Mapping the aberrations of a wide-field spectrograph using a photonic comb

We demonstrate a new approach to calibrating the spectral-spatial response of a wide-field spectrograph using a fibre etalon comb. Conventional wide-field instruments employed on front-line telescopes are mapped with a grid of diffraction-limited holes cut into a focal plane mask. The aberrated grid pattern in the image plane typically reveals n-symmetric (e.g. pincushion) distortion patterns over the field arising from the optical train. This approach is impractical in the presence of a dispersing element because the diffraction-limited spots in the focal plane are imaged as an array of overlapping spectra. Instead we propose a compact solution that builds on recent developments in fibre-based Fabry-Perot etalons. We introduce a novel approach to near-field illumination that exploits a 25cm commercial telescope and the propagation of skew rays in a multimode fibre. The mapping of the optical transfer function across the full field is represented accurately (<0.5% rms residual) by an orthonormal set of Chebyshev moments. Thus we are able to reconstruct the full 4Kx4K CCD image of the dispersed output from the optical fibres using this mapping, as we demonstrate. Our method removes one of the largest sources of systematic error in multi-object spectroscopy.