ATOCA: an algorithm to treat order contamination. Application to the NIRISS SOSS mode

After a successful launch, the James Webb Space Telescope is preparing to undertake one of its principal missions, the characterization of the atmospheres of exoplanets. The Single Object Slitless Spectroscopy (SOSS) mode of the Near Infrared Imager and Slitless Spectrograph (NIRISS) is the only observing mode that has been specifically designed for this objective. It features a wide simultaneous spectral range (0.6--2.8\,\micron) through two spectral diffraction orders. However, due to mechanical constraints, these two orders overlap slightly over a short range, potentially introducing a ``contamination'' signal in the extracted spectrum. We show that for a typical box extraction, this contaminating signal amounts to 1\% or less over the 1.6--2.8\,\micron\ range (order 1), and up to 1\% over the 0.85--0.95\,\micron\ range (order 2). For observations of exoplanet atmospheres (transits, eclipses or phase curves) where only temporal variations in flux matter, the contamination signal typically biases the results by order of 1\% of the planetary atmosphere spectral features strength. To address this problem, we developed the Algorithm to Treat Order ContAmination (ATOCA). By constructing a linear model of each pixel on the detector, treating the underlying incident spectrum as a free variable, ATOCA is able to perform a simultaneous extraction of both orders. We show that, given appropriate estimates of the spatial trace profiles, the throughputs, the wavelength solutions, as well as the spectral resolution kernels for each order, it is possible to obtain an extracted spectrum accurate to within 10\,ppm over the full spectral range.