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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 12 — Dec. 1, 1999
  • pp: 2866–2879

Redundant spacing calibration: phase restoration methods

André Lannes and Éric Anterrieu  »View Author Affiliations


JOSA A, Vol. 16, Issue 12, pp. 2866-2879 (1999)
http://dx.doi.org/10.1364/JOSAA.16.002866


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Abstract

New methods for redundant spacing calibration (RSC) are proposed. These are based on recent studies concerning phase calibration and the related phase unwrapping problem. In the corresponding theoretical framework, two subspaces of the baseline phase space, the variational spectral phase space K and the aberration baseline phase space L, play an important role. An interferometric device for which KL is reduced to {0} is said to be of full phase. For any imaging device of this type, including those for which the traditional recursive approach fails, the phase restoration problem can be solved in the least-squares sense. When the closure phases are strongly blurred, global instabilities may occur. Their analysis appeals to elementary concepts of algebraic number theory: ℤ lattice, reduced basis, and closest node. In all cases, the separation angle between K and L must be as large as possible. The imaging devices based on the RSC principle should be designed accordingly. All these points are illustrated by considering the phase restoration problems encountered in passive remote sensing by aperture synthesis. The difficulties related to possible correlator failures are examined in this context.

© 1999 Optical Society of America

OCIS Codes
(100.5070) Image processing : Phase retrieval
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

History
Original Manuscript: March 25, 1999
Revised Manuscript: July 27, 1999
Manuscript Accepted: July 27, 1999
Published: December 1, 1999

Citation
André Lannes and Éric Anterrieu, "Redundant spacing calibration: phase restoration methods," J. Opt. Soc. Am. A 16, 2866-2879 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-12-2866


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References

  1. A. Lannes, “Phase closure imaging in algebraic graph theory: a new class of phase calibration algorithms,” J. Opt. Soc. Am. A 15, 419–429 (1998). [CrossRef]
  2. A. Lannes, “Weak phase imaging in optical interferometry,” J. Opt. Soc. Am. A 15, 811–824 (1998). [CrossRef]
  3. A. Lannes, E. Anterrieu, “Image reconstruction methods for remote sensing by aperture synthesis,” in Proceedings of the International Geoscience and Remote Sensing Symposium, 1994 (Institute of Electrical and Electronics Engineers, New York, 1994), pp. 2892–2903.
  4. A. H. Greenaway, D. P. Cheese, J. D. Bregman, J. E. Noordam, “TOAST: a terrestrial optical aperture synthesis technique,” in Proceedings of Interferometry Imaging in Astronomy (European Space Agency/National Optical Astronomy Observatories, Garching, Germany, 1987), pp. 153–156.
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  6. A. Lannes, “Spectral reduction of phase closure data and stabilized image reconstruction via a new hybrid procedure,” in High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds., Vol. 39 of ESO Conference and Workshop Proceedings (European Southern Observatory, Garching, Germany, 1991), pp. 881–887.
  7. A. Lannes, “Phase calibration on interferometric graphs,” J. Opt. Soc. Am. A 16, 443–454 (1999). [CrossRef]
  8. A. Lannes, “Abstract holography,” J. Math. Anal. Appl. 74, 530–559 (1980). [CrossRef]
  9. P. Roman, Some Modern Mathematics for Physicists and Other Outsiders, Vol. 1 of Algebra, Topology, and Measure Theory (Pergamon, New York, 1975).
  10. J. Moré, “Recent developments in algorithms and software for trust region methods,” in Mathematical Programming, the State of the Art, A. Bachem, M. Grötschel, B. Korte, eds. (Springer-Verlag, Berlin, 1983), pp. 258–287.
  11. A. Lannes, E. Anterrieu, K. Bouyoucef, “Fourier interpolation and reconstruction via Shannon-type techniques. Part II: technical developments and applications,” J. Mod. Opt. 43, 105–138 (1996). [CrossRef]

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