Realization and theoretical limits of the spectral resolution in double Fourier interferometric imaging with an optical telescope array

The realization and theoretical limits of the spectral resolution in double Fourier interferometric imaging (DFII) with a phase telescope array are presented. The realization and the effects of optical path difference (OPD) modulations are discussed. Two basic requirements for OPD modulations must be met in the design and operation of a double Fourier interferometer: symmetric OPD modulations about zero OPD and identical OPD modulations at all the available spatial frequencies. The Gibbs phenomenon due to OPD modulations affects the source's spectral brightness distribution, but, for a point source, not the complex visibility. Theoretically, without loss in spatial image fidelity, it is not possible to perform DFII with a telescope array when the aperture synthesis is done only by the Earth's rotation. In practice, DFII can be realized under approximation. In this case, relations between the spectral resolution, the interferometer's parameters and the observed star's parameters are derived. For a two-aperture interferometer with an east-west baseline of 100 m and telescope diameter of 8 m, the spectral resolution is limited to several thousands or less for a star having a magnitude of five, six or fainter, a field of view equal to or larger than the Airy disc of the diffraction pattern of the single telescope aperture and a signal-to-noise ratio of three in the interferogram.