Design study for the KMOS spectrograph module

We present the results of a design study for the spectrograph module for KMOS - a cryogenic near-infrared multi-object spectrograph being developed as a second generation instrument for the VLT by a consortium of UK and German institutes. KMOS will consist of 24 deployable integral field units feeding three identical spectrograph units via image slicers. The spectrographs are designed to provide a resolving power greater than 3000, so as to provide adequate OH avoidance, whilst covering one of the J, H or K bands within a single exposure. We present the opto-mechanical layout of the spectrographs, together with an analysis of the impact of the image quality (and PSF uniformity) on the accuracy of sky background subtraction within each IFU's field of view.