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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. 10 — Oct. 1, 1998
  • pp: 2759–2768

Branch point problem in adaptive optics

David L. Fried  »View Author Affiliations


JOSA A, Vol. 15, Issue 10, pp. 2759-2768 (1998)
http://dx.doi.org/10.1364/JOSAA.15.002759


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Abstract

It is shown that when branch points are present in the phase of a turbulence-distorted optical field, the ability of an adaptive optics system that utilizes a least mean square error type of wave-front reconstructor to sense all of the turbulence-induced phase perturbations is limited. There is a portion of the turbulence-induced phase perturbation, which portion we refer to as the hidden phase, that such a least mean square error type of wave-front reconstructor will, in effect, ignore. It is shown that the presence of branch points indicates that the measured phase-difference vector field cannot be considered to be simply the gradient of some scalar potential—the phase function—but is in part also the curl of a vector potential function. A solution is developed for this vector potential, and from this a simple closed-form solution for the hidden phase is developed. Sample numerical results are presented showing the nature of the hidden phase. Suggestions are provided for a branch-point-tolerant wave-front reconstructor based on use of the closed-form solution for the hidden phase.

© 1998 Optical Society of America

OCIS Codes
(010.7060) Atmospheric and oceanic optics : Turbulence

History
Original Manuscript: May 1, 1998
Revised Manuscript: July 6, 1998
Manuscript Accepted: June 10, 1998
Published: October 1, 1998

Citation
David L. Fried, "Branch point problem in adaptive optics," J. Opt. Soc. Am. A 15, 2759-2768 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-10-2759


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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. 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]
  3. F. S. Woods, Advanced Calculus (Ginn, Boston, 1934), Eq. (80.8).
  4. W. K. H. Panofsky, M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, Mass., 1955), Eq. (1-1).
  5. R. V. Churchill, Introduction to Complex Variables and Applications (McGraw-Hill, New York, 1948), Sec. 18.

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