Holistic spectroscopy: Complete reconstruction of a wide-field, multi-object spectroscopic image using a photonic comb

The primary goal of Galactic archaeology is to learn about the origin of the Milky Way from the detailed chemistry and kinematics of millions of stars. Wide-field multi-fibre spectrographs are increasingly used to obtain spectral information for huge samples of stars. Some surveys (e.g. GALAH) are attempting to measure up to 30 separate elements per star. Stellar abundance spectroscopy is a subtle art that requires a very high degree of spectral uniformity across each of the fibres. However wide-field spectrographs are notoriously non-uniform due to the fast output optics necessary to image many fibre outputs onto the detector. We show that precise spectroscopy is possible with such instruments across all fibres by employing a photonic comb -- a device that produces uniformly spaced spots of light on the CCD to precisely map complex aberrations. Aberrations are parametrized by a set of orthogonal moments with $\sim100$ independent parameters. We then reproduce the observed image by convolving high resolution spectral templates with measured aberrations as opposed to extracting the spectra from the observed image. Such a forward modeling approach also trivializes some spectroscopic reduction problems like fibre cross-talk, and reliably extracts spectra with a resolution $\sim2.3$ times above the nominal resolution of the instrument. Our rigorous treatment of optical aberrations also encourages a less conservative spectrograph design in the future.