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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. 4 — Apr. 1, 1998
  • pp: 811–824

Weak-phase imaging in optical interferometry

André Lannes  »View Author Affiliations


JOSA A, Vol. 15, Issue 4, pp. 811-824 (1998)
http://dx.doi.org/10.1364/JOSAA.15.000811


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Abstract

The first imaging devices of optical interferometry are likely to be of weak phase, typically: a set of three-element arrays independently observing the same object. The study of their imaging capabilities refers to appropriate optimization methods, which essentially address the self-calibration process and its stability. A general survey of these techniques is given, and it is shown, in particular, how the related algorithms can be used for examining the imaging capabilities of weak-phase interferometric devices. The phase-calibration algorithm involved in the self-calibration cycles is based on the principle underlying the trust-region methods. It benefits from certain remarkable properties, the analysis of which appeals to algebraic graph theory. The Fourier synthesis operation, which is also involved in these cycles, is performed by means of Wipe, a methodology recently introduced in radio imaging and optical interferometry. (Wipe is reminiscent of Clean, a widely used technique in astronomy). In the related theoretical framework the stability of the image-reconstruction process is controlled by considering certain elements of the singular-value decomposition of the derivative of the self-calibration operator. For example, the largest singular value of this derivative, which depends on the interferometric configuration and on the object thus imaged, provides a key indication of the observational limits of these experimental devices.

© 1998 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(120.3180) Instrumentation, measurement, and metrology : Interferometry

History
Original Manuscript: October 1, 1997
Manuscript Accepted: October 27, 1997
Published: April 1, 1998

Citation
André Lannes, "Weak-phase imaging in optical interferometry," J. Opt. Soc. Am. A 15, 811-824 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-4-811


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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, E. Anterrieu, K. Bouyoucef, “Fourier interpolation and reconstruction via Shannon-type techniques: Part I: Regularization principle,” J. Mod. Opt. 41, 1537–1574 (1994). [CrossRef]
  3. 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]
  4. A. Lannes, E. Anterrieu, P. Maréchal, “Clean and Wipe,” Astron. Astrophys. Suppl. Ser. 123, 183–198 (1997). [CrossRef]
  5. T. J. Cornwell, P. N. Wilkinson, “New method for making maps with unstable interferometers,” Mon. Not. R. Astron. Soc. 196, 1067–1086 (1981).
  6. 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). [CrossRef]
  7. R. Merris, “Survey of graph Laplacians,” Linear Multilinear Algebra 39, 19–31 (1995).
  8. 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.

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