The Mathematics of Double‐Fourier Interferometers

Recent studies, which are the impetus for this paper, have investigated the possibility of astronomical wide-field double-Fourier interferometry at submillimeter and midinfrared wavelengths. Double-Fourier interferometry combines Michelson interferometry and Fourier transform spectroscopy. At the present time, it is the only technique that promises simultaneous high spatial and spectral resolution. First, we derive the near-general output response for widefielddouble-FourierinterferometersusingtheJonesandMuellercalculi.Weemploya‘‘systems’’approach,expressing the instrument behavior in terms of matrix electric field and intensity impulse responses (point-spread functions) between the sky and the focal plane. This approach is helpful for integrated modeling, Monte Carlo simulations, and developinginstrumentrequirementsfromsciencegoals.Second,wefurnishthreewavenumber-dependentobservables— visibilities, squared visibility magnitudes, and dirty/processed images—plus their (co)variances in the photon-rich regime. Third, to obtain a basic understanding of the mathematics in this paper, the output responses for perfect, phaseaberrated,andpolarization-mismatchedopticsareproduced.Last,wepresentideasforfutureresearchinwide-field double-Fourier interferometers, such as SPIRIT and SPECS. Subject headingg methods: analytical — methods: data analysis — techniques: high angular resolution — techniques: image processing — techniques: interferometric — techniques: spectroscopic