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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. 15, Iss. 2 — Feb. 1, 1998
  • pp: 419–429

Phase-closure imaging in algebraic graph theory: a new class of phase-calibration algorithms

André Lannes  »View Author Affiliations


JOSA A, Vol. 15, Issue 2, pp. 419-429 (1998)
http://dx.doi.org/10.1364/JOSAA.15.000419


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Abstract

A new class of phase-calibration algorithms is presented. The originality of these algorithms, as well as their efficiency, results from certain particular structures, the analysis of which calls on algebraic graph theory. The corresponding optimization process, which is based on the principle of the trust-region methods, proves to be well suited to these structures. The main message that emerges from the study is very clear: The traditional notions of phase closure imaging can be understood and refined in a wider framework. The implications of this research therefore concern all the fields in which the notion of phase closure plays a key role: weak-phase imaging in optical interferometry, radio imaging, remote sensing by aperture synthesis, etc.

© 1998 Optical Society of America

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(350.5030) Other areas of optics : Phase

Citation
André Lannes, "Phase-closure imaging in algebraic graph theory: a new class of phase-calibration algorithms," J. Opt. Soc. Am. A 15, 419-429 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-2-419


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References

  1. R. Merris, “A survey of graph Laplacians,” Linear Multilinear Algebra 39, 19–31 (1995). When the author began discovering the algebraic structures of phase closure imaging, 23 he was completely unaware of the existence of algebraic graph theory. Likewise, the mathematicians working in this very particular field of research were not aware of a possible application in interferometry (see for instance the long list of references given in this review paper).
  2. A. Lannes, “Remarkable algebraic structures of phase-closure imaging and their algorithmic implications in aperture synthesis,” J. Opt. Soc. Am. A 7, 500–512 (1990).
  3. A. Lannes, “Phase and amplitude calibration in aperture synthesis. Algebraic structures,” Inv. Probl. 7, 261–298 (1991).
  4. A. Lannes, E. Anterrieu, and K. Bouyoucef, “Fourier interpolation and reconstruction via Shannon-type techniques: Part I: Regularization principle,” J. Mod. Opt. 41, 1537–1574 (1994).
  5. A. Lannes, E. Anterrieu, and K. Bouyoucef, “Fourier interpolation and reconstruction via Shannon-type techniques: Part II: Technical developments and applications,” J. Mod. Opt. 43, 105–138 (1996).
  6. A. Lannes, E. Anterrieu, and P. Maréchal, “Clean and wipe,” Astron. Astrophys. Suppl. Ser. 123, 183–198 (1997).
  7. J. Moré, “Recent developments in algorithms and software for trust region methods,” in Mathematical Programming, the State of the Art, A. Bachem, M. Grötschel, and B. Korte, eds. (Springer-Verlag, Berlin, 1983), pp. 258–287.

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