Nutronics (United States)

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).

Coherent light of one color will form laser speckle upon reflection from a rough object. This laser speckle provides information about the shape of an object. Further information can be obtained if two colors are used, and if the colors are sufficiently close in wavelength that the interference is also measurable. The two speckle patterns and the interference can be shown to provide the minimum information sufficient to form a band-limited image of the object using a root-matching technique described herein. This root-matching technique is performed in the far-field or object plane. This technique is relatively slow and sensitive to noise, and so is supplemented with a technique that minimizes error in the pupil plane. A hybrid technique that combines the two approaches is shown to reproduce images effectively with reasonable computation time.