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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 53, Iss. 18 — Jun. 20, 2014
  • pp: 3821–3831

LSPV+7, a branch-point-tolerant reconstructor for strong turbulence adaptive optics

Michael J. Steinbock, Milo W. Hyde, and Jason D. Schmidt  »View Author Affiliations

Applied Optics, Vol. 53, Issue 18, pp. 3821-3831 (2014)

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Optical wave propagation through long paths of extended turbulence presents unique challenges to adaptive optics (AO) systems. As scintillation and branch points develop in the beacon phase, challenges arise in accurately unwrapping the received wavefront and optimizing the reconstructed phase with respect to branch cut placement on a continuous facesheet deformable mirror. Several applications are currently restricted by these capability limits: laser communication, laser weapons, remote sensing, and ground-based astronomy. This paper presents a set of temporally evolving AO simulations comparing traditional least-squares reconstruction techniques to a complex-exponential reconstructor and several other reconstructors derived from the postprocessing congruence operation. The reconstructors’ behavior in closed-loop operation is compared and discussed, providing several insights into the fundamental strengths and limitations of each reconstructor type. This research utilizes a self-referencing interferometer (SRI) as the high-order wavefront sensor, driving a traditional linear control law in conjunction with a cooperative point source beacon. The SRI model includes practical optical considerations and frame-by-frame fiber coupling effects to allow for realistic noise modeling. The “LSPV+7” reconstructor is shown to offer the best performance in terms of Strehl ratio and correction stability—outperforming the traditional least-squares reconstructed system by an average of 120% in the studied scenarios. Utilizing a continuous facesheet deformable mirror, these reconstructors offer significant AO performance improvements in strong turbulence applications without the need for segmented deformable mirrors.

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.3310) Atmospheric and oceanic optics : Laser beam transmission
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(290.5930) Scattering : Scintillation

ToC Category:
Atmospheric and Oceanic Optics

Original Manuscript: March 11, 2014
Revised Manuscript: April 21, 2014
Manuscript Accepted: May 2, 2014
Published: June 12, 2014

Michael J. Steinbock, Milo W. Hyde, and Jason D. Schmidt, "LSPV+7, a branch-point-tolerant reconstructor for strong turbulence adaptive optics," Appl. Opt. 53, 3821-3831 (2014)

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  1. D. L. Fried and J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31, 2865–2882 (1992). [CrossRef]
  2. D. L. Fried, “Adaptive optics wave function reconstruction and phase unwrapping when branch points are present,” Opt. Commun. 200, 43–72 (2001). [CrossRef]
  3. J. L. Vaughn, the Optical Sciences Company, 1341 South Sunkist Street, Anaheim, California, 92806 (personal communication, Jan. 2014).
  4. D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15, 2759–2768 (1998). [CrossRef]
  5. V. Aksenov, V. Banakh, and O. Tikhomirova, “Potential and vortex features of optical speckle fields and visualization of wave-front singularities,” Appl. Opt. 37, 4536–4540 (1998). [CrossRef]
  6. J. D. Barchers, D. L. Fried, and D. J. Link, “Evaluation of the performance of Hartmann sensors in strong scintillation,” Appl. Opt. 41, 1012–1021 (2002). [CrossRef]
  7. J. D. Barchers, D. L. Fried, D. J. Link, G. A. Tyler, W. Moretti, T. J. Brennan, and R. Q. Fugate, “Performance of wavefront sensors in strong scintillation,” Proc. SPIE 4839, 217–227 (2003). [CrossRef]
  8. T. A. Rhoadarmer, “Development of a self-referencing interferometer wavefront sensor,” Proc. SPIE 5553, 112–126 (2004). [CrossRef]
  9. T. M. Venema and J. D. Schmidt, “Optical phase unwrapping in the presence of branch points,” Opt. Express 16, 6985–6998 (2008). [CrossRef]
  10. M. J. Steinbock, “Implementation of branch-point-tolerant wavefront reconstructor for strong turbulence compensation,” Master’s thesis (Air Force Institute of Technology, 2012).
  11. C. J. Pellizzari and J. D. Schmidt, “Phase unwrapping in the presence of strong turbulence,” in Proceedings of IEEE Aerospace Conference (IEEE, 2010), pp. 1–10.
  12. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  13. M. J. Steinbock, J. D. Schmidt, and M. W. Hyde, “Comparison of branch point tolerant wavefront reconstructors in the presence of simulated noise effects,” in Proceedings of IEEE Aerospace Conference (IEEE, 2012), pp. 1–13.
  14. M. J. Steinbock and M. W. Hyde, “Phase discrepancy induced from least squares wavefront reconstruction of wrapped phase measurements with high noise or large localized wavefront gradients,” Proc. SPIE 8517, 85170W (2012). [CrossRef]
  15. T. M. Venema, “Closed-loop adaptive optics control in strong atmospheric turbulence,” Ph.D. dissertation (Air Force Institute of Technology, 2008).
  16. C. Pellizzari, “Phase unwrapping in the presence of strong turbulence,” Master’s thesis (Air Force Institute of Technology, 2010).
  17. M. J. Steinbock, M. W. Hyde, J. D. Schmidt, and S. J. Cusumano, “Comparison of wavefront reconstruction techniques for extended turbulence beam projection applications,” in Advanced High-Power Lasers Meeting (Directed Energy Professional Society, CO, 2012), pp. 1–22.
  18. T. Brennan, P. Roberts, and D. Mann, WaveProp: A Wave Optics Simulation System (Optical Sciences Company, 2008).
  19. J. D. Schmidt, Numerical Simulation of Optical Wave Propagation (SPIE, 2010).
  20. J. H. Churnside, “A spectrum of refractive turbulence in the turbulent atmosphere,” J. Mod. Opt. 37, 13–16 (1990). [CrossRef]
  21. R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms (SPIE, 2007).
  22. J. D. Schmidt, M. J. Steinbock, and E. C. Berg, “A flexible testbed for adaptive optics in strong turbulence,” Proc. SPIE 8038, 80380O (2011). [CrossRef]
  23. J. D. Barchers, “Control law for a high resolution self-referencing interferometer wavefront sensor used with a low resolution deformable mirror,” (SAIC, CO, 2002).
  24. R. H. Hudgin, “Wave-front reconstruction for compensated imaging,” J. Opt. Soc. Am. 67, 375–378 (1977). [CrossRef]
  25. Boston Micromachines, “Multi-DM,” Datasheet, (Retrieved Apr. 15, 2012 from http://www.bostonmicromachines.com/pdf/Multi-DM.pdf ).
  26. D. J. Wheeler and J. D. Schmidt, “Coupling of Gaussian Schell-model beams into single-mode optical fibers,” J. Opt. Soc. Am. A 28, 1224–1238 (2011). [CrossRef]
  27. T. A. Rhoadarmer and J. D. Barchers, “Noise analysis for complex field estimation using a self-referencing interferometer wave front sensor,” Proc. SPIE 4825, 215–227 (2002).
  28. Goodrich Corporation, “SU320KTSW-1.7RT SU320KTSVis-1.7RT InGaAs SWIR Camera,” Datasheet, (Retrieved Nov. 9, 2012 from http://www.sensorsinc.com/downloads/SU320KTS-SU320KTSVIS.pdf ).

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