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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 1 — Jan. 1, 2013
  • pp: 45–56

Phase retrieval algorithms: a personal tour [Invited]

James R. Fienup  »View Author Affiliations

Applied Optics, Vol. 52, Issue 1, pp. 45-56 (2013)

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This paper gives the reader a personal tour through the field of phase retrieval and related works that lead up to or cited the paper “Phase Retrieval Algorithms: a Comparison,” [Appl. Opt. 21, 2758 (1982)].

© 2012 Optical Society of America

OCIS Codes
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(030.0030) Coherence and statistical optics : Coherence and statistical optics
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(100.3010) Image processing : Image reconstruction techniques
(100.5070) Image processing : Phase retrieval
(110.0110) Imaging systems : Imaging systems

Original Manuscript: September 28, 2012
Manuscript Accepted: October 15, 2012
Published: December 21, 2012

Virtual Issues
(2013) Advances in Optics and Photonics

James R. Fienup, "Phase retrieval algorithms: a personal tour [Invited]," Appl. Opt. 52, 45-56 (2013)

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  1. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982). [CrossRef]
  2. J. R. Fienup, “Improved synthesis and computational methods for computer-generated holograms,” Ph.D. Thesis (Stanford University, 1975) (ProQuest, UMI No. 7525523, or at http://www.optics.rochester.edu/workgroups/fienup/Professor.htm ).
  3. R. J. Collier, C. B. Burkhardt, and L. H. Lin, Optical Holography (Academic, 1971).
  4. A. W. Lohmann and D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
  5. L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Devel. 13, 150–155 (1969). [CrossRef]
  6. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  7. J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).
  8. Paul Simon, “Kodachrome”.
  9. D. Kermisch, “Image reconstruction from phase information only,” J. Opt. Soc. Am. 60, 15–16 (1970). [CrossRef]
  10. N. C. Gallagher and B. Liu, “Method for computing kinoforms that reduces image reconstruction error,” Appl. Opt. l2, 2328–2335 (1973).
  11. B. Liu and N. C. Gallagher, “Convergence of a spectrum shaping algorithm,” Appl. Opt. l3, 2470–2471 (1974).
  12. P. M. Hirsch, J. A. Jordan, and L. B. Lesem, “Method of making an object-dependent diffuser,” U.S. patent 3,619,022(9Nov.1971).
  13. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  14. J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. l9, 297–305 (1980).
  15. R. Hanbury Brown, and R. Q. Twiss, “A test of a new type of stellar interferometer on Sirius,” Nature 178, 1046–1048(1956). [CrossRef]
  16. A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).
  17. E. Wolf, “Is a complete determination of the energy spectrum of light possible from measurements of the degree of coherence,” Proc. Phys. Soc. London 80, 1269–1272 (1962). [CrossRef]
  18. A. Walther, “The question of phase retrieval in optics,” Opt. Acta l0, 41–49 (1963).
  19. J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. 3, 27–29 (1978). [CrossRef]
  20. D. C. Chu, J. R. Fienup, and J. W. Goodman, “Multiemulsion on-axis computer generated hologram,” Appl. Opt. 12, 1386–1388 (1973). [CrossRef]
  21. B. R. Frieden and D. G. Currie, “On unfolding the autocorrelation function,” J. Opt. Soc. Am. 66, 1111 (1976) (Abstract).
  22. R. H. T. Bates, “Contributions to the theory of intensity interferometry,” Mon. Not. R. Astron. Soc. 142, 413–428 (1969).
  23. P. J. Napier and R. H. T. Bates, “Inferring phase information from modulus information in two-dimensional aperture synthesis,” Astron. Astrophys. Suppl. l5, 427–430 (1974).
  24. J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” presented at the Annual Meeting of the OSA, Toronto, Ontario, October 1977, Abstract: J. Opt. Soc. Am. 67, 1389 (1977).
  25. J. R. Fienup, “Space object imaging through the turbulent atmosphere,” Proc. SPIE 149, 71–81 (1978).
  26. J. R. Fienup, “Space object imaging through the turbulent atmosphere,” Opt. Eng. 18, 529–534 (1979). [CrossRef]
  27. G. B. Feldkamp and J. R. Fienup, “Noise properties of images reconstructed from Fourier modulus,” Proc. SPIE 231, 84–93 (1980). [CrossRef]
  28. J. R. Fienup and G. B. Feldkamp, “Astronomical imaging by processing stellar speckle interferometry data,” Proc. SPIE 243, 95–102 (1980).
  29. T. R. Crimmins and J. R. Fienup, “Ambiguity of phase retrieval for functions with disconnected support,” J. Opt. Soc. Am. 71, 1026–1028 (1981). [CrossRef]
  30. J. R. Fienup, T. R. Crimmins, and W. Holsztynski, “Reconstruction of the support of an object from the support of its autocorrelation,” J. Opt. Soc. Am. 72, 610–624 (1982). [CrossRef]
  31. J. R. Fienup, “Phase retrieval in astronomy,” in Signal Recovery and Synthesis with Incomplete Information and Partial Constraints, digest of papers (Optical Society of America, 1983), paper ThA8-1-5.
  32. J. R. Fienup, “Image reconstruction for stellar interferometry,” in Current Trends in Optics, F. T. Arecchi and F. R. Aussenegg, eds. (Taylor and Francis and Halsted, 1981), Invited Papers from ICO-12 Meeting, Graz, Austria, September 1981, pp. 95–102.
  33. J. R. Fienup, “Comparison of phase retrieval algorithms,” presented at the Annual Meeting of the O.S.A., Kissimmee, Florida, October 1981, Abstract: J. Opt. Soc. Am. 71, 1641 (1981).
  34. M. T. Manry and J. K. Aggarwal, “The design of multidimensional FIR digital filters by phase correction,” IEEE Trans. Circuits Syst. 23, 185–199 (1976). [CrossRef]
  35. J. A. Marozas, “Fourier transform-based continuous phase-plate design technique: a high-pass phase-plate design as an application for OMEGA and the National Ignition Facility,” J. Opt. Soc. Am. A 24, 74–83 (2007). [CrossRef]
  36. S. Buhling and F. Wyrowski, “Solving tolerancing and three-dimensional beam shaping problems by multifunctional wave optical design,” Opt. Eng. 40, 1590–1597 (2001). [CrossRef]
  37. E. G. Johnson and J. D. Brasher, “Phase encryption of biometrics in diffractive optical elements,” Opt. Lett. 21, 1271–1273 (1996). [CrossRef]
  38. Y. Ivankovski and D. Mendlovic, “High-rate-long-distance fiber-optic communication based on advanced modulation techniques,” Appl. Opt. 38, 5533–5540 (1999). [CrossRef]
  39. J. Skaar, “Iterative design of antireflection coatings based on the direct and inverse scattering transform,” Opt. Commun. 232, 45–48 (2004). [CrossRef]
  40. D. Morris, “Phase retrieval in the radio holography of reflector antennas and radio telescopes,” IEEE Trans. Antennas Propag. 33, 749–755 (1985). [CrossRef]
  41. J. N. Cederquist, J. R. Fienup, C. C. Wackerman, S. R. Robinson, and D. Kryskowski, “Wave-front phase estimation from Fourier intensity measurements,” J. Opt. Soc. Am. A 6, 1020–1026 (1989). [CrossRef]
  42. J. R. Fienup, J. C. Marron, T. J. Schulz, and J. H. Seldin, “Hubble Space Telescope characterized by using phase retrieval algorithms,” Appl. Opt. 32, 1747–1767 (1993). [CrossRef]
  43. B. H. Dean, D. L. Aronstein, J. S. Smith, R. Shiri, and D. S. Acton, “Phase retrieval algorithm for JWST flight and testbed telescope,” Proc. SPIE 6265, 626511 (2006). [CrossRef]
  44. G. R. Brady and J. R. Fienup, “Nonlinear optimization algorithm for retrieving the full complex pupil function,” Opt. Express 14, 474–486 (2006). [CrossRef]
  45. M. Guizar-Sicairos and J. R. Fienup, “Measurement of coherent x-ray focused beams by phase retrieval with transverse translation diversity,” Opt. Express 17, 2670–2685 (2009). [CrossRef]
  46. S. T. Thurman, R. T. DeRosa, and J. R. Fienup, “Amplitude metrics for field retrieval with hard-edge and uniformly illuminated apertures,” J. Opt. Soc. Am. A 26, 700–709(2009). [CrossRef]
  47. B. H. Dean and C. W. Bowers, “Diversity selection for phase-diverse phase retrieval,” J. Opt. Soc. Am. A 20, 1490–1504 (2003). [CrossRef]
  48. H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004). [CrossRef]
  49. M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 16, 7264–7278 (2008). [CrossRef]
  50. J. S. Smith, D. L. Aronstein, B. H. Dean, and D. S. Acton, “Phase retrieval on broadband and under-sampled images for the JWST testbed telescope,” Proc. SPIE 7436, 7436D (2009). [CrossRef]
  51. G. R. Brady and J. R. Fienup, “Effect of broadband illumination on reconstruction error of phase retrieval in optical metrology,” Proc. SPIE 6617, 66170I (2007). [CrossRef]
  52. M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. 73, 1434–1441 (1983). [CrossRef]
  53. D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993). [CrossRef]
  54. R. Trebino and D. J. Kane, “Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating,” J. Opt. Soc. Am. A 10, 1101–1111 (1993). [CrossRef]
  55. R. G. Lane, “Blind deconvolution of speckle images,” J. Opt. Soc. Am. A 9, 1508–1514 (1992). [CrossRef]
  56. C. M. Vest and I. Prikryl, “Tomography by iterative convolution: empirical study and application to interferometry,” Appl. Opt. 23, 2433–2440 (1984). [CrossRef]
  57. G. K. Datta and R. M. Vasu, “Non-interferometric methods of phase estimation for application in optical tomography,” J. Mod. Opt. 46, 1377–1388 (1999). [CrossRef]
  58. M. H. Maleki and A. J. Devaney, “Phase-retrieval and intensity-only reconstruction algorithms for optical diffraction tomography,” J. Opt. Soc. Am. A 10, 1086–1092 (1993). [CrossRef]
  59. R. P. Yu, D. M. Paganin, and M. J. Morgan, “Inferring generalized time-dependent complex Ginzburg-Landau equations from modulus and gauge-field information,” Phys. Rev. B. 77, 134512 (2008). [CrossRef]
  60. M. Carmody, E. Landree, L. D. Marks, and K. L. Merkle, “Determination of the current density distribution in Josephson junctions,” Phys. C 315, 145–153 (1999). [CrossRef]
  61. V. Elser, I. Rankenburg, and P. Thibault, “Searching with iterated maps,” Proc. Natl. Acad. Sci. 104, 418–423 (2007). [CrossRef]
  62. J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint,” J. Opt. Soc. Am. A 4, 118–123 (1987). [CrossRef]
  63. J. R. Fienup, “Lensless coherent imaging by phase retrieval with an illumination pattern constraint,” Opt. Express 14, 498–508 (2006). [CrossRef]
  64. J. R. Fienup and 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]
  65. P. S. Idell, J. R. Fienup, and R. S. Goodman, “Image synthesis from nonimaged laser speckle patterns,” Opt. Lett. 12, 858–860 (1987). [CrossRef]
  66. D. Sayre, “Some implications of a theorem due to Shannon,” Acta Cryst. 5, 843 (1952). [CrossRef]
  67. K. A. Nugent, D. Paganin, and T. E. Gureyev, “A phase odyssey,” Phys. Today 54, 27–32 (2001). [CrossRef]
  68. J. N. Cederquist, J. R. Fienup, J. C. Marron, and R. G. Paxman, “Phase retrieval from experimental far-field data,” Opt. Lett. 13, 619–621 (1988). [CrossRef]
  69. J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999). [CrossRef]
  70. H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–2000 (2006). [CrossRef]
  71. J. H. Seldin and J. R. Fienup, “Numerical investigation of the uniqueness of phase retrieval,” J. Opt. Soc. Am. A 7, 412–427 (1990). [CrossRef]
  72. J. R. Fienup and C. C. Wackerman, “Phase retrieval stagnation problems and solutions,” J. Opt. Soc. Am. A 3, 1897–1907 (1986). [CrossRef]
  73. H. Takajo, T. Takahashi, H. Kawanami, and R. Ueda, “Numerical investigation of the iterative phase-retrieval stagnation problem: territories of convergence objects and holes in their boundaries,” J. Opt. Soc. Am. A 14, 3175–3187 (1997). [CrossRef]
  74. H. Takajo, T. Takahashi, R. Ueda, and M. Taninaka, “Study on the convergence property of the hybrid input output algorithm used for phase retrieval,” J. Opt. Soc. Am. A 15, 2849–2861 (1998). [CrossRef]
  75. H. Takajo, T. Takahashi, and T. Shizuma, “Further study on the convergence property of the hybrid input–output algorithm used for phase retrieval,” J. Opt. Soc. Am. A 16, 2163–2168 (1999). [CrossRef]
  76. R. G. Lane, “Phase retrieval using conjugate gradient minimization,” J. Mod. Opt. 38, 1797–1813 (1991). [CrossRef]
  77. J. R. Fienup, “Phase-retrieval algorithms for a complicated optical system,” Appl. Opt. 32, 1737–1746 (1993). [CrossRef]
  78. J. R. Fienup, “Wave front sensing by nonlinear optimization,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper FML2.
  79. T. R. Crimmins, J. R. Fienup, and B. J. Thelen, “Improved bounds on object support from autocorrelation support and application to phase retrieval,” J. Opt. Soc. Am. A 7, 3–13 (1990). [CrossRef]
  80. D. C. Youla, “Generalized image restoration by method of alternating orthogonal projections,” IEEE Trans. Circuits Syst. 25, 694–702 (1978). [CrossRef]
  81. D. C. Youla and H. Webb, “Image restoration by the method of convex projections: Part 1—theory,” IEEE Trans. Med. Imag. 1, 81–94 (1982). [CrossRef]
  82. H. H. Bauschke, P. L. Combettes, and D. R. Luke, “Phase retrieval, error reduction algorithms, and Fienup variants: a view from convex optimization,” J. Opt. Soc. Am. A 19, 1334–1345 (2002). [CrossRef]
  83. H. H. Bauschke, P. L. Combettes, and D. R. Luke, “A hybrid projection reflection method for phase retrieval,” J. Opt. Soc. Am. A 20, 1025–1034 (2003). [CrossRef]
  84. V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am A 20, 40–55 (2003). [CrossRef]
  85. J. R. Fienup, “Phase retrieval with continuous version of hybrid input–output,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2003), paper ThI3.
  86. J. R. Fienup, “Invariant error metrics for image reconstruction,” Appl. Opt. 36, 8352–8357 (1997). [CrossRef]
  87. M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. 33, 156–158 (2008). [CrossRef]
  88. R. H. T. Bates, “Astronomical speckle imaging,” Phys. Rep. 90, 203–297 (1982). [CrossRef]
  89. J. C. Dainty and J. R. Fienup, “Phase retrieval and image reconstruction for astronomy,” Image Recovery: Theory and Application, H. Stark, ed. (Academic, 1987), pp. 231–275.
  90. W. O. Saxton, Computer Techniques for Image Processing in Electron Microscopy (Academic, 1978).
  91. R. P. Millane, “Phase retrieval in crystallography and optics,” J. Opt. Soc. Am. A 7, 394–411 (1990). [CrossRef]
  92. K. A. Nugent, “Coherent methods in the x-ray sciences,” Adv. Phys. 59, 1–99 (2010). [CrossRef]

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