Two-dimensional image recovery in intensity interferometry using the Cauchy-Riemann relations

Abstract

Intensity interferometry utilizes measurements of the squared-magnitude of the Fourier transform of an object using relatively simple, phase-insensitive hardware, and therefore holds the promise of extremely high spatial resolution in astronomy and various branches of physics. However, this promise has not been realized due to signal-noise-ratio (SNR) issues and due to the maturity of image recovery algorithms. To recover an image, the phase of the Fourier transform must be determined in addition to its magnitude. In a recent paper, relatively good one-dimensional (1-D) image recoveries were obtained with a fast non-iterative algorithm utilizing the Cauchy-Riemann relations and a mild constraint on the symmetry of the object. In this paper, the approach is extended to two spatial dimensions by combining multiple 1-D reconstructions, and ensuring mutual consistency between 1-D slices. Mutual consistency is enforced using several different approaches, including phase retrieval. This use of the Cauchy-Riemann approach combined with imposition of mutual consistency is found to reduce noise sensitivity significantly. Three approaches are evaluated for image quality for different objects using sparse Fourier-plane sampling, showing good reconstruction of images at SNR's as low as 7 at the origin in the Fourier plane (and thus even lower SNR's at higher angular frequencies).