We have developed in this article the generic optical model of two-dimensional cross-dispersed spectrographs starting from first principles. On this bases a model was formulated for the VLT instrument UVES, and its predictions have been compared with a ray tracing analysis. In this way it could be verified that local predictions of the model are in full agreement with Code V, and that the accuracy of the global geometry is only limited by the fact that we did not attempt to include the effect of aberrations and distortions. Similarly a model for the ESO La Silla instrument CASPEC was confronted with real observations in order to demonstrate the applicability of such models in two important areas, namely wavelength calibration and instrument configuration control. It has also been shown how to derive simplified, but still accurate formulations for practical use. Finally, the advantages of placing such models into operational scenarios for observatories have been discussed.
It is a pleasure to thank H. Dekker,
S. D'Odorico, J.L. Lizon, and S. Randich for helpful hints and fruitful discussions. We are particularly grateful to B. Delabre for providing us with the Code-V analysis and engineering data.