Strategies for spectroscopy on Extremely Large Telescopes – I. Image slicing

One of the problems of producing spectrographs for Extremely Large Telescopes (ELTs) is that the beam size is required to scale with telescope aperture if all other parameters are held constant, leading to enormous size and implied cost. This is a particular problem for image sizes much larger than the diffraction limit, as is likely to be the case if Adaptive Optics systems are not initially able to deliver highly corrected images over the full field of the instrument or if signal/noise considerations require large spatial samples. In this case, there is a potential advantage in image slicing to reduce the effective slitwidth and hence the beam size. However, this implies larger detectors and oversizing of the optics which may cancel out the advantage. By the means of a toy model of a spectrograph whose dimensions are calibrated using existing instruments, the size and relative cost of spectrographs for ELTs have been estimated. Using a range of scaling laws derived from the reference instruments, it is possible to estimate the uncertainties in the predictions and to explore the consequences of different design strategies. The model predicts major cost savings (2-100×) by slicing with factors of 5-20 depending on the type of spectrograph. The predictions suggest that it is better to accommodate the multiplicity of slices within a single spectrograph rather than distribute them among smaller, cheaper replicas in a parallel architecture, but the replication option provides an attractive upgrade path to integral field spectroscopy (IFS) as the input image quality is improved. Another major issue is whether the camera speed should be adapted to minimize the cost of the detector, or conversely, the camera simplified by means of redundant oversampling which requires larger detector formats. This tradeoff is the main reason for the minimum in the size and cost predictions for moderate slicing.