The Mathematics of Double-Fourier Interferometers

Details The Mathematics of Double-Fourier Interferometers The Mathematics of Double-Fourier Interferometers

Mar 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007apj...657.1178e&link_type=abstract

The Astrophysical Journal, Volume 657, Issue 2, pp. 1178-1200.

Astronomy and Astrophysics

Astronomy

4

Methods: Analytical, Methods: Data Analysis, Techniques: High Anular Resolution, Techniques: Image Processing, Techniques: Interferometric, Techniques: Spectroscopic

Scientific paper

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 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 as SPIRIT and SPECS.

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