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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. 7 — Jul. 1, 1999
  • pp: 1724–1729

Theory of branch-point detection and its implementation

Eric-Olivier Le Bigot and Walter J. Wild  »View Author Affiliations


JOSA A, Vol. 16, Issue 7, pp. 1724-1729 (1999)
http://dx.doi.org/10.1364/JOSAA.16.001724


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Abstract

It is shown that branch points present in a turbulence-distorted optical field can be visualized as peaks and valleys of a certain potential function. Peaks correspond to positive branch points and valleys correspond to negative ones, thus allowing one to study the formation, movements, and merging of branch points. A closed-form formula is given for the potential in terms of wave-front-sensor measurements; branch points appear as logarithmic singularities that are easy to detect visually through computer-generated images. In fact, the branch-point potential is obtained by means of a single matrix multiplication. An electrostatic analogy is given, as well as a proof that the continuous part of the wave front does not change the location of the potential singularities. Applications can be found in adaptive optics, in the airborne laser system, in speckle or coherent imaging, and in high-bandwidth laser communication.

© 1999 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(110.6150) Imaging systems : Speckle imaging
(120.1880) Instrumentation, measurement, and metrology : Detection
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(350.1370) Other areas of optics : Berry's phase

History
Original Manuscript: November 3, 1998
Revised Manuscript: February 26, 1999
Manuscript Accepted: February 26, 1999
Published: July 1, 1999

Citation
Eric-Olivier Le Bigot and Walter J. Wild, "Theory of branch-point detection and its implementation," J. Opt. Soc. Am. A 16, 1724-1729 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-7-1724


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References

  1. D. L. Fried, J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31, 2865–2882 (1992). [CrossRef] [PubMed]
  2. V. V. Voitsekhovich, D. Kouznetsov, D. K. Morozov, “Density of turbulence-induced phase dislocations,” Appl. Opt. 37, 4525–4535 (1998). [CrossRef]
  3. D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15, 2759–2768 (1998). [CrossRef]
  4. E.-O. Le Bigot, W. J. Wild, E. J. Kibblewhite, “Branch point reconstructors for discontinuous light phase functions,” in Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3381, 76–87 (1998). [CrossRef]
  5. E.-O. Le Bigot, W. J. Wild, E. J. Kibblewhite, “Reconstruction of discontinuous light phase functions,” Opt. Lett. 23, 10–12 (1998). [CrossRef]
  6. V. Aksenov, V. Banakh, O. Tikhomirova, “Potential and vortex features of optical speckle fields and visualization of wave-front singularities,” Appl. Opt. 37, 4536–4540 (1998). [CrossRef]
  7. M. C. Roggemann, D. J. Lee, “Two-deformable-mirror concept for correcting scintillation effects in laser beam propagation through the turbulent atmosphere,” Appl. Opt. 37, 4577–4578 (1998). [CrossRef]
  8. J. Matthew, R. Walker, Mathematical Methods of Physics, 2nd ed. (Benjamin, New York, 1970).
  9. R. H. Hudgin, “Wave-front reconstruction for compensated imaging,” J. Opt. Soc. Am. 67, 375–378 (1977). [CrossRef]
  10. B. R. Hunt, “Matrix formulation of the reconstruction of phase values from phase differences,” J. Opt. Soc. Am. 69, 393–399 (1979). [CrossRef]
  11. The Mathematica code that we wrote for this purpose can be obtained by sending a request to Eric.Le.Bigot@ens.fr.

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