Compact high-resolution spectrographs for large and extremely large   telescopes: using the diffraction limit
  As telescopes get larger, the size of a seeing-limited spectrograph for a given resolving power becomes larger also, and for ELTs the size will be so great that high resolution instruments of simple design will be infeasible. Solutions include adaptive optics (but not providing full correction for short wavelengths) or image slicers (which give feasible but still large instruments). Here we develop the solution proposed by Bland-Hawthorn and Horton: the use of diffraction-limited spectrographs which are compact even for high resolving power. Their use is made possible by the photonic lantern, which splits a multi-mode optical fiber into a number of single-mode fibers. We describe preliminary designs for such spectrographs, at a resolving power of R ~ 50,000. While they are small and use relatively simple optics, the challenges are to accommodate the longest possible fiber slit (hence maximum number of single-mode fibers in one spectrograph) and to accept the beam from each fiber at a focal ratio considerably faster than for most spectrograph collimators, while maintaining diffraction-limited imaging quality. It is possible to obtain excellent performance despite these challenges. We also briefly consider the number of such spectrographs required, which can be reduced by full or partial adaptive optics correction, and/or moving towards longer wavelengths. 
J. Gordon Robertson and Joss Bland-Hawthorn
astro-ph.IM