Spectro-Perfectionism: An Algorithmic Framework for Photon Noise-Limited Extraction of Optical Fiber Spectroscopy

We describe a new algorithm for the “perfect” extraction of one-dimensional (1D) spectra from two-dimensional (2D) digital images of optical fiber spectrographs, based on accurate 2D forward modeling of the raw pixel data. The algorithm is correct for arbitrarily complicated 2D point-spread functions (PSFs), as compared to the traditional optimal extraction algorithm, which is only correct for a limited class of separable PSFs. The algorithm results in statistically independent extracted samples in the 1D spectrum, and preserves the full native resolution of the 2D spectrograph without degradation. Both the statistical errors and the 1D resolution of the extracted spectrum are accurately determined, allowing a correct χ² comparison of any model spectrum with the data. Using a model PSF similar to that found in the red channel of the Sloan Digital Sky Survey spectrograph, we compare the performance of our algorithm to that of cross-section based optimal extraction, and also demonstrate that our method allows coaddition and foreground estimation to be carried out as an integral part of the extraction step. This work demonstrates the feasibility of current and next-generation multifiber spectrographs for faint-galaxy surveys even in the presence of strong night-sky foregrounds. We describe the handling of subtleties arising from fiber-to-fiber cross talk, discuss some of the likely challenges in deploying our method to the analysis of a full-scale survey, and note that our algorithm could be generalized into an optimal method for the rectification and combination of astronomical imaging data.