Modeling echelle spectrographs

A generic description of spectrographs based on first optical principles is developed. It incorporates off-plane grating equations and rotations in three dimensions in order to adequately account for line tilt and order curvature. This formalism is validated by confronting the models for two actual spectrographs (UVES and CASPEC) with ray tracing results and arc lamp exposures. The versatility of these models for the control of instrument configurations, for the generation of calibration databases, and for the preparation of observations is shown. As an important application, we derive from this formulation various forms of the echelle relation which can be used to implement automatic wavelength calibration procedures. Finally, we discuss possible applications of such analytical models of astronomical instruments for calibration, data analysis and observatory operations.