The Mathematics of Double-Fourier Interferometers

• Published in: The Astrophysical journal Vol. 657; no. 2; pp. 1178 - 1200
• Main Authors: Elias II, Nicholas M, Harwit, Martin, Leisawitz, David, Rinehart, Stephen A
• Format: Journal Article
• Language: English
• Published: Chicago, IL IOP Publishing 10.03.2007; University of Chicago Press
• Subjects: Astronomy; Earth, ocean, space; Exact sciences and technology; Data analysis; methods: data analysis; Image processing; techniques: image processing; double-Fourier interferomsters, such as SPIRIT and SPECS. Subject headings: methods: analytical; techniques: spectroscopic; Analytical method; techniques: high angular resolution; techniques: interferometric
• ISSN: 0004-637X; 1538-4357
• DOI: 10.1086/510878

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-Fourie: 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 wide-field double-Fourier interferometers using the Jones and Mueller calculi. We employ a "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 developing instrument requirements from science goals. Second, we furnish three wavenumber-dependent observables--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, phase-aberrated, and polarization-mismatched optics are produced. Last, we present ideas for future research in wide-field double-Fourier interferometers, such a SPIRIT and SPECS.