The analyticity of the generalized Fourier spectrum is used to estimate unmeasured visibilities with data obtained from an amplitude–phase optical interferometer. According to the Van Cittert–Zernike theorem, the complex visibilities are a scaled version of the spatial spectrum of the object. Hence an image of the object can be reconstructed from this measurement. However, since interferometers sparsely sample the object’s frequency spectrum, estimation of the unmeasured visibilities is crucial to obtaining a good spatial description of the object. This paper presents two techniques derived from the analyticity of the generalized Fourier spectrum that implement the estimation process. Both techniques are tailored specifically to interferometric data in that (1) all measured data is kept and used and (2) the sparseness of the sampling is taken into account.
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