Abstract

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.

© 1997 Optical Society of America

Reconstruction of low-light images by use of the vector Wiener filter

Stephen D. Ford, Byron M. Welsh, Michael C. Roggemann, and David J. Lee
J. Opt. Soc. Am. A 14(10) 2678-2691 (1997)

Model-based image reconstruction by means of a constrained least-squares solution

Michael C. Roggemann and David W. Tyler
Appl. Opt. 36(11) 2360-2369 (1997)

Analytic design of computer-generated Fourier-transform holograms for plane curves reconstruction

Zbigniew Jaroszewicz, Andrzej Kołodziejczyk, Dolores Mouriz, and Salvador Bara
J. Opt. Soc. Am. A 8(3) 559-565 (1991)

Fourier spectrum of radially periodic images

Isaac Amidror
J. Opt. Soc. Am. A 14(4) 816-826 (1997)

Reconstructing symmetric images from their undersampled Fourier intensities

R. P. Millane and W. J. Stroud
J. Opt. Soc. Am. A 14(3) 568-579 (1997)