Modeling echelle spectrographs

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Abstract
A generic description of spectrographs based on rst optical principles is developed. It incorporates o- plane grating equations and rotations in three dimensions in order to adequately account for line tilt and order curva- ture. This formalism is validated by confronting the mod- els for two actual spectrographs (UVES and CASPEC) with ray tracing results and arc lamp exposures. The ver- satility of these models for the control of instrument con- gurations, for the generation of calibration databases, and for the preparation of observations is shown. As an im- portant application, we derive from this formulation var- ious 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.

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