Design trade-offs for a reduced-size cross-dispersed echelle spectrograph with a Cassegrain collimator

Cross-dispersed echelle spectrographs (CDES) are a fundamental tool for modern astronomy. Their performance relies on the echelle pupil size and collimator focal length. Due to this, ground-based observatories, that are seeing limited, often necessitate larger instrument sizes to achieve high spectral resolutions. In contrast, space observatories, operating in a diffraction-limited regime, can utilize CDES with a smaller footprint to achieve HR performances. The most obvious solution for size reduction is to employ a three-mirror anastigmat (TMA) telescope in a double-pass configuration. This design minimizes instrument size without compromising optical performance, but with drawbacks in its alignment sensitivity. Alternatively, a monolithic parabolic mirror provides a simpler and sturdier option but results in increased non-usable space. Our work presents a first approach design of a CDES using a Cassegrain telescope as the spectrograph collimator. This approach effectively increases the instrument layout efficiency in terms of used space while achieving high spectral capabilities.