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 20cm aperture 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 4K x 4K CCD image of the dispersed output from the optical fibres using this mapping, as we demonstrate. Our method targets one of the largest sources of systematic error in multi-object spectroscopy, i.e. spectral distortion due to instrumental aberrations, and provides a comprehensive solution to their calibration and removal.