OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 20, Iss. 6 — Jun. 1, 2003
  • pp: 1013–1024

Rapidly convergent phase-retrieval strategy for use with reflected laser light

Jeffrey D. Barchers  »View Author Affiliations


JOSA A, Vol. 20, Issue 6, pp. 1013-1024 (2003)
http://dx.doi.org/10.1364/JOSAA.20.001013


View Full Text Article

Enhanced HTML    Acrobat PDF (341 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

An approach for wave-front sensing using reflected laser light from a rough object is proposed. Light from a single laser beam is split into two beams, and the beams are launched from spatially separated apertures to illuminate an object. The reflected laser light is measured in the pupil plane of a receive telescope and in a plane conjugate to the object. By modulation of one of the two illuminator beams, the intensity pattern associated with each beam, as well as the field cross product of the two beams, is measured in each plane. A phase-retrieval algorithm is formulated by using projections onto constraint sets to recover the complex field associated with each illuminator. The algorithm is found to converge rapidly to the correct solution, particularly when compared with the convergence rates of more conventional phase-retrieval approaches. The new algorithm exhibits excellent performance in strong scintillation and is very tolerant to noise, exhibiting only a very small noise gain.

© 2003 Optical Society of America

OCIS Codes
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence

History
Original Manuscript: July 15, 2002
Revised Manuscript: February 10, 2003
Manuscript Accepted: February 10, 2003
Published: June 1, 2003

Citation
Jeffrey D. Barchers, "Rapidly convergent phase-retrieval strategy for use with reflected laser light," J. Opt. Soc. Am. A 20, 1013-1024 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-6-1013


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. Hardy, J. Lefebvre, C. Koliopouosis, “Real-time atmospheric compensation,” J. Opt. Soc. Am. 67, 360–369 (1977). [CrossRef]
  2. J. C. Wyant, “Use of an AC heterodyne lateral shear interferometer with real-time wave-front correction systems,” Appl. Opt. 14, 2622–2626 (1975). [CrossRef] [PubMed]
  3. T. R. O’Meara, “The multidither principle in adaptive optics,” J. Opt. Soc. Am. 67, 306–315 (1977). [CrossRef]
  4. D. Y. Gezari, A. Labeyrie, R. V. Stachnik, “Speckle interferometry: diffraction-limited measurements of nine stars with the 200-inch telescope,” Astrophys. J. 173, L1–L5 (1972). [CrossRef]
  5. K. T. Knox, B. J. Thompson, “Recovery of images from atmospherically degraded short-exposure photographs,” Astrophys. J. 193, L45–L48 (1974). [CrossRef]
  6. C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature 353, 141–143 (1991). [CrossRef]
  7. R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wave-front distortion using scattered light from a laser guide star,” Nature 353, 144–146 (1991). [CrossRef]
  8. J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, D. J. Link, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, K. B. Wilson, J. L. Wynia, W. J. Wild, “The Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optical Systems and Technologies, D. Bonaccini, ed., Proc. SPIE3353, 22–33 (1998). [CrossRef]
  9. J. C. Shelton, T. G. Schneider, D. McKenna, S. L. Baliunar, “First tests of the Cassegrain adaptive optics system of the Mount Wilson 100-inch telescope,” in Adaptive Optical Systems and Technologies, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 72–77 (1995). [CrossRef]
  10. D. L. Fried, “Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements,” J. Opt. Soc. Am. 67, 370–374 (1977). [CrossRef]
  11. R. V. Shack, B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).
  12. J. D. Barchers, D. L. Fried, D. J. Link, “Evaluation of the performance of Hartmann sensors in strong scintillation,” Appl. Opt. 41, 1012–1021 (2002). [CrossRef] [PubMed]
  13. D. L. Fried, “Adaptive optics wave function reconstruction and phase unwrapping when branch points are present,” Opt. Commun. 200, 43–72 (2002). [CrossRef]
  14. D. L. Fried, J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31, 2865–2882 (1992). [CrossRef] [PubMed]
  15. D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15, 2759–2768 (1998). [CrossRef]
  16. G. A. Tyler, “Reconstruction and assessment of the least-squares and slope discrepancy components of the phase,” J. Opt. Soc. Am. A 17, 1828–1839 (2000). [CrossRef]
  17. J. D. Barchers, D. L. Fried, D. J. Link, “Evaluation of the performance of a shearing interferometer in strong scintillation in the absence of additive measurement noise,” Appl. Opt. 41, 3674–3684 (2002). [CrossRef] [PubMed]
  18. J. D. Barchers, T. A. Rhoadarmer, “Evaluation of phase-shifting approaches for a point-diffraction interferometer with the mutual coherence function,” Appl. Opt. 41, 7499–7509 (2002). [CrossRef]
  19. R. B. Holmes, K. Hughes, P. Fairchild, B. Spivey, A. Smith, “Description and simulation of an active imaging technique utilizing two speckle fields: root reconstructors,” J. Opt. Soc. Am. A 19, 444–457 (2002). [CrossRef]
  20. R. B. Holmes, K. Hughes, P. Fairchild, B. Spivey, A. Smith, “Description and simulation of an active imaging technique utilizing two speckle fields: iterative reconstructors,” J. Opt. Soc. Am. A 19, 458–471 (2002). [CrossRef]
  21. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane images,” Optik (Stuttgart) 35, 225–246 (1972).
  22. J. R. Fienup, “Phase-retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982). [CrossRef] [PubMed]
  23. J. R. Fienup, C. C. Wackerman, “Phase-retrieval stagnation problems and solutions,” J. Opt. Soc. Am. A 3, 1897–1907 (1986). [CrossRef]
  24. J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of it Fourier transform using a support constraint,” J. Opt. Soc. Am. A 4, 118–123 (1987). [CrossRef]
  25. Y. M. Bruck, L. G. Sodin, “On the ambiguity of the image reconstruction problem,” Opt. Commun. 30, 304–308 (1979). [CrossRef]
  26. C. C. Wackerman, A. E. Yagle, “Use of Fourier domain real-plane zeros to overcome phase retrieval stagnation,” J. Opt. Soc. Am. A 8, 1898–1904 (1991). [CrossRef]
  27. C. C. Wackerman, A. E. Yagle, “Phase retrieval and estimation with use of real-plane zeros,” J. Opt. Soc. Am. A 11, 2016–2026 (1994). [CrossRef]
  28. R. G. Paxman, T. J. Schulz, J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9, 1072–1085 (1992). [CrossRef]
  29. H. Stark, Y. Yang, Vector Space Projections (Wiley, New York, 1998).
  30. A. Levi, H. Stark, “Image restoration by the method of generalized projections with application to restoration from magnitude,” J. Opt. Soc. Am. A 1, 932–943 (1984). [CrossRef]
  31. T. Kotzer, J. Rosen, J. Shamir, “Application of serial and parallel projection methods to correlation filter design,” Appl. Opt. 34, 3883–3895 (1995). [CrossRef] [PubMed]
  32. H. H. Bauschke, P. L. Combettes, D. R. Luke, “Phase retrieval and error reduction algorithm, and Fienup variants: a view from convex optimization,” J. Opt. Soc. Am. A 19, 1334–1345 (2002). [CrossRef]
  33. J. Von Neumann, Functional Operators, Vol. II of Annals Mathematical Studies (Princeton U. Press, Princeton, N.J., 1950).
  34. L. G. Gubin, B. T. Polyak, E. V. Raik, “The method of projections for finding the common point in convex sets,” USSR Comput. Math. Math. Phys. 7, 1–24 (1967). [CrossRef]
  35. D. C. Youla, H. Webb, “Image restoration by the method of convex projections: part 1—theory,” IEEE Trans. Med. Imaging MI-1, 81–94 (1982). [CrossRef]
  36. D. L. Misell, “A method for the solution of the phase problem in electron microscopy,” J. Phys. D Appl. Phys. 6, L6–L9 (1973). [CrossRef]
  37. D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics: I. Test calculations,” J. Phys. D Appl. Phys. 6, 2200–2216 (1973). [CrossRef]
  38. D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics: II. Sources of error,” J. Phys. D Appl. Phys. 6, 2217–2225 (1973). [CrossRef]
  39. J. R. Fienup, A. M. Kowalczyk, “Phase retrieval for a complex-valued object by using a low-resolution image,” J. Opt. Soc. Am. A 7, 450–458 (1990). [CrossRef]
  40. J. R. Fienup, “Phase-retrieval algorithms for a complicated optical system,” Appl. Opt. 32, 1737–1746 (1993). [CrossRef] [PubMed]
  41. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  42. J. D. Barchers, “Evaluation of the impact of finite resolution effects on scintillation compensation using two deformable mirrors,” J. Opt. Soc. Am. A 18, 3098–3109 (2001). [CrossRef]
  43. J. D. Barchers, “Application of the parallel generalized projection algorithm to the control of two finite-resolution deformable mirrors for scintillation compensation,” J. Opt. Soc. Am. A 19, 54–63 (2002). [CrossRef]
  44. H. Stark, Y. Yang, D. Gurkan, “Factors affecting convergence in the design of diffractive optics by iterative vector-space methods,” J. Opt. Soc. Am. A 16, 149–159 (1999). [CrossRef]
  45. D. L. Fried, P.O. Box 680, Moss Landing,Calif. 95038 (personal communication, 2000).
  46. D. L. Fried, “Scaling laws for propagation through turbulence,” J. Atmos. Ocean. Opt. 11, 982–990 (1998).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited