Kernel-phase detection limits

Abstract

Context. The James Webb Space Telescope (JWST) will offer high angular resolution observing capability in the near-infrared with masking interferometry on the Near-Infrared Imager and Slitless Spectrograph (NIRISS), and coronagraphic imaging on the Near-Infrared Camera (NIRCam) and the Mid-Infrared Instrument (MIRI). Full-aperture kernel-phase-based interferometry complements these observing modes by allowing us to probe for companions at small angular resolution while preserving the telescope throughput. Aims. Our goal is to derive both theoretical and operational contrast-detection limits for the kernel-phase analysis of JWST NIRISS full-pupil observations using tools from hypothesis testing theory. The study is immediately applied to observations of faint brown dwarfs with this instrument, but the tools and methods introduced here are applicable in a wide variety of contexts. Methods. We construct a statistically independent set of observable quantities from a collection of aberration-robust kernel phases. Three detection tests based on these observable quantities are designed and analysed, all having the property of guaranteeing a constant false-alarm rate for phase aberrations smaller than about one radian. One of these tests, the likelihood ratio or Neyman-Pearson test, provides a theoretical performance bound for any detection test. Results. The operational detection method considered here is shown to exhibit only marginal power loss with respect to the theoretical bound. In principle, for the test set to a false-alarm probability of 1%, companions at contrasts reaching 103 and separations of 200 mas around objects of magnitude 14.1 are detectable with a probability of 68%. For the brightest objects observable using the full pupil of JWST and NIRISS, contrasts of up to 104 at separations of 200 mas could ultimately be achieved, barring significant wavefront drift. We also provide a statistical analysis of the uncertainties affecting the contrasts and separations that are estimated for the detected companions. Conclusions. The proposed detection method is close to the ultimate bound and offers guarantees on the probability of making a false detection for binaries, as well as on the error bars for the estimated parameters of the binaries that will be detected by JWST NIRISS. This method is not only applicable to JWST NIRISS but to any imaging system with adequate sampling.