Estimation and correction of the instrumental perturbations of Vainu Bappu Telescope Echelle spectrograph using a model-based approach

Abstract

The Echelle spectrograph operating at Vainu Bappu Telescope (VBT), India, is a general purpose instrument used for many high-resolution spectroscopic observations. A concerted effort is being made to expand the scientific capability of the instrument in emerging areas of observational astronomy. The present study is aimed at evaluating the feasibility of the spectrograph to carry out precision Radial Velocity (RV) measurements. In the current design, major factors limiting the RV precision of the spectrograph arise from the movable grating and slit; optical aberrations; positional uncertainty associated with optomechanical mounts and environmental and thermal instabilities in the spectrograph room. RV instabilities due to temperature and pressure variations in the environment are estimated to vary around 120 $ \textrm{ms}^{-1} $ and 400 $ \textrm{ms}^{-1} $ respectively. The positional uncertainty of the grating in the spectrograph could induce a spectral shift $\sim1.4\,\textrm{kms}^{-1} $ across the Echelle orders. A Zemax model is used to overcome the uncertainty in the zero-positioning and lack of repeatability of the moving components. We propose to obtain the ThAr lamp observations and using the Zemax model as the reference, predict the drifts in the positions of the optical components. The perturbations of the optical components from the nominal position are corrected at the beginning of the observational run. After a good match is obtained between the model and the observations, we propose to use a Zemax model to improve the wavelength calibration solution. We could match the observations and model within $\pm$~1 pixels accuracy after the model parameters were perturbed in a real-time setup of the spectrograph. In this paper, we present the estimation of the perturbations of optical components and the effect on the RV obtained.