal $X$ centroid position of the optical component is compared with the perturbed position from the spot diagram. The results of the sensitivity analysis for the perturbation of grating, prism, input optics, collimator, and feed-mirror are summarized in Table \[tab:perturbations\]. In the table, the maximum to the minimum pixel shift from the nominal positions for individual perturbation is listed.

The Echelle grating shows the maximum sensitivity in the dispersion direction. A $\pm$0.01 $^\circ$ perturbation of grating angle of incidence from the nominal position produces a shift up to $\approx 20 $ pixels across different echelle orders. In the current optomechanical design of the spectrograph, the grating position uncertainty is about 25 arc-sec ($\approx$ 0.01$^\circ$), thus making this analysis essential. The measured RMS scatter of $\pm 4.5$ pixels from the grating uncertainty shown in Figure \[fig:repeatability\] is well within the range predicted from the sensitivity analysis. From the spectrograph dispersion, 1 pixel shift in velocity units corresponds to $\sim1 \textrm{kms}^{-1}$. Figure \[fig:grating\_Yrv\] shows the motion of the spectra on the detector due to grating perturbation along the dispersion direction. The residual shift of the spectra after removing the mean motion (-20.95 pixels) corresponds 